title: Quantum chaos of atoms in a resonant cavity.
abstract: 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.
authors.affiliation: 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.
authors.forename: G. P.
authors.initials: GP
authors.lastname: Berman
authors.forename: E. N.
authors.initials: EN
authors.lastname: Bulgakov
authors.forename: G. M.
authors.initials: GM
authors.lastname: Zaslavsky