skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Oscillator potential for the four-dimensional Hall effect

Abstract

We suggest an exactly solvable model of an oscillator on a four-dimensional sphere interacting with an SU(2) Yang monopole. We show that the properties of the model essentially depend on the monopole charge.

Authors:
;  [1]
  1. Artsakh State University, Stepanakert and Yerevan State University, Yerevan (Armenia)
Publication Date:
OSTI Identifier:
20787768
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. B, Condensed Matter and Materials Physics; Journal Volume: 72; Journal Issue: 23; Other Information: DOI: 10.1103/PhysRevB.72.233303; (c) 2005 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; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; EXACT SOLUTIONS; FOUR-DIMENSIONAL CALCULATIONS; HALL EFFECT; MONOPOLES; OSCILLATORS; POTENTIALS; SPHERES; SU-2 GROUPS

Citation Formats

Mardoyan, Levon, and Nersessian, Armen. Oscillator potential for the four-dimensional Hall effect. United States: N. p., 2005. Web. doi:10.1103/PHYSREVB.72.2.
Mardoyan, Levon, & Nersessian, Armen. Oscillator potential for the four-dimensional Hall effect. United States. doi:10.1103/PHYSREVB.72.2.
Mardoyan, Levon, and Nersessian, Armen. Thu . "Oscillator potential for the four-dimensional Hall effect". United States. doi:10.1103/PHYSREVB.72.2.
@article{osti_20787768,
title = {Oscillator potential for the four-dimensional Hall effect},
author = {Mardoyan, Levon and Nersessian, Armen},
abstractNote = {We suggest an exactly solvable model of an oscillator on a four-dimensional sphere interacting with an SU(2) Yang monopole. We show that the properties of the model essentially depend on the monopole charge.},
doi = {10.1103/PHYSREVB.72.2},
journal = {Physical Review. B, Condensed Matter and Materials Physics},
number = 23,
volume = 72,
place = {United States},
year = {Thu Dec 15 00:00:00 EST 2005},
month = {Thu Dec 15 00:00:00 EST 2005}
}
  • The Zeeman Hamiltonian for (spinless) hydrogen in a constant magnetic field is shown to be equivalent to a four-dimensional anisotropic anharmonic oscillator. Using this relation, Rayleigh-Schroedinger perturbation series expansions of both systems can be related to each other and analyzed in a unified way. Special emphasis is laid upon analytical estimates of their behavior in large orders of perturbation theory. Employing the path-integral approach, a new large-order formula is derived for the expansion of the ground-state energy of the oscillator system. With use of known Bender-Wu formulas for isotropic anharmonic oscillators, the major part of this calculation becomes straightforward. Combinedmore » with the new equivalence, this calculation represents the simplest path-integral derivation of large-order formulas for the Zeeman system.« less
  • The nonequilibrium state of a two-dimensional electron gas in the quantum-Hall-effect regime is studied in Hall bars equipped with additional inner contacts situated within the bar. The magnetic-field dependence of the voltage drop between different contact pairs are studied at various temperatures. It was found that the voltage between the inner and outer contacts exhibits peaks of significant amplitude in narrow magnetic-field intervals near integer filling factors. Furthermore, the magnetic-field dependence of the voltage in these intervals exhibits a hysteresis, whereas the voltage between the outer contacts remains zero in the entire magnetic-field range. The appearance of the observed voltagemore » peaks and their hysteretic behavior can be explained by an imbalance between the chemical potentials of edge and bulk states, resulting from nonequilibrium charge redistribution between the edge and bulk states when the magnetic field sweeps under conditions of the quantum Hall effect. The results of the study significantly complement the conventional picture of the quantum Hall effect, explicitly indicating the existence of a significant imbalance at the edge of the two-dimensional electron gas: the experimentally observed difference between the electrochemical potentials of the edge and bulk exceeds the distance between Landau levels by tens of times.« less
  • By means of the SU(1, 1) algebra the authors study the relationships between the coordinates, energy, angular momentum, spherical harmonics, and radial function of a hydrogen atom and those of a four-dimensional harmonic oscillator. The energies and angular momenta of the two quantum systems are found to correspond to one another.