Quantum mechanical settings inspired by RLC circuits

Salvatore Spagnolo, Francesco Gargano, Fabio Bagarello, Bagarello

Risultato della ricerca: Article

Abstract

In some recent papers, several authors used electronic circuits to construct loss and gain systems. This is particularly interesting in the context of PT-quantum mechanics, where this kind of effects appears quite naturally. The electronic circuits used so far are simple, but not so much. Surprisingly enough, a rather trivial RLC circuit can be analyzed with the same perspective and it produces a variety of unexpected results, both from a mathematical and on a physical side. In this paper, we show that this circuit produces two biorthogonal bases associated with the Liouville matrix L used in the treatment of its dynamics, with a biorthogonality which is linked to the value of the parameters of the circuit. We also show that the related loss RLC circuit is naturally associated with a gain RLC circuit and that the relation between the two is rather naturally encoded in L. We propose a pseudo-fermionic analysis of the circuit, and we introduce the notion of m-equivalence between electronic circuits.
Lingua originaleEnglish
pagine (da-a)1-13
Numero di pagine13
RivistaJournal of Mathematical Physics
Volume59
Stato di pubblicazionePublished - 2018

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RLC circuits
electronics
Electronics
Biorthogonality
equivalence
quantum mechanics
Quantum Mechanics
Trivial
matrices
Equivalence

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cita questo

Quantum mechanical settings inspired by RLC circuits. / Spagnolo, Salvatore; Gargano, Francesco; Bagarello, Fabio; Bagarello.

In: Journal of Mathematical Physics, Vol. 59, 2018, pag. 1-13.

Risultato della ricerca: Article

Spagnolo, S, Gargano, F, Bagarello, F & Bagarello 2018, 'Quantum mechanical settings inspired by RLC circuits', Journal of Mathematical Physics, vol. 59, pagg. 1-13.
Spagnolo S, Gargano F, Bagarello F, Bagarello. Quantum mechanical settings inspired by RLC circuits. Journal of Mathematical Physics. 2018;59:1-13.
Spagnolo, Salvatore ; Gargano, Francesco ; Bagarello, Fabio ; Bagarello. / Quantum mechanical settings inspired by RLC circuits. In: Journal of Mathematical Physics. 2018 ; Vol. 59. pagg. 1-13.
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AB - In some recent papers, several authors used electronic circuits to construct loss and gain systems. This is particularly interesting in the context of PT-quantum mechanics, where this kind of effects appears quite naturally. The electronic circuits used so far are simple, but not so much. Surprisingly enough, a rather trivial RLC circuit can be analyzed with the same perspective and it produces a variety of unexpected results, both from a mathematical and on a physical side. In this paper, we show that this circuit produces two biorthogonal bases associated with the Liouville matrix L used in the treatment of its dynamics, with a biorthogonality which is linked to the value of the parameters of the circuit. We also show that the related loss RLC circuit is naturally associated with a gain RLC circuit and that the relation between the two is rather naturally encoded in L. We propose a pseudo-fermionic analysis of the circuit, and we introduce the notion of m-equivalence between electronic circuits.

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