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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}
}