Psedo-hermitian Hamiltonians at finite temperature

TL;DR

This paper extends the Double Green Function Formalism to pseudo-hermitian Hamiltonians, enabling the study of PT-symmetric systems at finite temperature and analyzing their behavior under periodic perturbations.

Contribution

It introduces a novel extension of the formalism to include pseudo-hermitian Hamiltonians, specifically applied to PT-symmetric systems at finite temperature.

Findings

Formalism successfully applied to PT-symmetry Swanson Hamiltonian

Analyzed system behavior in PT-unbroken and broken phases

Studied effects of periodic perturbations on the system

Abstract

The Double Green Function Formalism has been extensively used in dealing with the thermodynamics of quantum systems which evolved in time under the action of a given self-adjoint Hamiltonian. In this work, we extend the formalism to include pseudo-hermitian Hamiltonians. We apply the formalism to study the PT-symmetry Swanson Hamiltonian at finite temperature, both in the PT-unbroken and in the PT-broken symmetry phase. We analyse the behaviour of the system, which is initially at equilibrium at a given temperature, when it is perturbed by a periodic interaction.