Dynamical complexity in the quantum to classical transition

TL;DR

This paper investigates how the dynamical complexity of an open quantum double-well oscillator depends on quantum effects and environmental coupling, revealing that quantum systems can be more complex than their classical counterparts, especially in regimes of chaos.

Contribution

It provides a detailed analysis of the quantum-classical transition in dynamical complexity, highlighting cases where quantum systems exhibit greater complexity and chaos than classical systems.

Findings

Quantum systems are least complex when most quantum (smallest $eta$).

Chaotic classical limits correspond to most complex quantum dynamics.

Quantum systems can be more complex or chaotic even when classical limits are regular.

Abstract

We study the dynamical complexity of an open quantum driven double-well oscillator, mapping its dependence on effective Planck's constant $\hbar_{eff}\equiv\beta$ and coupling to the environment, $\Gamma$. We study this using stochastic Schrodinger equations, semiclassical equations, and the classical limit equation. We show that (i) the dynamical complexity initially increases with effective Hilbert space size (as $\beta$ decreases) such that the most quantum systems are the least dynamically complex. (ii) If the classical limit is chaotic, that is the most dynamically complex (iii) if the classical limit is regular, there is always a quantum system more dynamically complex than the classical system. There are several parameter regimes where the quantum system is chaotic even though the classical limit is not. While some of the quantum chaotic attractors are of the same family as the classical limiting attractors, we also find a quantum attractor with no classical counterpart. These phenomena occur in experimentally accessible regimes.