论文标题
在Bose-Hubbard模型中前往量子混乱的最佳途径
Optimal route to quantum chaos in the Bose-Hubbard model
论文作者
论文摘要
Bose-Hubbard Hamiltonian对粒子数$ n $，系统大小$ L $和粒子密度的混乱阶段的依赖性根据光谱和特征性特征研究。我们分析了混乱阶段的发展，因为无限希尔伯特空间维度的极限沿着不同的方向接近，并表明到混乱的最快途径是固定密度$ n \ lyssim 1 $的路径。在常数$ l $处的极限$ n \ to \ infty $导致混乱阶段降低了趋于较慢的矩阵理论基准。在这种情况下，从本征态概括性分形维度的分布中，沿巨像的阶段与较大$ n $的随机矩阵理论更具区别，其方式与沿固定密度下的轨迹相似。
The dependence of the chaotic phase of the Bose-Hubbard Hamiltonian on particle number $N$, system size $L$ and particle density is investigated in terms of spectral and eigenstate features. We analyze the development of the chaotic phase as the limit of infinite Hilbert space dimension is approached along different directions, and show that the fastest route to chaos is the path at fixed density $n \lesssim 1$. The limit $N \to \infty$ at constant $L$ leads to a slower convergence of the chaotic phase towards the random matrix theory benchmarks. In this case, from the distribution of the eigenstate generalized fractal dimensions, the ergodic phase becomes more distinguishable from random matrix theory for larger $N$, in a similar way as along trajectories at fixed density.
