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.