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Algebraic methods for obtain analytical solutions in networks of coupled dissipative quantum oscillator

Grant number: 17/06280-6
Support type:Scholarships in Brazil - Scientific Initiation
Effective date (Start): July 01, 2017
Effective date (End): June 30, 2018
Field of knowledge:Physical Sciences and Mathematics - Physics - General Physics
Principal researcher:Mickel Abreu de Ponte
Grantee:Laura Cavalcante de Campos
Home Institution: Universidade Estadual Paulista (UNESP). Campus Experimental de Itapeva. Itapeva , SP, Brazil


This project has as main objective to develop algebraic methods to obtain analytical solutions related to the problem of a network of N coupled dissipative quantum oscillators. In view of the recent results, we will consider in this project that these oscillators are strongly coupled through the rotating and counter-rotating terms of interaction. In addition, we will also consider the rotating and counter-rotating terms in the weak interaction of the system with the reservoir, which is an essential ingredient in [1] for protecting the network against the effects of the reservoir in the case where N = 1, when a strong parametric amplification process is present. (For this reason, we will also consider that each oscillator in the network is subjected to a parametric amplification process.) Since the analysis of the coherence and decoherence dynamics for a network of quantum oscillators can be written as a function of the eigenvalues and coefficients of the eigenvectors, associated to the network Hamiltonian, it is interesting to identify the algebraic properties that can be used to obtain these eigenvalues and eigenvectors. Once we reach this goal, solutions to the desired problem of coupled oscillator network can be obtained as a consequence. In the situation in which the interaction between the oscillators of the system and the interaction of this with the reservoir is described only through the rotating terms was analyzed in Refs. [1,2], where it was considered the degenerate case in which all oscillators of the network have the same natural frequency, besides the same coupling constant.