论文标题
时间周期性线性电势中一维量子多体系统的动力学
Dynamics of one-dimensional quantum many-body systems in time-periodic linear potentials
论文作者
论文摘要
我们研究了一维相互作用的量子粒子的系统，该系统在空间中受到时间周期性电势线性。在讨论了驱动的单粒子系统和两粒子系统的病例之后，我们在存在一般相互作用的两体势和相应的浮雕的哈密顿量的情况下得出了许多粒子情况的类似结果。当非传播模型是可以集成的时，浮标hamitlonian也被证明是可集成的。我们确定了微动算子和系统的一般时间演化状态的表达式。我们讨论了系统动力学的各个方面，无论是在频镜和中间时间，尤其是通用波袋质量中心的运动及其随着时间的推移而扩散。我们还讨论了质量中心加速运动的情况，当时线性势的系数strenght的积分在时间段内的积分不可变，并且我们表明，在这种情况下，弗洛克特·汉密尔顿（Floquet Hamiltonian）获得了额外的静态线性电位。我们还讨论了获得的结果在Lieb-Liniger模型中的应用。
We study a system of one-dimensional interacting quantum particles subjected to a time-periodic potential linear in space. After discussing the cases of driven one- and two-particles systems, we derive the analogous results for the many-particles case in presence of a general interaction two-body potential and the corresponding Floquet Hamiltonian. When the undriven model is integrable, the Floquet Hamitlonian is shown to be integrable too. We determine the micro-motion operator and the expression for a generic time evolved state of the system. We discuss various aspects of the dynamics of the system both at stroboscopic and intermediate times, in particular the motion of the center of mass of a generic wavepacket and its spreading over time. We also discuss the case of accelerated motion of the center of mass, obtained when the integral of the coeffcient strenght of the linear potential on a time period is non-vanishing, and we show that the Floquet Hamiltonian gets in this case an additional static linear potential. We also discuss the application of the obtained results to the Lieb-Liniger model.
