# Fermionic model with a non-Hermitian Hamiltonian

## TL;DR

This paper analyzes a fermionic system governed by a non-Hermitian Hamiltonian with real eigenvalues, providing spectral analysis, physical interpretation, and thermodynamic expressions based on temperature and chemical potential.

## Contribution

It offers a mathematical spectral analysis and thermodynamic description of a non-Hermitian fermionic system with real eigenvalues, including approximate formulas for key observables.

## Key findings

- Spectral analysis of non-Hermitian fermionic Hamiltonian
- Physical interpretation of the system's real eigenvalues
- Approximate thermodynamic expressions for energy and number operator

## Abstract

This paper deals with the mathematical spectral analysis and physical interpretation of a fermionic system described by a non-Hermitian Hamiltonian possessing real eigenvalues. A statistical thermodynamical description of such a system is considered. Approximate expressions for the energy expectation value and the number operator expectation value, in terms of the absolute temperature $T$ and of the chemical potential $\mu$, are obtained, based on the Euler-Maclaurin formula.