Gamow vectors formalism applied to the Loschmidt echo

TL;DR

This paper applies Gamow vectors formalism to analyze the Loschmidt echo, revealing a connection between quantum irreversibility and decoherence through non-Hermitian dynamics.

Contribution

It introduces a non-Hermitian Gamow vector approach to describe the Loschmidt echo, linking it to decoherence phenomena and their characteristic decay times.

Findings

Loschmidt echo and decoherence share similar decay characteristics

Non-Hermitian formalism effectively models quantum irreversibility

Mathematical relationship established between decay times

Abstract

Gamow vectors have been developed in order to give a mathematical description for quantum decay phenomena. Mainly, they have been applied to radioactive phenomena, scattering and to some decoherence models. They play a crucial role in the description of quantum irreversible processes, and in the formulation of time asymmetry in quantum mechanics. In this paper, we use this formalism to describe a well-known phenomenon of irreversibility: the Loschmidt echo. The standard approach considers that the irreversibility of this phenomenon is the result of an additional term in the backward Hamiltonian. Here, we use the non-Hermitian formalism, where the time evolution is non-unitary. Additionally, we compare the characteristic decay times of this phenomenon with the decoherence ones. We conclude that the Loschmidt echo and the decoherence can be considered as two aspects of the same phenomenon, and that there is a mathematical relationship between their corresponding characteristic times.