Numerical studies of transport in complex many-particle systems far from equilibrium

Abstract

In this Thesis, transport in complex nonequilibrium many-particle systems is studied using numerical master equation approach and Monte Carlo simulations. We focus on the transport of the center-of-mass of deformable objects with internal structure. Two physical systems are studied in detail: linear polymers using the Rubinstein-Duke model and single-layer metal-on-metal atomic islands using a semi-empirical lattice model. Polymers and islands are driven out of thermodynamic equilibrium by strong static and time-dependent external forces. Topics covered in this work include introductions to nonequilibrium statistical mechanics, master equations and computational methods, with construction and numerical solving of master equations, and numerical optimization. For small systems (up to ∼106 states), solving master equations numerically is found to be efficient, especially when studying parameter sensitive and elusive properties, such as drifts caused by the ratchet effect. Speed and accuracy of the method allows optimization with respect to continuous model parameters and transition cycles, which helps in understanding the coupling between the internal dynamics of deformable objects and their center-of-mass displacement. Firstly, we study transport of polymers in spatially periodic time-dependent potentials using a standard and relaxed versions of the Rubinstein-Duke model. Two types of potentials, flashing and traveling, are considered with stochastic and deterministic time-dependency schemes. Rich non-linear behavior for the transport velocity, diffusion and energetic efficiency is found. By varying the polymer length, we find current inversions caused by a ’rebound’ effect that is only present for objects with internal structure. These results are different between reptating and non-reptating polymers. Transport is found to become more coherent for deterministic time-dependency scheme and as the polymer gets longer. The results show that small changes in the molecule structure (e.g. the charge configuration) and the environment variables can lead to a large change in the velocity.Secondly, we study transport of single-layer metal-on-metal islands using a semiempirical lattice model for Cu atoms on Cu(001) surface. Two types of time-dependent driving are considered: a pulsed rotated field and an alternating field with a zero average force (an electrophoretic ratchet). The main results are that a pulsed field can increase the velocity in both diagonal and axis directions as compared to a static field, and there exists a current inversion in an electrophoretic ratchet. In addition to a ’magic size’ effect for islands in equilibrium, a stronger odd-even effect is found in the presence of large fields. Master equation computations reveal nonmonotonous behavior of the leading relaxation constant and effective Arrhenius parameters. Optimized transition cycles shed light on microscopic mechanisms responsible for island transport in strong fields.