Pseudo-fermions in an Electronic Loss-Gain Circuit

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 used in the treatment of the dynamics. We relate these bases to and , 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 Heisenberg-like representation, driven by a non self-adjoint Hamiltonian.