How complex is the quantum motion?

TL;DR

This paper introduces a new measure of complexity for quantum systems, linking it to their stability and reversibility, contrasting classical and quantum behaviors.

Contribution

It proposes a novel quantum complexity measure and explores its relationship with system stability and reversibility, filling a gap in understanding quantum dynamical complexity.

Findings

Quantum complexity relates to stability and reversibility.

Quantum systems retain memory of initial states longer than classical systems.

The introduced measure provides insights into quantum dynamical behavior.

Abstract

In classical mechanics the complexity of a dynamical system is characterized by the rate of local exponential instability which effaces the memory of initial conditions and leads to practical irreversibility. In striking contrast, quantum mechanics appears to exhibit strong memory of the initial state. Here we introduce a notion of complexity for a quantum system and relate it to its stability and reversibility properties.