In this article, we study the thermalizability of a system consisting of two atoms in a circular, transversely harmonic waveguide in the multimode regime. While showing some signatures of the quantum-chaotic behavior, the system fails to reach a thermal equilibrium in a relaxation from an initial state, even when the interaction between the atoms is infinitely strong. We relate this phenomenon to the previously addressed unattainability of a complete quantum chaos in the ˇ Seba billiard [P. ˇ Seba, Phys. Rev. Lett., 64 , 1855 (1990)], and we conjecture the absence of a complete thermalization to be a generic property of integrable quantum systems perturbed by a non-integrable but well localized perturbation. PACS numbers: 67.85.-d, 37.10.Gh, 05.45.Mt, 05.70.Ln Introduction .– The ultracold quantum gases have been long proven to be an ideal testbench for studying the fundamental properties of quantum systems. One of the most interesting and frequently addressed topics is the behavior of quantum systems in the vicinity of an inte- grable point. Experimental results already include the suppression of relaxation of the momentum distribution [1] and the modified decay of coherence [2]. Note that the fully developed quantum chaos with ultracold atoms has been investigated in experiments [3]. Traditionally, the underlying integrable system is rep- resented by the Lieb-Liniger gas [4] that is well suited to describe the dynamics of Van-der-Waals interacting bosons in a monomode atomic guide (see [5] for a re- view). The nontrivial integrals of motion there are inti- mately related to both the one-dimensional character of the atomic motion and to the effectively zero value of the two-body interaction range. The causes for lifting inte- grability include the virtual excitation of the transverse modes during the collision [6] and the coupling between two parallel weakly interacting Lieb-Liniger gases [2]. One would expect that in the multimode regime , when the motion becomes substantially multidimensional, no remnants of the former integrals of motion will survive. However, in this article we show that for the case of only two interacting atoms a strong separation between the transverse and longitudinal degrees of freedom remains, even in the case of the infinitely strong interaction be- tween the atoms. We attribute this effect to the short- range nature of the interaction. For our system we study both the degree of the eigen- state thermalization and the actual thermalization in an expansion from a class of realistic initial states. The eigenstate thermalization [7–9] – the suppression of the eigenstate-by-eigenstate variance of quantum expecta- tion values of simple observables – provides an ultimate The system .– Consider two short-range-interacting atoms in a circular, transversally harmonic waveguide. In this case the center-of-mass and the relative motion can be separated. Note that the harmonic approximation for the transverse confinement has been proven to model real life atom waveguides with high accuracy. Predictions of the analogous model involving an infinite waveguide [16, 17] has been confirmed by a direct experiment-theory comparison of the energies of the quasi-one-dimensional dimers [18] and numerical calculations involving anhar- We relate the absence of thermalization in our system to the previously addressed unattainability of a complete quantum chaos in the ˇ Seba billiard – flat two-dimensional rectangular billiard with a zero-range scatterer in the middle [11]. Similarly to our system, the ˇ Seba billiard does show some signatures of the quantum-chaotic be- havior, although both the level statistics [12–14] and the momentum distributions in individual eigenstates [15] show substantial deviations from the quantum chaos pre- dictions. Both the ˇ Seba billiard (first suggested and solved in Ref. [11]) and our system allow for an exact analytic solution, in spite of the absence of a complete set of integrals of motion. upper bound for a possible deviation of the relaxed value of an observable from its thermodynamical expectation, for any initial state in principle. However, recently a new direction of research has emerged: quantum quench in many-body interacting systems [1, 2, 9, 10]. In this class of problems, the initial state is inevitably decomposed into a large superposition of the eigenstates of the Hamil- tonian governing the dynamics, and the discrepancy be- tween the result of the relaxation and thermal values is expected to be diminished. In our article we show that in the case of two short-range-interacting atoms in a har- monic waveguide, a complete thermalization can never be reached under either scenario. arXiv:1001.0225v1 [physics.atom-ph] 1 Jan 2010 Restricted Thermalization for Two Interacting Atoms in a Multimode Harmonic Waveguide V. A. Yurovsky School of Chemistry, Tel Aviv University, 69978 Tel Aviv, Israel M. Olshanii Department of Physics, University of Massachusetts Boston, Boston MA 02125, USA (Dated: October 27, 2018)