Eur. Phys. J. Plus (2020) 135: 738
https://doi.org/10.1140/epjp/s13360-020-00756-3

Regular Article

Gamow vectors formalism applied to the Loschmidt echo

¹ CONICET - Universidad de Buenos Aires, Buenos Aires, Argentina
² Departamento de Física Teórica, Atómica y Óptica and IMUVA, Universidad de Valladolid, 47011, Valladolid, Spain
³ Instituto de Física La Plata, UNLP, CONICET, Facultad de Ciencias Exactas, La Plata, Argentina
⁴ CONICET - FAMAF, Universidad Nacional de Córdoba, Córdoba, Argentina

^a sfortin@conicet.gov.ar

Received: 10 May 2020
Accepted: 5 September 2020
Published online: 18 September 2020

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.