Processos de relaxação em sistemas quânticos e álgebra de operadores não-lineares

Abstract

On this thesis some aspects of relaxation processes and decoherence processes using deformed algebras of the harmonic oscillator, particularly the generalized deformed algebra (GDA algebra) and Kerr algebra were studied.Two situations were considered for this study: a) The system of interest is described as a non-linear harmonic oscillator interacting with a dissipative environment (thermal reservoir), b) the system of interest ( non deformed harmonic oscillator) interacts with a thermal reservoir described by a group of nonlinear quantum harmonic oscillators. An interesting result was found for the two situations , where we notice that the master equation and the expressions found, show the strong dependence of the nonlinearity introduced by the deformed algebra. On case (b) the obtained equations have a form identical to the nondeformed equations, but show new nonlinear coefficients not obtained in the reading.The influence of the reservoirs nonlinearity is noticed in the coefficients found. The phenomenon of decoherence, considered the thermal nonlinear reservoir and the compressed air reservoir that were studied. The master equation that rules the dynamics of the system and an estimated a time of decoherence were obtained , along with important results. It was observed that when there is an increase on the deformed parameter there is also an increase on the decoherence time, showing the nonlinearity contained in the reservoir acts in a significant way over the time of decoherence of the system.