6533b7defe1ef96bd12769d7
RESEARCH PRODUCT
Quantum mechanical settings inspired by RLC circuits
Francesco GarganoSalvatore SpagnoloG. AlicataFabio Bagarellosubject
Relation (database)010308 nuclear & particles physicsComputer scienceFOS: Physical sciencesStatistical and Nonlinear PhysicsContext (language use)Hardware_PERFORMANCEANDRELIABILITYMathematical Physics (math-ph)Topology01 natural sciencesComputer Science::Hardware ArchitectureMatrix (mathematics)Computer Science::Emerging TechnologiesSimple (abstract algebra)Biorthogonal system0103 physical sciencesHardware_INTEGRATEDCIRCUITSRLC circuit010306 general physicsSettore MAT/07 - Fisica MatematicaQuantumMathematical PhysicsStatistical and Nonlinear PhysicElectronic circuitHardware_LOGICDESIGNdescription
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 to the Liouville matrix $\Lc$ 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 to a gain RLC circuit, and that the relation between the two is rather naturally encoded in $\Lc$. We propose a pseudo-fermionic analysis of the circuit, and we introduce the notion of $m$-equivalence between electronic circuits.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2018-04-11 |