de Broglie-Bohm analysis of a nonlinear membrane: From quantum to classical chaos

TL;DR

This paper investigates how quantum chaos emerges in a two-dimensional anharmonic oscillator within de Broglie-Bohm theory, revealing vortices and chaotic behavior similar to classical chaos through numerical analysis.

Contribution

It provides a detailed numerical study of quantum chaos in a nonlinear membrane using de Broglie-Bohm theory, highlighting the role of vortices and nonlinear interactions.

Findings

Detection of dynamical vortices in quantum velocity fields

Identification of chaos signatures like unpredictability and sensitivity

Quantum chaos closely resembles classical chaos in the studied system

Abstract

Within the de Broglie-Bohm theory, we numerically study a generic two-dimensional anharmonic oscillator including cubic and quartic interactions. 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 off-diagonal and nonlinear terms leads to robust quantum chaos very analogous to its classical version.