FIG. 3: Radial phase space probability for a harmonic oscillator under Nos´ e-Hoover controlled Bulgac-Kusnezov dynamics. The continuous line shows the theoretical value while the black bullets display the numerical results. The inset displays a plot of the phase space distribution of points along the single trajectory used to compute the radial probability. 32  0  0.02  0.04  0.06  0.08  0  0.5  1  1.5  2  2.5  3  3.5  4 P r$^{-4}$ -3 -2 -1  0  1  2  3  4 -4-3-2 -1 0 1 2 3 4 p q