Chaos in the quantum Duffing oscillator in the semiclassical regime under parametrized dissipation

TL;DR

This paper investigates how environmental factors influence quantum chaos in the dissipative Duffing oscillator, revealing a specific system size where classical and quantum models diverge significantly and challenging assumptions about chaos and quantum-classical differences.

Contribution

It introduces a comprehensive analysis of quantum-classical differences in the dissipative Duffing oscillator using novel complexity metrics and identifies a critical system size for accurate modeling.

Findings

A meta-attractor emerges at a specific length scale.

Classically regular orbits can exhibit large quantum-classical differences.

Quantum-classical divergence is not solely determined by classical chaos.

Abstract

We study the quantum dissipative Duffing oscillator across a range of system sizes and environmental couplings under varying semiclassical approximations. Using spatial (based on Kullback-Leibler distances between phase-space attractors) and temporal (Lyapunov exponent-based) complexity metrics, we isolate the effect of the environment on quantum-classical differences. Moreover, we quantify the system sizes where quantum dynamics cannot be simulated using semiclassical or noise-added classical approximations. Remarkably, we find that a parametrically invariant meta-attractor emerges at a specific length scale and noise-added classical models deviate strongly from quantum dynamics below this scale. Our findings also generalize the previous surprising result that classically regular orbits can have the greatest quantum-classical differences in the semiclassical regime. In particular, we show that the dynamical growth of quantum-classical differences is not determined by the degree of classical chaos.