### Abstract

Original language | English |
---|---|

Pages (from-to) | 1-13 |

Number of pages | 13 |

Journal | Journal of Mathematical Physics |

Volume | 59 |

Publication status | Published - 2018 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Mathematical Physics*,

*59*, 1-13.

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

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 59, pp. 1-13.

}

TY - JOUR

T1 - Quantum mechanical settings inspired by RLC circuits

AU - Spagnolo, Salvatore

AU - Gargano, Francesco

AU - Bagarello, Fabio

AU - Bagarello, null

PY - 2018

Y1 - 2018

N2 - 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.

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.

UR - http://hdl.handle.net/10447/288822

UR - http://scitation.aip.org/content/aip/journal/jmp

M3 - Article

VL - 59

SP - 1

EP - 13

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

ER -