Abstract We study time evolution of Wigner function of an initially interacting one-dimensional quantum gas following the switch-off of the interactions. For the scenario where at t = 0 the interactions are suddenly suppressed, we derive a relationship between the dynamical Wigner function and its initial value. A two-particle system initially interacting through two different interactions of Dirac delta type is examined. For a system of particles that is suddenly let to move ballistically (without interactions) in a harmonic trap in d dimensions, and using time evolution of one-body density matrix, we derive a relationship between the time dependent Wigner function and its initial value. Using the inverse Wigner transform we obtain, for an initially harmonically trapped noninteracting particles in d dimensions, the scaling law satisfied by the density matrix at time t after a sudden change of the trapping frequency. Finally, the effects of interactions are analyzed in the dynamical Wigner function.

中文翻译：

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Wigner 相空间中非平衡动力学的精确结果

摘要 我们研究了初始相互作用的一维量子气体在相互作用关闭后的 Wigner 函数的时间演化。对于在 t = 0 时相互作用突然被抑制的情况，我们推导出动态 Wigner 函数与其初始值之间的关系。检查了最初通过狄拉克 delta 类型的两种不同相互作用进行相互作用的双粒子系统。对于突然被允许在 d 维谐波陷阱中弹道运动（没有相互作用）的粒子系统，并使用单体密度矩阵的时间演化，我们推导出时间相关的 Wigner 函数与其初始值之间的关系。使用逆 Wigner 变换，我们得到，对于 d 维中初始谐波捕获的非相互作用粒子，在捕获频率突然变化后，密度矩阵在时间 t 满足的标度律。最后，在动态 Wigner 函数中分析了相互作用的影响。