Quantum chaos: a route through mixed-mode dynamics

Abstract

The quantal-classical mixed-mode dynamics provides a convenient tool for studying the transition from classical to quantum dynamics. In this work nonlinearly coupled oscillator systems whose classical motion display chaos are investigated under the time-dependent self-consistent-field approach so that one of the modes can be treated quantum mechanically. Lyapunov exponents for the mixed-mode system are defined through the use of Hamilton-Jacobi-like equations of motion for the quantal wavepacket. The classical modes seem to be more regularized when they are under the effect of quantum fields, however the Lyapunov exponents of the mixed-mode dynamics agree extremely well with those from classical calculations showing that chaos still survives in the mixed-mode philosophy.