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

Abstract

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.