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arXiv · 1309.0678

Pseudo-fermions in an electronic loss-gain circuit

Fabio Bagarello·Giuseppe Pantano
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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.

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Fabio Bagarello, Giuseppe Pantano. 2013-09-03. Pseudo-fermions in an electronic loss-gain circuit. https://doi.org/10.1007/s10773-013-1769-y

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