Pseudo-fermions in an electronic loss-gain circuit

TL;DR

This paper applies the pseudo-fermion formalism to analyze a loss-gain electronic circuit within the framework of PT-quantum mechanics, exploring its dynamics and biorthogonal basis structures.

Contribution

It introduces a novel application of pseudo-fermions to a loss-gain circuit, connecting it with biorthogonal bases and non-self-adjoint operators in quantum-like dynamics.

Findings

Biorthogonal bases associated with the Liouville matrix are constructed.

The circuit's time evolution is described using a Heisenberg-like representation.

A self-adjoint Liouville-like operator can be introduced for the system.

Abstract

In some recent papers a loss-gain electronic circuit has been introduced and analyzed within the context of PT-quantum mechanics. In this paper we show that this circuit can be analyzed using the formalism of the so-called pseudo-fermions. In particular we discuss the time behavior of the circuit, and we construct two biorthogonal bases associated to the Liouville matrix $\Lc$ used in the treatment of the dynamics. We relate these bases to $\Lc$ and $\Lc^\dagger$, and we also show that a self-adjoint Liouville-like operator could be introduced in the game. Finally, we describe the time evolution of the circuit in an {\em Heisenberg-like} representation, driven by a non self-adjoint hamiltonian.