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Identifier

000381548

Title

Directed motion in Tight-Binding lattices

Alternative Title

Κατευθυνόμενη κίνηση σε πλέγματα ισχυρής δέσμευσης

Author

Τσατραφύλλης, Νικόλαος

Thesis advisor

Τσιρώνης, Γεώργιος

Abstract

Classical directed motion and quantum diffusion for a particle are studied in onedimension. In the Classical regime, we examined through stochastic simulations in the Langevin picture the motion of an over-damped Brownian particle in a periodic, non-symmetric ratchet potential driven by time-correlated forces. We focused on two extreme limits, the white noise limit where the correlation time goes to zero, where we found numerically that white uncorrelated fluctuations cannot induce macroscopic current. In the other extreme limit when the correlation time is very large, we noticed that the time correlations of the noise can create a non zero current due to the asymmetry of the potential, the well-known Ratchet effect. In the quantum regime we studied the motion of a charged particle through the stochastic Liouville equation, using analytical as well as numerical means, in three different one - dimensional discrete tight-binding lattices : (i) the single-band, (ii) the two-band and (iii) the tree-band lattice, in the presence/absence of a sinusoidal electric field. Additionally, the coupling of the charged particle to the environment was taken into account in a phenomenological way by adding proper terms in the Liouville equation. Quantum diffusion can been seen in all cases except for the very special case of the linear lattice with an AC drive, where dynamic localization appears for special values of the electric field’s parameters. The phenomenon of dynamic localization, for the same parameter regime disappears for the other types of lattices.

Language

English

Subject

Brownian motion

Diffusion

Discrete lattice

Liouville-von Neumann equation

Nonlinear system

Διακριτό Πλέγμα

Εξίσωση Liouville-von Neumann

Κίνηση Μπράουν

Μη-γραμμικό σύστημα