Discrepancies between decoherence and the Loschmidt echo

TL;DR

This paper investigates the differences between the Loschmidt echo and purity in quantum systems, revealing that despite similarities, they exhibit fundamental distinctions in their decay behaviors.

Contribution

The study provides numerical evidence highlighting key differences between the decay of Loschmidt echo and purity in finite-dimensional quantum systems.

Findings

Loschmidt echo and purity decay differ fundamentally in finite systems.

Numerical simulations show non-equivalence of the two quantities.

Differences challenge the assumption of universality in chaotic quantum systems.

Abstract

The Loschmidt echo and the purity are two quantities that can provide invaluable information about the evolution of a quantum system. While the Loschmidt echo characterizes instability and sensitivity to perturbations, purity measures the loss of coherence produced by an environment coupled to the system. For classically chaotic systems both quantities display a number of -- supposedly universal -- regimes that can lead on to think of them as equivalent quantities. We study the decay of the Loschmidt echo and the purity for systems with finite dimensional Hilbert space and present numerical evidence of some fundamental differences between them.