Complexity for Open Quantum System

TL;DR

This paper investigates the complexity of an open quantum system, specifically a harmonic oscillator coupled to a scalar field bath, analyzing how complexity measures behave for different oscillator regimes and interactions.

Contribution

It introduces a detailed analysis of complexity measures in open quantum systems, revealing saturation behaviors and regulation of instability through bath interactions.

Findings

COP saturates quickly for regular oscillators

Underdamped oscillators show kink-like COP saturation behavior

Inverted oscillators exhibit linear COP growth over time

Abstract

We study the complexity for an open quantum system. Our system is a harmonic oscillator coupled to a one-dimensional massless scalar field, which acts as the bath. Specifically, we consider the reduced density matrix by tracing out the bath degrees of freedom for both regular and inverted oscillator and computed the complexity of purification (COP) and complexity by using the operator-state mapping. We found that when the oscillator is regular the COP saturates quickly for both underdamped and overdamped oscillators. Interestingly, when the oscillator is underdamped, we discover a kink like behaviour for the saturation value of COP with varying damping coefficient. For the inverted oscillator, we found a linear growth of COP with time for all values of bath-system interaction. However, when the interaction is increased the slope of the linear growth decreases, implying that the unstable nature of the system can be regulated by the bath.