Quantum chaos of atoms in a resonant cavity.
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.
Berman
G. P.
GP
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.
Bulgakov
E. N.
EN
Zaslavsky
G. M.
GM