text:
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Curious about the newer model? Check out the 2016 Chrysler 300
By KBB.com Editors
KBB Expert Rating: 8.7
Chrysler's 300 sedan for 2013 continues the Detroit tradition of producing big, rear-wheel-drive (RWD) V8-powered sedans that are all about power, comfort and style. The 300 improves upon this formula by adding all-wheel drive (AWD) and a potent yet fuel-efficient V6 to the mix, as well as a high-performance version, the SRT8. Despite its family-car roots, the 2013 Chrysler 300 handles like a well-heeled German sport sedan, is as smooth and silent as the best Lexus and can be had for thousands less than most premium luxury competitors. Still, the 300 has not abandoned its mission as a true 5-passenger vehicle, offering copious amounts of rear-seat head and legroom. Unfortunately, the trade-off for the 300's roomy back seat is a somewhat small trunk.
If you love the driving performance provided by a rear-drive sedan, yet you also need room for five people, great fuel economy and a sophisticated set of electronic information and entertainment systems, the 2013 Chrysler 300 should prove most satisfying.
There is a price to pay for the 300's opulent interior and upgraded navigation, audio and performance options. You can likely find a V6-powered, front-wheel-drive competitor from Ford, Toyota or Hyundai that offers similar performance, fuel economy and technology for much less money.
For 2013, the base Chrysler 300 receives standard leather seating, an 8.4-inch voice-controlled touchscreen radio and heated front seats. The 300S gains a 300-horsepower upgrade. A limited-run Glacier Edition includes AWD and unique design appointments, while the SRT8 gets an improved adaptive dampening suspension and standard launch control.
It's hard to argue against the 2013 Chrysler 300, which offers a choice of a potent V6 or V8 engine, a responsive suspension and steering setup and the option of...
... AWD. Our test of the 300C equipped with the 3.6-liter V6 and 8-speed transmission revealed a car capable of delivering Lexus-like quiet and comfort on the highway, while feeling more like an Infiniti sedan in the curves. We did find the 8-speed's shifter a bit imprecise, especially when trying to select reverse, but the transmission itself delivers seamless shifts and excellent fuel economy. If, however, you seek a sedan on par with the best from BMW or Audi, look to the powerful 300 SRT8. Its 470-horsepower HEMI V8 can rocket it from zero to 60 mph in under 5 seconds and achieve a top speed of 175 mph. You'll sacrifice some ride comfort and quiet, but the trade-off for the SRT8's blistering performance is something most enthusiasts can accept.
The 2013 Chrysler 300 sedan's big 8.4-inch view screen features clear, easy-to-read-and-operate controls for the audio and available navigation. The UConnect Touch infotainment system allows control of an iPod via the steering-wheel remotes or voice activation and features hands-free texting.
Chrysler's 300 sedan for 2013 certainly offers a plethora of tech-based features worth highlighting, but the most memorable first impression is the remarkably quiet cabin and supple ride.
Compared to the last-generation 300, the 2013 sedan's interior is the difference between an army-surplus cot and a goose-down feather bed. Gone are the drab gray plastics and hard surfaces, replaced by warm tones, padded armrests and console and a dazzling array of back-lit instrumentation. If you like thick-rimmed steering wheels, you'll be happy to find in the Chrysler 300 one of the world's thickest. The flagship 300C Luxury Series models are even more luxurious, offering such items as a leather-stitched dash cap, two-tone leather seating and heated and cooling 12-way power seats.
The familiar silhouette of the original 300 is still easily recognizable on the Chrysler 300 for 2013, but there is a softer, more mature feel to the design. Intricate details, such as the vertical crease in the rear tail lamps, the chrome air-intake surrounds and LED daytime running lamps speak to the Chrysler 300's luxury status. The 300 SRT8 makes no such claim, displaying a more monochrome exterior with low ground effects and 7-spoke lightweight forged-aluminum wheels. But even the base 300 gets the star treatment, with attractive paint and chrome trim, 17-inch wheels and a host of available upgrades.
For 2013, the entry-priced Chrysler 300 sedan represents a lot of car for the money. Standard equipment includes keyless entry and start, a big 8.4-inch touchscreen with climate and music controls, Bluetooth phone and streaming audio, USB/iPod/SD card connectivity, dual-zone automatic climate control, leather seating, a 12-way power driver's seat with 4-way power lumbar support, tilt/telescopic steering wheel, cruise control, heated front seats, 17-inch painted aluminum wheels, one-touch up/down windows all around and a full complement of active and passive safety features including side-curtain airbags, driver's-knee airbag, hill-start assist and electronic stability control.
In addition to the 363-horsepower V8 engine, all-wheel drive and navigation system a 2013 Chrysler 300C AWD loaded with all the options will include an impressive list of high-tech luxuries: Radar-based adaptive cruise control and forward collision warning systems up front, rear cross-path sensors out back and blind-spot monitoring to help out on the side. In-cabin highlights include heated and cooled cup holders and a 900-watt, 19-speaker harman/kardon audio system.
The 2013 Chrysler 300's 3.6-liter Pentastar V6 is the most powerful base engine in the category. The 300S trim receives a cold-air induction unit and sport-tuned exhaust for an increase of eight horsepower. The 5.7-liter HEMI V8 has just slightly less horsepower than the Ford SHO's twin-turbocharged EcoBoost V6, but a substantially larger amount of torque. The SRT8's 6.4-liter monster pumps out 470 horsepower, more than anything in this class. On V6 trims a new 8-speed ZF transmission helps boost fuel economy figures to best in class. The V8-powered 300s retain a 5-speed Auto Stick automatic.
3.6-liter V6 (300, 300C)
292 horsepower @ 6,350 rpm
260 lb-ft of torque @ 4,800 rpm
EPA city/highway fuel economy: 19/31 mpg (RWD), 14/23 mpg (RWD, E85), 18/27 mpg (AWD), 14/20 mpg (AWD, E85)
3.6-liter V6 (300S)
300 horsepower @ 6,350 rpm
264 lb-ft of torque @ 4,800 rpm
EPA city/highway fuel economy: 19/31 mpg (RWD), 14/23 mpg (RWD, E85), 18/27 mpg (AWD), 14/20 mpg (AWD, E85)
5.7-liter V8 (300S, 300C)
363 horsepower @ 5,200 rpm
394 lb-ft of torque @ 4,200 rpm
EPA city/highway fuel economy: 16/25 mpg (RWD), 15/23 mpg (AWD)
6.4-liter V8 (SRT-8)
470 horsepower @ 6,000 rpm
470 lb-ft of torque @ 4,200 rpm
EPA city/highway fuel economy: 14/23 mpg
To compare current market prices, check out KBB.com's car classifieds to view the new and used Chrysler 300 vehicles for sale near you.
Based on 125 Ratings for the 2011 - 2014 models.Review this car
By MyCar on Friday, July 8, 2016
I own this car - My approximate mileage is 18,500overall rating 10 of 10rating details
Likely to recommend this car? (1-10): 10
"This is a Chrysler 300 Touring Model in excellent shape. What it doesn't have is Key fob exterior start, navigation system (but can be upgraded)no leather seats."
Was this review helpful to you? yes | no | report abuse
By Dave on Wednesday, June 1, 2016
I own this car - My approximate mileage is 31,500overall rating 10 of 10rating details
Pros: "A lot of car for the $$$"
Cons: "Shift stick is hard to get use to"
Likely to recommend this car? (1-10): 9
"I have owned my 300 for 3 1/2 yrs. 31500 miles and never had to take it into the dealer for repair. 8 speed & near 300 hp V6 is a great combo good mileage & great power. Its a lot of car for the $$$"
Was this review helpful to you? yes | no | report abuse
By steve on Saturday, February 6, 2016
I own this car - My approximate mileage is 26,500overall rating 10 of 10rating details
Pros: "looks great, runs smooth, loaded with options!!!!!"
Cons: "i wish it were a little faster!"
Likely to recommend this car? (1-10): 10
"i love my pearl red hemi 2012 300c. my wife loves it too for all the same reasons. we bought it used with only 21,000 miles. rides like a dream and love all the options. all we did was tint the windows and convert to synthetic oil. AWESOME machine. it has been 100% trouble free. excellent quality of workmanship."
10 people out of 19 found this review helpful
Was this review helpful to you? yes | no | report abuse
By DeeDee on Monday, January 25, 2016
I own this car - My approximate mileage is 25,000overall rating 10 of 10rating details
Pros: "Comfort level are off the charts, V8 Power!,"
Cons: "N/A"
Likely to recommend this car? (1-10): 10
"This vehicle was the best purchase I ever made. I get into the car and its like being in the most comfortable chair you have at home. What the questions above didn't ask me was, Does your car have heating and cooling cup holders? Yes! Does you car have a button that will raise a shade in the rear window for blinding headlights at night? Yes! Does your car have every bell and whistle you can think of? Yes! I love this car and have not had one second thought from the moment of purchase. Garage kept, one owner before myself. Beautiful vehicle, just beautiful."
2 people out of 4 found this review helpful
Was this review helpful to you? yes | no | report abuse
By Paul B on Monday, December 14, 2015
I own this car - My approximate mileage is 30,000overall rating 9 of 10rating details
Pros: "Price, handling, style and MPG"
Cons: "offer GPS in all models"
Likely to recommend this car? (1-10): 10
"So... I have owned this car now for 15 months. It has and is a pleasure to drive. We have a limousine company and use this car for errands, wedding pick up, long distance runner. All my customers can not believe it is a Chrysler 300. I get many compliments on it. The ride is incredible, thanks Mercedes E Class. The 8 speed transmission is awesome. The Pentastar 3.6 Engine is flawless. Thanks Mercedes! Fit and finish it is still looking great. I highly recommend this car for anyone not wanting to spend $50K more than you need too. I just bought one in a Limousine, and people flock all over it. Same drive train. Do yourself a favor and test drive one before you spend all your money on a materialistic one. BTW... 36 mpg at 80 mph is great!!"
10 people out of 11 found this review helpful
Was this review helpful to you? yes | no | report abuse
By Timmy on Friday, December 11, 2015
I own this car - My approximate mileage is 20,141overall rating 10 of 10rating details
Pros: "Great luxurious car for under $30k !!"
Cons: "Actually.....none that I can think of?"
Likely to recommend this car? (1-10): 10
"We promptly named her Sabrina since she is black and chrome. The quality, ride, comfort, easily used controls, and quietness all exceed the others. If the car has a problem it is too quiet.....you have to watch the speedometer constantly as there is absolutely no wind noise to gauge speed. The mileage on the car is actually high for the around-town driving since we have taken it on 3 trips. The mileage would only be about 12k if we hadn't. If you're considering a luxury car at least give this one a test drive. I have found only one thing that needs correction and that is the gauges are kind of difficult to read (if you are a tall guy like me)through the steering wheel without bending your head. I would have loved to have chrome rims, not brushed aluminum, since the rest of the trim is bright chrome, so that does not make sense to me."
5 people out of 5 found this review helpful
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text:
to save this item to your jcp.com account
Baby Bullet® Blender1dac9cd
web ID: 7804355
Product Description
Make a week's worth of all-natural baby food in less than five minutes with the amazing Baby Bullet blender.
- complete baby care system
- has everything you need to feed your baby the best food possible
Baby Bullet includes:
- power base
- batch bowl
- baby blend blade
- milling blade
- easy-pop batch tray
- 6 date dial storage cups
- spatula
- short cup
- resealable lid
- tip-proof tray
- user manual, cookbook and pocket nutritionist
200 watts. Dishwasher-safe removable parts; base wipes clean. Imported.
Rated 5 out of 5 by Natasha Singh Really Enjoyed this priduct I bought my bullet and it had stop working, I thought it was broken but when I called the warranty company to address my concerns the representative was able to advice how make it work again...apparently I overload it...I was happy it worked again.. May 1, 2016
Rated 2 out of 5 by Caitlin Not worth the money The only difference between a baby bullet and a regular blender is you get the storage cups and tray. Any blender can do the same thing this blender does. For the price you pay for this set you can buy a blender and plenty of storage cups/bowls. I have had my baby bullet for two months. I use it about twice a week. I noticed one day that the bigger container was leaking in the machine while blending sweet peas. You can not clean this food out once it leaks down into the machine because you can get down inside the machine. Then, the night before last I went to blend a shake and the big container leaked again. This time I noticed it had went through the machine and started coming out of the bottom, which means there is still food inside this machine that is not going to be able to be cleaned. I will be returning mine to Target tomorrow. August 22, 2015
Rated 1 out of 5 by Johnrtenn Horrible Was given as gift at my sons baby shower. I have made only a few things in it, and now it smells of burnt electronics. The people you talk to on the phone are of no help. I would never recommend this product to anyone. If you have the money buy a better blender that you can actually use for more than a month. March 1, 2016
Rated 5 out of 5 by sybil904 Great customer service and friendliness We had issues with the blade and the motor base and these items were replaced for us quickly and Efficiently. The customer service was fantastic! January 28, 2016
Rated 5 out of 5 by Perkishopper This product really helps with keeping the parents organized What an awesome product. Both grandparents bought this same product for our first grandbaby. I love it. It keeps the parents organized and made the grandparents happy. I think babygirl will be happy for years to come. January 6, 2016
Rated 5 out of 5 by Chris76 Customer service was awesome! ! The best investment in my child development that I could have ever made!! They really stand behind their product and have really great representatives to help with any problems!! A win all around!! January 5, 2016
Rated 4 out of 5 by loyal user great product and service I've been using this daily and love it. The only issue I find is the 4 blade leaks from the centre and makes a mess on the motor base. But I am so glad that I bought the warranty at toys r us. Today, I'm very impressed with help that the lady at customer service provided. She is awesome. Hopefully my replacement arrives soon. Thank you for excellent service and help! November 19, 2015
Rated 4 out of 5 by Robdob Customer Service Great, Product not We purchased our BB about over a year ago but only started using it about 2 months ago. Within that two months the 4 blade attachment failed and the safety latches stick. Disappointing. CS on the other hand was great. They helped me diagnose the issue, correct the sticking latches and order a replacement 4 blade accessory. I am hoping the new blade last longer. November 12, 2015
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Olivia Scott-Perkins
Revolving Door
Who's coming and who's going. Tell us about your job move! Receive the Revolving Door Newsletter with expert analysis by email twice a week.
November 2, 2012: Olivia Scott-Perkins has been named founder & principal consultant at Omerge Alliances. She had been chief marketing officer at Carol's Daughter. (mb)
August 11, 2008: Olivia Scott-Perkins has been named associate publisher of marketing at Vibe Media Group. She had been vice president, alliances at Live Nation. (release)


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"Ghostbusters": 11 Things the Sequel Needs to Do to Succeed
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Orange Park, FL
The BBC has released a brief teaser video and two delightfully retro posters that (quite literally) unveil the title mystery from the upcoming special Sherlock: The Abominable Bride.
Starring Benedict Cumberbatch and Martin Freeman, the New Year's Day special finds Sherlock Holmes and John Watson in 1895 London, where they're faced with an enemy from "seemingly beyond the grave."
The posters, which promise "Friendship, Adventure, Murder," are a throwback to the the classic "Sherlock Holmes" films of the 1930s and '40s, only with Cumberbatch and Freeman in place of Basil Rathbone and Nigel Bruce.
Also starring Amanda Abbington, Rupert Graves, Una Stubbs and Louise Brealey, "Sherlock: The Abominable Bride" will premiere Jan. 1 on PBS and BBC One, and in select theaters.
We've been here before – but what if this wasn't the modern day but the late Victorian period? What if the world's most famous consulting detective and his best friend lived in a Baker Street of steam trains, hansom cabs, top hats and frock-coats?
Welcome to 'Sherlock' in 1895!
Some things, though, remain reassuringly the same. Friendship, adventure and especially, MURDER…
Why is Thomas Ricoletti a little surprised to see his wife dressed in her old wedding gown? Because, just a few hours before, she took her own life…
Mrs Ricoletti's ghost now appears to be prowling the streets with an unslakeable thirst for revenge. From fog-shrouded Limehouse to the bowels of a ruined church, Holmes, Watson and their friends must use all their cunning to combat an enemy seemingly from beyond the grave and the final, shocking truth about… the Abominable Bride!
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It's not a throwback to Nigel Bruce, most of whose episodes were set in the 1940s having Holmes do such idiotic things as battling Nazi U-boats. It is a throwback to the excellent pitch perfect and very best dramatization of Sherlock Holmes ever made, the series starring Jeremy Brett in the 1980s and 1990s.
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All Music Headlines
Skip Or Repeat? New albums from Tori Kelly, Kacey Musgraves, Leon Bridges, more
Capsule album reviews from new June 23 releases
Jun 23, 2015
Skip Or Repeat: Kacey Musgraves, Tori Kelly, Leon Bridges, Wolf Alice
Capsule critiques of new albums for the week of June 23
Jun 23, 2015
The Snap Daily: We have no song of the summer.
Wiz Khalifa? Taylor Swift? The Weeknd? Madonna? None of these people have given us the song of the summer.
Jun 22, 2015
'Why did nobody stop it?': Director Asif Kapadia on Amy Winehouse documentary
What does the 'Amy' helmer have to say about Winehouse's father Mitch?
Jun 18, 2015
Skip Or Repeat: New albums from Nate Ruess, Hilary Duff, Adam Lambert
Capsule reviews of new music, including James Taylor, Giorgio Moroder, Mika
Jun 16, 2015
Skip Or Repeat: Nate Ruess, Hilary Duff, James Taylor, Adam Lambert and more
Who comes out on top in this week's crop?
Jun 16, 2015


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This week, we played tracks from GLAAD Media Award nominees, including Frank Ocean, The Gossip, and Scissor Sisters. We also heard a new track from Tegan & Sarah!
Click HERE to listen to an archive of this week's program.
WORT: Sticking It In Your Ears for 40 Years. Donate Today!


text:
A Morphometric Investigation on Breed-Specific Features Affecting Sagittal Rotational and Lateral Bending Mobility in the Canine Cervical Spine (C3–C7)
Version of Record online: 6 JUL 2004
DOI: 10.1111/j.1439-0264.2004.00546.x
Anatomia, Histologia, Embryologia
Volume 33, Issue 4, pages 244–250, August 2004
Additional Information
How to Cite
Breit, S. and Künzel, W. (2004), A Morphometric Investigation on Breed-Specific Features Affecting Sagittal Rotational and Lateral Bending Mobility in the Canine Cervical Spine (C3–C7). Anatomia, Histologia, Embryologia, 33: 244–250. doi: 10.1111/j.1439-0264.2004.00546.x
Publication History
- Issue online: 6 JUL 2004
- Version of Record online: 6 JUL 2004
- Received August 2003; accepted for publication December 2003
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We analyze the ground-state phase diagram of an ultracold Bose-Fermi mixture placed in an optical lattice. The quantum phases involve pairing of fermions and one or several bosons. Depending on the physical parameters these composites can form a Fermi liquid, a density wave, a superfluid or a domain insulator. We determine by means of a mean-field formalism the phase boundaries for finite tunneling, and analyze the experimental feasibility of these sort of phases.
© 2004 Optical Society of America
1. Introduction
During the last few years, the loading of ultracold atomic gases in optical lattices has attracted a considerable attention, mainly due to the resemblance to solid-state physics [1, 2, 3, 4]. The advances on atomic trapping and cooling, and the manipulation of the atomic interactions via Feshbach resonances [5, 6], allow nowadays for the analysis of strongly correlated ultracold atomic gases in optical lattices. In this respect, the observation of the superfluid (SF) to Mottinsulator (MI) transition in bosonic gases [7, 8] constitutes so far the most important result. Strong correlations are also predicted to play a dominant role in low-dimensional systems [9, 10], and in rapidly-rotating 2D gases [11, 12].
Recently, the possibility of employing sympathetic cooling techniques to cool fermions in contact with bosons, has triggered the interest on Fermi-Bose (FB) mixtures [13, 14, 15, 16, 17]. Although the main goal of these experiments has been the Bardeen-Cooper-Schrieffer (BCS) transition [18] in ultracold trapped Fermi gases, recently, the rich physics of FB mixtures has become itself one of the central topics of the physics of ultracold gases [19, 20, 21, 22, 23, 24, 25, 26, 27, 28].
The success obtained in lattice bosons [8], has lead to a growing attention on the physics of FB mixtures in optical lattices. This physics can be well described under proper conditions by the Bose-Fermi Hubbard model (BFH) model, which has been carefully derived in Ref. [29]. Effects characteristic for BFH in 1D have been discussed in Refs. [29, 30, 31]. The BFH allows for the interesting possibility to produce fermionic composites, formed by a fermion and a boson (or bosonic hole) [32, 33, 34]). These composites present at low temperatures a much more complex behavior than the lattice bosons. In Ref. [33], we have discussed the limit of strong atom-atom interactions (strong coupling regime) at low temperatures, and have predicted the existence of novel quantum phases in lattices that involve the previously mentioned composite fermions, which for attractive (repulsive) interactions between fermions and bosons, are formed by fermion and bosons (bosonic holes). The resulting composite fermions present a remarkably rich phase diagram, and may form, depending on the system parameters, a normal Fermi liquid, a density wave, a superfluid liquid, or an insulator with fermionic domains. In Ref. [35] we have employed mean-field theory [36] to determine the phase diagram of the system for arbitrary values of the chemical potential, the Fermi-Bose coupling, and the tunneling (hopping) amplitudes.
In this paper, we review in a comprehensive way our recent results on Fermi-Bose mixtures in optical lattices [33, 35], and discuss in great detail some important issues, especially concerning the derivation of the effective Hamiltonian of Ref. [33], the mean-field treatment of Ref. [35], and the numerical method employed in our calculations.
2. Bose-Fermi Hubbard model
Let us consider a sample of ultracold bosonic and (polarized) fermionic atoms trapped in an optical lattice, e.g. 7Li-6Li or 87Rb-40K. The lattice potential is practically the same for both species in a 7Li and 6Li mixture, and accidentally very similar for the 87 Rb and 40K case (for detunings corresponding to the wavelength 1064 nm of a Nd:Yag laser [37]). Due to the periodicity of this potential, the single-atom states form energy bands. If the temperature is low enough and/or the lattice potential wells are sufficiently deep, the atoms occupy only the lowest energy band. Of course, for fermions this is only possible if their number is strictly smaller than the number of lattice sites (filling factor ρF ≤1). To describe the system under these conditions, we choose a particularly suitable set of single particle states in the lowest energy band, the so-called Wannier states, which are essentially localized at each lattice site. The system is then described by the so-called tight-binding Bose-Fermi-Hubbard (BFH) model (for a derivation from a microscopic model, see e.g. Ref. [29]), which is a generalization of the fermionic Hubbard model, extensively studied in condensed matter theory (c.f. [38]):
where , bj , , fj are the bosonic and fermionic creation-annihilation operators, respectively, ni =bi , mi =fi , and µ is the bosonic chemical potential. The fermionic chemical potential is absent in H BFH, since the fermion number is fixed. The BFH model describes: i) nearest neighbor boson (fermion) hopping, with an associated negative energy, -JB (-JF ); in Secs. 3 and 4 we shall assume JF =JB =J, while the more general case of different tunneling rates will be analyzed in Secs. 5 and 6; ii) on-site repulsive boson-boson interactions with an associated energy V; iii) on-site boson-fermion interactions with an associated energy U, which is positive (negative) for repulsive (attractive) interactions.
3. Effective Hamiltonian for composites fermions
This section is devoted to the analysis of the strong-coupling regime, J≪U,V. We shall show that the zero-temperature physics of this regime can be well described by an effective Hamiltonian for composites fermions consisting in a fermion and a boson(s) (or bosonic hole(s)). We shall discuss in detail the derivation of this effective Hamiltonian, as well as the possible expected quantum phases.
At zero temperature, for vanishing hopping (J=0), and in absence of Bose-Fermi interactions (U=0), the bosons are in a MI phase with ñ=[µ̃]+1 bosons per site, where [µ̃] is the integer part of µ̃=µ/V. The fermions can be in any available state, since the energy of the system is independent of their configuration. If U > 0 is sufficiently large, U > µ -(ñ-1)V, the fermions push the bosons out of the sites that they occupy, and localized composite fermions are formed, consisting of one fermion and the corresponding number of missing bosons (bosonic holes) (Fig. 1(a)). Similarly, for attractive Bose-Fermi interactions, if U <µ -ñV, the fermions attract bosons to the sites they occupy, and localized composite fermions are formed, but in this case consisting of one fermion and one or several bosons (Fig. 1(b)).
Figure 2(a) shows the phase diagram of the system in the α-µ̄ plane, where α=U/V. For µ̄-[µ̄]+s>α>µ̄-[µ̄]+s-1, a single fermion pairs with s holes to form a composite fermion, annihilated by . If s<0, -s bosons pair with a fermion to generate a composite fermion annihilated by the operator . Note than in every site i the number of fermions, mi , and the number of bosons, ni , must fulfill the condition ni +smi =ñ.
Fig. 1.
In general, the operators f̃ i fulfill the following anticommutation relation:
However, when applied on the degenerated ground state, since ñ=ni +mis, we recover the desired fermionic anticommutation relation {f̃ i , }=1.
The maximal number of holes per site cannot of course exceed the number of bosons per site for U=0, n̂, and as a consequence, s cannot be greater than ñ. On the contrary, s can attain arbitrary negative integer values, i.e., we may have fermion composites of one fermion and many bosons in the case of very strong attractive interactions, α<0, and |α|≫1. In Fig. 2(a) the different regions in the phase diagram are denoted with Roman numbers I, II, III, IV etc, which denote the number of particles (fermion + bosons or bosonic holes) that form the corresponding composite fermion. Additionally, a bar over a Roman number indicates composite fermions with one fermion and bosonic holes.
From Fig. 2(a) we observe that even for the simple J=0 case the phase diagram presents a complex structure. Therefore one can expect a very rich physics for nonzero hopping. The latter can be investigated on the basis of an effective theory for composite fermions, which can be derived using degenerate perturbation theory (to second order in J) along the lines of the derivation of the t-J model (see, e.g., Ref. [38]).
Let 𝓟 be the projector onto the degenerated ground-state of H 0. This state has the form discussed above. Let =1-𝓟. Applying these operators on the time-independent Schrödinger equation Eψ=HBFHψ, and expressing ψ as a function of ϕ=𝓟ψ, we obtain:
Expanding in powers of H 1 we obtain:
where E 0 is the ground-state energy. One can proceed to evaluate the effective Hamiltonian in the different regions of the phase diagram of Fig. 2. The terms involving only bosonic or only fermionic operators have a major contribution at second order, and lead to an interaction term between composites. Those terms involving the product of bosonic and fermionic operators, lead to hopping terms of the composites from one site to the nearest neighbor. We must note at this point, that at second order only those contributions coming from the regions II and contribute. At third order regions III and , and so on.
Proceeding in this way, one obtains after a lengthy but straightforward calculation a resulting effective Hamiltonian which (except for unimportant constant terms) has a similar form for all the distinct regions in the phase diagram of Fig. 2(a):
This Hamiltonian is determined by two effective parameters describing: i) nearest neighbor hopping of composite fermions with the corresponding negative energy -Jeff ; ii) nearest neighbor composite fermion-fermion interactions with the associated energy Keff , which may be repulsive (>0) or attractive (<0). In Eq. (6) we employ the number operator m̃ i =f̃†̃ i ̃f̃ i . This effective model is equivalent to that of spinless interacting fermions (c.f., [36, 39]), and, despite its simplicity, has a rich phase diagram. The coefficient Keff has the universal form
whereas the dependence of Jeff on J, V, and U, presents different forms in different regions of the phase diagram in Fig. 2(a). E.g. for 0<µ̃<1:
and etc. Note that although Keff is always proportional to J 2/V, the dependence of the hopping constant Jeff is different for different number of particles in the composite. This is clear, since we previously commented that only terms of order contribute to the hopping term of composites formed by one fermion and s bosonic holes (or -s bosons). Hence, the effective hopping depends as J(J/V) s . The physics of the effective model is determined by the ratio Δ=Keff /2Jeff , and by the sign of Keff . In Fig. 2(a) the subindex A (R) denotes attractive (repulsive) interactions.
4. Ground-state of the effective Hamiltonian
Once we have derived the effective Hamiltonian Heff for the different composites, our initial problem of finding the ground state of the BFH model is reduced to the analysis of the ground state of the spinless Fermi model (6). In this section we discuss the possible quantum phases that may occur in this model.
4.1. Repulsive effective interactions
Let us first consider the case in which the effective interactions are repulsive, i.e., Keff >0. If the filling factor is close to zero, ρF ≪1, or one, 1-ρF ≪1, the ground state of Heff corresponds to a Fermi liquid (a metal), and is well described in the Bloch representation. In addition, in the cases under consideration, the relevant momenta are small compared to the inverse lattice constant (the size of the Brillouin zone). One can thus take the continuous limit, in which the hopping term in Heff corresponds to a quadratic dispersion with a positive (negative) effective mass for particles (holes), while the nearest neighbor interactions become p-wave interactions. The lattice is irrelevant in this limit, and the system becomes equivalent to a Fermi gas of spinless fermions (for ρF ≪1), or holes (for 1-ρF ≪1). Remarkably, this gas is weakly interacting for every value of Keff , even when Keff →∞. In the latter case, the sites which surround an occupied site are excluded from the space available for other fermions. As a result, the scattering length remains finite, being of the order of the lattice spacing. Therefore, 1-ρF (ρF ) acts as the gas parameter for the gas of holes (particles). This picture can be rigorously justified using renormalization group approach [39].
Fig. 2.
The weakly-interacting picture becomes inadequate near half-filling, ρF →1/2, and for large Δ, where the effects of the interactions between fermions become important. One expects then the appearance of localized phases. A physical insight on the properties of this regime can be obtained by using the so-called Gutzwiller ansatz (GA) [40, 41], in which the ground state is assumed to be a product of on-site states with 0 or 1 composites:
Note that this parametrization ensures the normalization in each lattice site. This Ansatz is well-suited for describing states with reduced mobility and, therefore, with small correlations between different sites. It has been employed, e.g., in the analysis of MI phases in lattice bosons [7]. Such an approach allows to determine the boundaries of various quantum phases relatively well in 3D and 2D, but does not provide the correct description of correlations and excitations. The failures of the GA become particularly important in 1D, where, strictly speaking, the GA approach is inappropriate.
For Keff >0 the GA approach maps Heff onto the classical antiferromagnetic spin model with spins of length 1, S⃗ i =(sinθi cosϕi , sinθi sinϕi ,cosθi ) [38]. In the following we shall define Δ crit =(1+ )/(1- ), where mz =2ρF -1 is the "magnetization per spin". For Δ<Δ crit , the ground state is a canted antiferromagnet [38, 36] with a constant density. For Δ>Δ crit , the GA ground state of the classical spin model exhibits modulations of mz with a periodicity of two lattice constants. Coming back to the composite fermion picture, we predict thus that the ground state for Δ < Δ crit is a Fermi liquid, while for Δ>Δ crit it is a density wave. For the special case of half filling, ρF =1/2, the ground state is the so-called checkerboard state, with every second site occupied by one composite fermion.
We expect that the employed GA formalism predicts the phase boundary Δ crit accurately for ρF close to 1/2. One should however stress that the GA value of Δ crit is incorrect for filling factors ρF close to 0 or 1. In particular, the GA approach predicts that Δ crit tends gradually to infinity and the density wave phase gradually shrinks as ρF →0 or 1, i.e. 1- →0. As discussed above, an analysis beyond the GA approach shows the disappearance of the density wave phase already for a finite non-zero value of 1- .
4.2. Attractive effective interactions
The situation is different when the effective interaction is attractive, i.e., when Keff <0. In the spin description this corresponds to ferromagnetic spin couplings. In the GA approach the ground state for 0>Δ≥-1 is ferromagnetic and homogeneous. In this description, fixing the fermion number means fixing the z component of the magnetization Mz =N(2ρF -1). When |Δ|≪1, and ρF is close to zero (one), i.e. low (high) lattice filling, a very good approach to the ground state is given by a BCS Ansatz [42], in which the composite fermions (holes) of opposite momentum build p-wave Cooper pairs,
where vk ̄ and uk ̄ are the coefficients of the corresponding Bogoliubov transformation.
The ground state becomes more complex for arbitrary ρF , and for Δ approaching -1 from above. The system becomes strongly correlated, and the composite fermions in the SF phase may build not only pairs, but also triples, quadruples etc. The situation becomes simpler when Δ<-1. In the spin picture the spins form then ferromagnetic domains with spins ordered along the z-axis. This mean-field result is in fact exact: one can rigorously prove that for Δ<-1, the composite fermions will group into a domain, forming what one could call a "domain" insulator.
Fig. 2(b) shows cases I, II and for 0<µ<1, with the predicted quantum phases. This completes our analysis of the model in 2D and 3D. As we observe the phase diagram in the strong coupling limit is enormously rich, and contains several novel types of quantum phases involving composite fermions, including localized phases (density wave, domain insulator) and delocalized ones (Fermi liquid and superfluid).
4.3. One-dimensional case
In the 1D case, due to the leading role of fluctuations, the mean field theories become rather inaccurate, and can only be employed as a guiding approximation. In 1D we can, however, use the Wigner-Jordan transformation and convert the effective model to the quantum spin 1/2 chain, the so-called quantum Heisenberg-Ising, or XXZ model [36]. The coefficient characterizing the spin coupling on the x-y plane will then be Jeff /2, whereas that in the z direction will be Keff /4. The z component of the magnetization per spin will be fixed by the total number of fermions, mz =ρF -1/2. The ground state of the XXZ chain with a fixed magnetization is somehow similar to the one in a magnetic field, and it is known exactly from the Bethe Ansatz solution [48, 49].
5. Mean-field theory
In this section we shall discuss the case in which the hopping becomes relevant. For a sufficiently large tunneling a phase transition occurs between the strong-coupling phases discussed in the previous section and a phase composed by superfluid bosons and fermions in a Fermi liquid. In this section we shall find the analytical expression for the phase boundaries by employing mean-field techniques [36, 50, 51].
In the following we shall consider the case of vanishing temperature, T→0, and JF ≪JB ,U,V. We shall analyze only homogeneous phases (it is possible to prove that within the mean-field limit supersolid phases are energetically unfavorable).
We shall employ in the following the splitting HBFH =H 0F+H 1B, where H 1B=-∑〈 ij 〉 (JB bj +h.c.) and H 0F=H 0-JF ∑〈 ij 〉 ( fj +h.c.) describes the fermions moving in the field of the "frozen" self-interacting bosons. We introduce a complex c-number field ψi (τ), 0≤τ≤1/T, and decouple the bosonic hopping term H 1 by means of the Hubbard-Stratonovich transformation (see e.g. Ref. [36]). In this way the partition function, Z, corresponding to HBFH can be written in the form
where Z 0=Tr(-H 0/T) is the partition function corresponding to H 0F. In Eq. 13, we have introduced the effective action
where ( ) ij is the inverse of the matrix of bosonic hopping coefficients, (τ)=exp(τH 0F) exp(-τH 0F) are the operators in the interaction representation, and the average is taken in the ensemble corresponding to H 0F. We notice then that near a superfluid transition point, 〈bi 〉 is linearly related to 〈ψi 〉 and, therefore, the field ψi can be considered as a superfluid order parameter.
The first term in S(ψ) is diagonal in the basis of Bloch states, while the second one can be computed as a cumulant expansion in powers of ψ. To determine the superfluid transition point, only the lowest second order in ψ term is relevant. The corresponding contribution reads
where 𝓖 ij (τ 1-τ 2)=-〈T τ[ (τ1)bj (τ2)]〉0 is the bosonic Green function corresponding to the Hamiltonian H 0F, which is diagonal in indices i and j, 𝓖i j (τ)=δ ij 𝓖(τ), due to the absence of bosonic hopping in H 0F.
For vanishing temperature, T→0, the leading contribution to G(τ) originates from the lowest energy states of the Hamiltonian H 0F. As previously discussed, in the regime of strong coupling, U,V≫JF , the ground state corresponds to bosonic Mott-Hubbard insulator with ñ bosons per site coexisting with fermions or composite fermions, depending on the ratio between U and V. The fermions could have various phases that are controlled by an effective interfermionic interaction, but these effects are of the order of JF ≪U,V or smaller and therefore can be neglected. As a result, the ground state can be written as with corresponding energy per site E 0=E 0(ñ,0)(1-ρF )+E 0(ñ-s,1)ρF with
where ρF is the fermionic filling factor, ñ the bosonic occupation number in the Mott-Hubbard state, and s the number of bosons (or bosonic holes) participating in the formation of a composite fermion.
In the mean-field approximation, ψi (τ) is a constant, ψi (τ)=ψ, and the lowest order contribution to the effective action is
where N is the number of sites, z the coordinate number of the lattice (z=2d for the considered d dimensional square lattice), and 𝓖(ω=0) is the Fourier transform of the Green function at zero frequency. In the considered approximation
where ε(n,m)=E 0(n+1,m)-E 0(n,m)=Vn +Um-µB . The first line in the above expression corresponds to the sites with no fermions, while the second one comes from the sites with fermions, on which composite fermions are formed. The effective action can now be written in the form S(ψ)=Nr |ψ|2, where
If r>0 the system minimizes the energy by having ψ=0 (normal phase), whereas if r<0 a nonzero ψ (superfluid) is energetically favorable. Therefore, the curve r=0 describes the boundaries between the phase with a superfluid bosonic gas, and the interaction-dominated phases. In Fig. 3 we have depicted the curves r=0 for different values of α, and different regions of the µ-JB phase space.
6. Numerical results
We have compared the previous analytical results with numerical calculations based in the GA approach. This method allows the extension of our analytical results to more general situations, in which JF and JB can attain arbitrary independent values. In this section we shall discuss in detail our numerical method.
We first evaluate the Bloch functions for the lowest energy band of the square lattice, and properly combine them to obtain the corresponding Wannier functions, largely localized at each lattice site. Using the Wannier functions it is easy to obtain the coefficients JB , JF , U and V [7]. Once the coefficients of the Hamiltonian HBFH are known, we introduce a GA for the wavefunction:
where |nm〉 are Fock states with n bosons and m fermions, and are the Gutzwiller coefficients at site i. We have checked that the value of the maximal bosonic occupation, Nmax , does not affect the calculations. The coefficients f n,m must satisfy the normalization condition ∑ nm |f n,m|2=1. The number of particles is determined by the chemical potential. In the following, we consider only homogeneous phases, although the calculation can be straightforwardly extended to inhomogeneous phases.
Fig. 3.
By employing Eq. (20), the energy of the system acquires the form
where Φ(k)=∑ nm √n. The chemical potential µF is introduced to control the number of fermions.
The ground-state is initially calculated for a given number of bosons and fermions, and for the case U=0, V=0 and a relative low lattice potential (large JB ). These initial conditions are assumed due to two main reasons. For |U|>0, Eq. (21) is minimized by the non-physical situation in which the number of atoms of one of the species becomes zero; on the contrary a finite number of particles for both species corresponds to a saddle-point of Eq. (21). To provide a system with both species of atoms, the interaction between bosons and fermions must be turned-off for the initial minimization of the energy. In addition for JB ≫V the system is in an homogeneous superfluid phase. With these constraints we obtain appropriate initial conditions for the real-time simulations described below. Due to homogeneity, the ground-state can be found by minimizing the energy on a single cell, while using periodic boundary conditions. The energy is minimized by changing the values of the coefficients f n,m using a standard downhill technique. In order to guarantee the normalization of the Gutzwiller coefficients, we assume these coefficients as lying on an 2Nmax -dimensional hypersphere of unit radius
Therefore the actual variational parameters are the angles α on the hypersphere. Starting from the chosen ground-state, we evolve in the phase space by adiabatically varying the parameters of the system. The time evolution of the f n,m coefficients is obtained by employing the proper minimization , which results in the equations:
where ϕ(i)= *√n.
These equations determine the dynamics of the f n,m coefficients in the phase space, and constitute the basis of what has been called dynamic GA [52]. Since the total number of bosons and fermions is conserved during the time evolution, the chemical potential will be time dependent. This time dependence can be evaluated by calculating two initial ground-states ψ 0(t=0) ψ 1(t=0) with, respectively, a number of bosons Nb and Nb +δN, where δN≪Nb . We evolve the parallel trajectories while reducing JB . The chemical potential can be then approximated as (µ(t)≈〈ψ 1(t)|H(t)|ψ 1(t)〉-〈ψ 0(t)|H(t)|ψ 0(t)〉)/δN. By launching various trajectories, we can explore those regions with an incommensurate total number of bosons plus fermions. Consequently, the trajectories do not enter into the regions of the phase diagram in which commensurate phases are expected. Therefore the expected lobular gaps are opened. As shown in Fig. 4, our numerical and analytical results are in rather good agreement. As expected, our numerical method provides worse results at the tip of the lobes and for those phases which are narrower in the µ̃ direction (e.g., phases A in Fig. 4(a) and phases B in Fig. 4(b)), since to recover the boundaries close to the tip of the lobe we must employ very close packed numerical trajectories through the phase space, which close to the tips behave badly.
We must stress that the effects of the fermionic tunneling are not taken into account in the analytic calculations, but they can be easily included in our numerics. In Fig. 4, we also depict a case with finite fermionic tunneling (JB =JF ). As expected, the lobes of the phases with composite fermions (phases B in Fig. 4) shrink due to the larger mobility of the fermions.
7. Experimental accessibility
The observation of the predicted phases, constitutes a challenging, but accessible, goal for experiments. Systems of different dimensionalities are nowadays achievable by controlling the potential strength in different directions [43, 44, 45, 46, 47]. The conditions for the exclusive occupancy of the lowest band, and for J≪V,U, are fulfilled for sufficiently strong lattice potentials, as those typically employed in current experiments [8] (10–20 recoil energies). Additionally, our T=0 analysis is valid for T much lower than the smallest energy scale in our problem, namely the tunneling rate. This experimental constraint is probably the most difficult to fulfill in current experiments. Additionally, the presence of an inhomogeneous trapping potential leads to the appearance of regions of different phases [7, 53], and it is crucial for the observation of MI phases [8]. The inhomogeneity controls thus the bosonic chemical potential, which can also be tailored by changing the number of bosons in the lattice, regulating the strength of the lattice potential, and/or modifying the interatomic interactions by means of Feshbach resonances [5, 6]. We would like also to note that for J≪V, phases I, II and II are easier to study, since the fermions, or composite fermions, attain effective hopping energies that are not too small, and can compete with the effective interactions Keff . The predicted phases can be detected by using two already widely employed techniques. First, the removal of the confining potentials, and the subsequent presence or absence of interferences in the time of flight image, would distinguish between phase-coherent and incoherent phases. Second, by ramping-up abruptly the lattice potential, it is possible to freeze the spatial density correlations, which could be later on probed by means of Bragg scattering. The latter should allow to distinguish between homogeneous and modulated phases. An independent Bragg analysis for fermions and bosons should reveal the formation of composite fermions.
Fig. 4.
8. Conclusions
In this paper we have reviewed in detail the extraordinarily rich physics predicted for Bose-Fermi lattice gases. We have discussed the expected phase diagram in the strong-coupling limit, which contains several novel types of quantum phases involving composite fermions, which for attractive (repulsive) Bose-Fermi interactions are formed by a fermion and one or several bosons (bosonic holes). The predicted ground-state solutions include delocalized phases (metallic, superfluid), and localized ones (density wave and domain insulator). The analysis of the system have been completed by the discussion of the phase boundaries between strong-coupling phases and the weak-coupling phase (composed by superfluid bosons and a Fermi liquid). This phase boundary can be obtained under some conditions analytically using mean-field techniques. Finally, we have presented our numerical method based in a combination of time-independent and time-dependent Gutzwiller Ansatz, which is in good agreement with our analytical results, and additionally provide a physical insight into situations which lie beyond our analytics.
The remarkable development of the experimental techniques for cold atomic gases allows not only for the observability of the predicted phases, but also for an unprecedented degree of control not available in other condensed matter systems. We hope that the amazing richness of this system will encourage future experiments in this direction.
We thank B. Damski, F. Eßler, H. J. Everts and J. Zakrzewski for fruitful discussions. We acknowledge support from the Deutsche Forschungsgemeinschaft SFB 407 and SPP1116, the RTN Cold Quantum Gases, IST Program EQUIP, ESF PESC BEC2000+. and the Alexander von Humboldt Foundation.
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The easiest way you can help the children, is through a donation to Active Child Aid.
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30 Rock: Seasons 1-3
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The show is amazing- funny, intelligent and very well made. If you are a fan of Seinfeld or Arrested Development, you will love this. I might even rate this a bit higher. Everyone in the cast does a great job. The show is fast with a lot of witty comments so you can watch it over and still find stuff you had missed before.
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and a complete collection of the first three seasons
This is a good show. Tina F. is awesome! Highly recommended for comedy lovers.Published on June 5, 2010 by WingsMediaGuy
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In Australia we have 30 Rock on cable tv, but it is behind here with season two only just beginning, I couldn't wait and ordered Seasons 1-3, what a great buy, this sidesplitting... Read morePublished on November 1, 2009 by OZNat
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WASHINGTON — The United Fresh Produce Association is seeking nominations for the 2013 Retail Produce Manager Award. The 25 award winners will be presented at the United Fresh 2013 Convention in San Diego on May 14-16 at an award dinner. The celebrated produce managers will receive free registration to the conference as well as airfare and lodging to attend. Nomination forms can be downloaded online. The award winners are judged based on community service, customer ...
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Let's go with a healthy breakfast this month! We'll get back to bacon, cheese, chocolate, etc. later on...
Some suggestions: veggie quiches or casseroles, turkey sausages or bacon, fruit salad, berries, whole grain muffins, banana bread, yogurt, egg beaters or egg whites, granola bars, fruit juices, spring water, coffee (!), whole grain bagels with veggie cream cheese (ok, that's a stretch, but you get the idea!).
Come and experience breakfast on the beach! We will be hosting a monthly Sunday Morning "Pitch In" Breakfast at Wiggins State Park.
Location: Wiggins State Park PARKING LOT #5 (NORTH end of lot) PROMPTLY at 9:00 am. Follow the boardwalk to the end, turn right down the path, and turn left into the area with several picnic tables. We will be as close to the beach as possible.
Please bring an item to share (coffee, fruit juice, water, fruit, muffins, frittata, bacon, quiche, sausages, pastries, bagels, etc.). You don't need enough for an army, just enough for 4 to 5 people.
After breakfast if you have time join us for a walk on the beach, swimming, fishing, or just sunbathing. This is a very nice way to start a Sunday Morning, relaxing with friends over breakfast on the beach!
We will utilize the park supplied picnic tables (and sometimes the grills).
***Please take your left-overs home with you!***
Hosting: Fabienne & Steve
Link: Delnor Wiggins State Park
Admission into the park:
$6.00 per vehicle. Limit 2-8 people per vehicle.
$4.00 Single Occupant Vehicle.
$2.00 Pedestrians, bicyclists, extra passengers, passengers in vehicle with holder of Annual Individual Entrance Pass.
Hours of Operation: 8am to sunset
Location: Wiggins State Park Parking Area #5 (NORTH end of lot)
Things to Bring:
Bathing suit
Empty stomach
Something to share
Towel, beach chair, umbrella
So glad I came to B on the B. Met some very nice people and enjoyed relaxing at the beach - food and coffe were good as well
2 · May 18, 2014
Hi Everyone, If you have not already done so, please indicate what you will be bringing in the comment section. We could use fruit juices, water, yogurt, etc. It doesn't have to be "healthy". Our usual spot is at the North end of Lot #5, to the right of the boardwalk toward beach, picnic tables right next to the beach. Looks like great weather, see you on the beach! Steve and Fabienne
0 · May 17, 2014
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Until more information surfaces, we have 44 screen shots and 9 pieces of character artwork.
Date Updated:December 6th, 1999
Time Updated:3:42 PM
Stahn Mahn
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