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Title: Oscillatory multiband dynamics of free particles: The ubiquity of zitterbewegung effects

Abstract

In the Dirac theory for the motion of free relativistic electrons, highly oscillatory components appear in the time evolution of physical observables such as position, velocity, and spin angular momentum. This effect is known as zitterbewegung. We present a theoretical analysis of rather different Hamiltonians with gapped and/or spin-split energy spectrum (including the Rashba, Luttinger, and Kane Hamiltonians) that exhibit analogs of zitterbewegung as a common feature. We find that the amplitude of oscillations of the Heisenberg velocity operator v(t) generally equals the uncertainty for a simultaneous measurement of two linearly independent components of v. It is also shown that many features of zitterbewegung are shared by the simple and well-known Landau Hamiltonian, describing the dynamics of two-dimensional (2D) electron systems in the presence of a magnetic field perpendicular to the plane. Finally, we also discuss the oscillatory dynamics of 2D electrons arising from the interplay of Rashba spin splitting and a perpendicular magnetic field.

Authors:
; ;  [1];  [2];  [3];  [4]
  1. Department of Physics, Northern Illinois University, DeKalb, Illinois 60115 (United States) and Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106 (United States)
  2. (New Zealand)
  3. (United States)
  4. (Germany)
Publication Date:
OSTI Identifier:
21045877
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. B, Condensed Matter and Materials Physics; Journal Volume: 75; Journal Issue: 20; Other Information: DOI: 10.1103/PhysRevB.75.205314; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; AMPLITUDES; ELECTRON GAS; ELECTRONS; ENERGY SPECTRA; HAMILTONIANS; HEISENBERG MODEL; L-S COUPLING; MAGNETIC FIELDS; OSCILLATIONS; PARTICLES; RELATIVISTIC RANGE; SPIN; TWO-DIMENSIONAL CALCULATIONS; VELOCITY; ZITTERBEWEGUNG

Citation Formats

Winkler, R., Zuelicke, U., Bolte, Jens, Institute of Fundamental Sciences and MacDiarmid Institute for Advanced Materials and Nanotechnology, Massey University, Private Bag 11 222, Palmerston North, and Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, and Institut fuer Theoretische Physik, Universitaet Ulm, Albert-Einstein-Allee 11, D-89069 Ulm. Oscillatory multiband dynamics of free particles: The ubiquity of zitterbewegung effects. United States: N. p., 2007. Web. doi:10.1103/PHYSREVB.75.205314.
Winkler, R., Zuelicke, U., Bolte, Jens, Institute of Fundamental Sciences and MacDiarmid Institute for Advanced Materials and Nanotechnology, Massey University, Private Bag 11 222, Palmerston North, and Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, & Institut fuer Theoretische Physik, Universitaet Ulm, Albert-Einstein-Allee 11, D-89069 Ulm. Oscillatory multiband dynamics of free particles: The ubiquity of zitterbewegung effects. United States. doi:10.1103/PHYSREVB.75.205314.
Winkler, R., Zuelicke, U., Bolte, Jens, Institute of Fundamental Sciences and MacDiarmid Institute for Advanced Materials and Nanotechnology, Massey University, Private Bag 11 222, Palmerston North, and Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, and Institut fuer Theoretische Physik, Universitaet Ulm, Albert-Einstein-Allee 11, D-89069 Ulm. Tue . "Oscillatory multiband dynamics of free particles: The ubiquity of zitterbewegung effects". United States. doi:10.1103/PHYSREVB.75.205314.
@article{osti_21045877,
title = {Oscillatory multiband dynamics of free particles: The ubiquity of zitterbewegung effects},
author = {Winkler, R. and Zuelicke, U. and Bolte, Jens and Institute of Fundamental Sciences and MacDiarmid Institute for Advanced Materials and Nanotechnology, Massey University, Private Bag 11 222, Palmerston North and and Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106 and Institut fuer Theoretische Physik, Universitaet Ulm, Albert-Einstein-Allee 11, D-89069 Ulm},
abstractNote = {In the Dirac theory for the motion of free relativistic electrons, highly oscillatory components appear in the time evolution of physical observables such as position, velocity, and spin angular momentum. This effect is known as zitterbewegung. We present a theoretical analysis of rather different Hamiltonians with gapped and/or spin-split energy spectrum (including the Rashba, Luttinger, and Kane Hamiltonians) that exhibit analogs of zitterbewegung as a common feature. We find that the amplitude of oscillations of the Heisenberg velocity operator v(t) generally equals the uncertainty for a simultaneous measurement of two linearly independent components of v. It is also shown that many features of zitterbewegung are shared by the simple and well-known Landau Hamiltonian, describing the dynamics of two-dimensional (2D) electron systems in the presence of a magnetic field perpendicular to the plane. Finally, we also discuss the oscillatory dynamics of 2D electrons arising from the interplay of Rashba spin splitting and a perpendicular magnetic field.},
doi = {10.1103/PHYSREVB.75.205314},
journal = {Physical Review. B, Condensed Matter and Materials Physics},
number = 20,
volume = 75,
place = {United States},
year = {Tue May 15 00:00:00 EDT 2007},
month = {Tue May 15 00:00:00 EDT 2007}
}
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  • Dissipative self-assembly is the formation of ordered structures far from equilibrium, which continuously uptake energy and dissipate it into the environment. Due to its dynamical nature, dissipative self-assembly can lead to new phenomena and possibilities of self-organization that are unavailable to equilibrium systems. Understanding the dynamics of dissipative self-assembly is required in order to direct the assembly to structures of interest. In the present work, Brownian dynamics simulations and analytical theory were used to study the dynamics of self-assembly of a mixture of particles coated with weak acids and bases under continuous oscillations of the pH. The pH of themore » system modulates the charge of the particles and, therefore, the interparticle forces oscillate in time. This system produces a variety of self-assembled structures, including colloidal molecules, fibers and different types of crystalline lattices. The most important conclusions of our study are: (i) in the limit of fast oscillations, the whole dynamics (and not only those at the non-equilibrium steady state) of a system of particles interacting through time-oscillating interparticle forces can be described by an effective potential that is the time average of the time-dependent potential over one oscillation period; (ii) the oscillation period is critical to determine the order of the system. In some cases the order is favored by very fast oscillations while in others small oscillation frequencies increase the order. In the latter case, it is shown that slow oscillations remove kinetic traps and, thus, allow the system to evolve towards the most stable non-equilibrium steady state.« less