论文标题
三个位置玻色 - 哈伯德模型中的混乱 - 经典与量子
Chaos in the three-site Bose-Hubbard model -- classical vs quantum
论文作者
论文摘要
我们考虑了一个量子多体系统 - 三个站点上的Bose -Hubbard系统 - 具有经典的极限，既不是混乱的也不是可混合的，而是显示了两种类型的行为的混合物。我们将量子系统中混乱（特征值统计和特征向量结构）的量子测量与相应经典系统中的混乱（Lyapunov指数）的经典测量。作为能量和相互作用强度的函数，我们证明了两种情况之间的强大总体对应关系。与强烈的混乱和可混合的系统相反，最大的Lyapunov指数被证明是能量的多值函数。
We consider a quantum many-body system - the Bose-Hubbard system on three sites - which has a classical limit, and which is neither strongly chaotic nor integrable but rather shows a mixture of the two types of behavior. We compare quantum measures of chaos (eigenvalue statistics and eigenvector structure) in the quantum system, with classical measures of chaos (Lyapunov exponents) in the corresponding classical system. As a function of energy and interaction strength, we demonstrate a strong overall correspondence between the two cases. In contrast to both strongly chaotic and integrable systems, the largest Lyapunov exponent is shown to be a multi-valued function of energy.
