论文标题
强烈混乱多体自旋模型的量子古典对应关系
Quantum-classical correspondence of strongly chaotic many-body spin models
论文作者
论文摘要
我们研究具有相互作用的自旋粒子的系统的量子古典对应关系，这些系统在经典极限上非常混乱。这是在与单个自旋的固定角动量相关的运动常数的情况下完成的。我们对Lyapunov光谱的分析表明，最大的Lyapunov指数与Lyapunov指数一致，该指数决定了每个单个旋转在所有其他自旋影响下移动的局部不稳定。在这张图片中，我们为旋转运动引入了严格而简单的终身测验，并使用它来识别何时在相位空间中经典混乱何时既强大又全球。在量子结构域中，我们对适当表示中的哈密顿矩阵的分析使我们能够获得量子混沌发作的条件，这是模型参数的函数。从量子和经典结构域之间的比较，我们证明了量子量，例如状态的局部密度（LDOS）以及以非相互作用的多体基础编写的混乱本征函数的形状，具有明确定义的经典对应物。另一个核心发现是Kolmogorov-Sinai熵与LDOS宽度之间的关系，这对于多体动力学的研究很有用。
We study the quantum-classical correspondence for systems with interacting spin-particles that are strongly chaotic in the classical limit. This is done in the presence of constants of motion associated with the fixed angular momenta of individual spins. Our analysis of the Lyapunov spectra reveals that the largest Lyapunov exponent agrees with the Lyapunov exponent that determines the local instability of each individual spin moving under the influence of all other spins. Within this picture, we introduce a rigorous and simple test of ergodicity for the spin motion, and use it to identify when classical chaos is both strong and global in phase space. In the quantum domain, our analysis of the Hamiltonian matrix in a proper representation allows us to obtain the conditions for the onset of quantum chaos as a function of the model parameters. From the comparison between the quantum and classical domains, we demonstrate that quantum quantities, such as the local density of states (LDOS) and the shape of the chaotic eigenfunctions written in the non-interacting many-body basis, have well-defined classical counterparts. Another central finding is the relationship between the Kolmogorov-Sinai entropy and the width of the LDOS, which is useful for studies of many-body dynamics.
