Berman G. P., Bulgakov E. N., Zaslavsky G. M.
The University of Chicago, Department of MathematicsKirensky Institute of Physics, Krasnoyarsk, 660036 RussiaCourant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York 10012.
Chaos. 1992 Apr;2(2):257-265. doi: 10.1063/1.165912.
A system of atoms interacting with a radiation field in a resonant cavity is studied under conditions when the dynamics in the classical limit is stochastic. This situation is called quantum chaos. Equations of motion are obtained for the quantum-mechanical expectation values which take into account the quantum correlation functions. It is shown that in a situation corresponding to quantum chaos, the quantum corrections grow exponentially, making the evolution of the system essentially quantal after a certain time tau( variant Planck's over 2pi ) has elapsed. Analytical and numerical analysis show that in this regime the time tau( variant Planck's over 2pi ) obeys the logarithmic law tau( variant Planck's over 2pi ) approximately ln N (N is the number of atoms), and not the law tau( variant Planck's over 2pi ) approximately N(alpha) (alpha is a certain constant of order unity), as would be the case in the absence of chaos.
在经典极限下动力学为随机的条件下，研究了与共振腔内辐射场相互作用的原子系统。这种情况被称为量子混沌。得到了考虑量子关联函数的量子力学期望值的运动方程。结果表明，在对应于量子混沌的情况下，量子修正呈指数增长，使得系统在经过一定时间τ（普朗克常数除以2π）后，其演化本质上变为量子化的。分析和数值分析表明，在这种情况下，时间τ（普朗克常数除以2π）服从对数定律τ（普朗克常数除以2π）≈lnN（N是原子数），而不是在无混沌情况下的定律τ（普朗克常数除以2π）≈N^α（α是某个量级为1的常数）。
