标题： ETH单调性在二维系统中 显示英文标题

标题： ETH-monotonicity in two-dimensional systems

摘要： 我们研究了二维系统中最近发现的多体量子混沌系统的一个特性，称为ETH单调性。 我们的新结果进一步支持了这些高维系统中的ETH单调性。 我们表明，$f$函数的展平率与系统的自由度数量成正比，因此当$L^2$时，$L$是系统的线性尺寸，在一般情况下，预期为$L^d$，其中$d$是系统的空间维度。 我们还表明，对于相同空间尺寸的系统，展平率与粒子（或空穴）数量成正比。 显示英文摘要

摘要： We study a recently discovered property of many-body quantum chaotic systems called ETH-monotonicity in two-dimensional systems. Our new results further support ETH-monotonicity in these higher dimensional systems. We show that the flattening rate of the $f$-function is directly proportional to the number of degrees of freedom in the system, so as $L^2$ where $L$ is the linear size of the system, and in general, expected to be $L^d$ where $d$ is the spatial dimension of the system. We also show that the flattening rate is directly proportional to the particle (or hole) number for systems of same spatial size.