Termoforese em sistemas quânticos

Abstract

In this master degree dissertation we treat of the effects of a thermal gradient acting on elementary quantum systems. The presence of a gradient of temperature on macroscopic systems can induct several effects, for example, a heat transport, which satisfies Fourier’s Law, and Thermophoresis (also known as Soret Effect), which represents a increased concentration of particles, immersed in a fluid, on the coolest side. The heat flux in quantum systems has already been studied previously, including a quantum formulation for the Fourier’s Law. The objective of this dissertation is to show that an analogous effect to thermoforesis occurs in a three level system in a Λ configuration subjected to a thermal gradient. In order to properly establish such an analogy, firstly we’ve got an expression for the local force that emerges on a classical Brownian particle subjected to a thermal gradient using the Langevin model. Afterwards, we have studied the dynamics of a quantum particle confined to a bi-stable potential, whose energy levels structure resembles those of Λ system, so that we were able to get a quantum version of the thermophoretic force, which coincides with classical one in adequate regimes. With an analogous procedure, we’ve found negative thermophoresis in a three-level quantum system in a V configuration. This effect emerges when the particle of interest has its mass much less than the fluid molecules where it is immersed, therefore causing a displacement to the hotter side. This effect can also be found in mixtures containing impurity as bubbles.