论文标题
时间依赖性和与时间无关的量子多体汉密尔顿人之间的地图
A map between time-dependent and time-independent quantum many-body Hamiltonians
论文作者
论文摘要
给定时间无关的Hamiltonian $ \ widetilde h $，可以通过量规变换来构建时间依赖时间的汉密尔顿$ h_t $。这里$ u_t $是将相应的schrodinger方程解决方案的解决方案相关联的统一转换。在多体案例中，通常对具有很少体（通常是两体）相互作用的哈密顿人感兴趣。我们将这种汉密尔顿人称为“身体”。我们在$ u_t $上制定足够的条件，以确保$ h_t $是物理的，只要$ \ widetilde h $是物理（反之亦然）。这样，我们获得了一种通用方法，可以找到这对物理汉密尔顿人$ h_t $，$ \ widetilde h $，由于$ h_t $统治的驱动的多体动力学可以将其减少到Quench Dynamics，这是由于时间依赖时间$ \ \ \ \ \ \ \ \ \ \ \ widetilde h $。我们将此方法应用于许多多体系统。首先，我们通过各向同性海森堡相互作用和任意时间依赖的磁场对旋转系统的映射到没有磁场的时间无关的系统[F。 Yan，L。Yang，B。Li，物理。 Lett。 A 251，289（1999）;物理。 Lett。 A 259，207（1999）]。然后，我们证明，本质上相同的量规变换消除了从相互作用的费米子系统中取消任意时间依赖的磁场。此外，我们将该方法应用于量子旋转系统，并将自旋耦合到骨环环境。我们还讨论了一个更一般的情况，其中$ \ widetilde h = \ widetilde h_t $是时间依赖但动态整合的。
Given a time-independent Hamiltonian $\widetilde H$, one can construct a time-dependent Hamiltonian $H_t$ by means of the gauge transformation $H_t=U_t \widetilde H \, U^\dagger_t-i\, U_t\, \partial_t U_t^\dagger$. Here $U_t$ is the unitary transformation that relates the solutions of the corresponding Schrodinger equations. In the many-body case one is usually interested in Hamiltonians with few-body (often, at most two-body) interactions. We refer to such Hamiltonians as "physical". We formulate sufficient conditions on $U_t$ ensuring that $H_t$ is physical as long as $\widetilde H$ is physical (and vice versa). This way we obtain a general method for finding such pairs of physical Hamiltonians $H_t$, $\widetilde H$ that the driven many-body dynamics governed by $H_t$ can be reduced to the quench dynamics due to the time-independent $\widetilde H$. We apply this method to a number of many-body systems. First we review the mapping of a spin system with isotropic Heisenberg interaction and arbitrary time-dependent magnetic field to the time-independent system without a magnetic field [F. Yan, L. Yang, B. Li, Phys. Lett. A 251, 289 (1999); Phys. Lett. A 259, 207 (1999)]. Then we demonstrate that essentially the same gauge transformation eliminates an arbitrary time-dependent magnetic field from a system of interacting fermions. Further, we apply the method to the quantum Ising spin system and a spin coupled to a bosonic environment. We also discuss a more general situation where $\widetilde H = \widetilde H_t$ is time-dependent but dynamically integrable.
