Transitions toward Quantum Chaos: With Supersymmetry from Poisson to Gauss
Transitions toward Quantum Chaos: With Supersymmetry from Poisson to Gauss
复制标题
向量子混沌的转变：超对称性从泊松到高斯
DOI：
10.1006/aphy.1996.0091
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发表时间：
1995
影响因子：
3
通讯作者：
Thomas Guhr
中科院分区：
文献类型：
--
作者：
Thomas Guhr;Thomas Guhr
摘要在随机矩阵模型中研究了量子系统中从任意涨落到混沌涨落的转变。假设哈密顿量可以表示为任意部分与混沌产生部分之和。高斯系综被用来模拟混沌部分。在时间反演不变性破缺的情况下，利用超对称性和分次本征值方法导出了所有关联的封闭积分表示。特别地，两级相关函数被表示为二重积分。对于一个固定的相关性指数，精确的扩散方程推导出所有三个普适性类描述过渡到混沌政权从任意初始条件。作为应用，讨论了泊松正则性到混沌的转变.两个层次的相关函数成为一个双重积分的过渡参数的所有值。
Abstract The transition from arbitrary to chaotic fluctuation properties in quantum systems is studied in a random matrix model. It is assumed that the Hamiltonian can be written as the sum of an arbitrary part and a chaos-producing part. The Gaussian ensembles are used to model the chaotic part. A closed integral representation for all the correlations in the case of broken time reversal invariance is derived by employing supersymmetry and the graded eigenvalue method. In particular, the two level correlation function is expressed as a double integral. For a fixed correlation index, exact diffusion equations are derived for all three universality classes which describe the transition to the chaotic regime from arbitrary initial conditions. As an application, the transition from Poisson regularity to chaos is discussed. The two level correlation function becomes a double integral for all values of the transition parameter.