Quantum Ratchets

Abstract

In this thesis, ratchet systems operating in the quantum regime are investigated. Ratchet systems, also known as Brownian motors, are periodic systems presenting an intrinsic asymmetry which can be exploited to extract work out of unbiased forces. As a model for ratchet systems, we consider the motion of a particle in a one-dimensional periodic and asymmetric potential, interacting with a thermal environment, and subject to an unbiased driving force. In quantum ratchets, intrinsic quantum fluctuations as well as the tunnel effect enrich the transport mechanisms. The investigation of quantum ratchets allows one to gain fundamental understanding on the dynamics of quantum dissipative systems. Starting from a continuous ratchet potential and applying a path integral formalism, we develop two approaches, beyond a semiclassical description, where the dynamics can be mapped onto that of an effective tight-binding model. In the first approach, a parameter regime is chosen such that only few low energy quantum states in each well of the periodic potential are involved in the dynamics of the particle. The second approach leads to a duality relation between the original system and a single-band tight-binding model. The two methods are valid in different regimes of parameters, the second one including the classical limit. We get an analytical expression for the stationary velocity of the particle, which shows reversals as a function of the driving force and of the temperature. The second method allows us to extract the explicit dependence of the velocity on the parameters of the potential, and thus to characterize the potentials which lead to the highest rectification efficiency. We also discuss the connection between this theoretical model and measurements of the dynamics of vortices in quasi one-dimensional Josephson junction arrays.