The approach to classical chaos in an anharmonic quantum oscillator

Christopher C. Gerry

Henrique Santos Lima, Matheus M. A. Paixão, Constantino Tsallis

Within the de Broglie-Bohm theory, we numerically study a generic two-dimensional anharmonic oscillator including cubic and quartic interactions in addition to a bilinear coupling term. Our analysis of the quantum velocity fields and trajectories reveals the emergence of dynamical vortices. In their vicinity, fingerprints of chaotic behavior such as unpredictability and sensitivity to initial conditions are detected. The simultaneous presence of the off-diagonal -kxy and nonlinear terms leads to robust quantum chaos very analogous to its classical version.

Wu -, Xinxing, Жу +1 more

Klimenty N. Yugay, Stanislav D. Tvorogov

A theory allowing to describe of quantum chaos in the term of nonlinear classical dynamics is proposed. It is showed that a solution of a quantum problem in quasiclassical region is connected with a solution of a corresponding classical problem which is the classical limit of the quantum one. It is showed also that the wave function phase is satisfied an own equation of motion and it is a classical dynamic equation. Dynamical chaos of nonlinear classical dynamics results to irregularity of the wave function phase and a strange attractor in a classical dynamics of the wave function phase leads to irregularity in probabilities of transitions of anharmonic oscillator in an external time-dependent field. In the pure quantum and the pure classical region corresponding solutions are independent.

Sankhasubhra Nag

H. Kröger

We discuss the concept of the quantum action with the purpose to characterize and quantitatively compute quantum chaos. As an example we consider in quantum mechanics a 2-D Hamiltonian system - harmonic oscillators with anharmonic coupling - which is classically a chaotic system. We compare Poincaré sections obtained from the quantum action with those from the classical action.