Multiplication of distributions in a linear gain and loss system

Abstract

We consider a model of coupled oscillators which can be seen as a gain and loss system. In the attempt to quantize the system we propose a new definition of multiplication between distributions, and we check that this definition can be adopted when checking the biorthonormality of the eigenstates of the Hamiltonian $H$ of the system, and of its adjoint $H^{†}$. In the analysis carried out here, the role of {\em weak pseudo-bosonic} ladder operators is relevant.

arXiv commentin press in ZAMP

References in corpus (9)

• Experimental Study of Active LRC Circuits with PT-Symmetries
• Bypassing the bandwidth theorem with PT symmetry
• On the Lagrangian and Hamiltonian description of the damped linear harmonic oscillator
• Quantization of the Damped Harmonic Oscillator Revisited
• Two quantization approaches to the Bateman oscillator model
• A no-go result for the quantum damped harmonic oscillator
• Weak pseudo-bosons
• Quantum mechanical settings inspired by RLC circuits
• Lagrangian for RLC circuits using analogy with the classical mechanics concepts

Cited by in corpus (1)

• Extended coupled SUSY, pseudo-bosons and weak squeezed states