A USEFUL REPRESENTATION FOR STUDYING QUANTUM HALL EFFECT

1996 ◽  
Vol 10 (12) ◽  
pp. 523-529 ◽  
Author(s):  
HONG-YI FAN ◽  
YONG REN
Keyword(s):  
Magnetic Field ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Uniform Magnetic Field ◽  
Quantum Hall ◽  
Algebraic Approach ◽  
Wave Functions

We show that the complete and orthonormal representation 〈λ|, which is constructed in terms of guiding centers and canonical momenta for describing the coordinate of an electron in a uniform magnetic field, provides us with a direct algebraic approach to deriving the correct wave functions for studying quantum Hall effect. The squeezing transformation for electron’s motion radius in the 〈λ| representation is also discussed, normally ordered squeezing operators are derived by virtue of the technique of integration within an ordered product of operators.

Squeezing Transformation for Dynamics of An Electron in Uniform Magnetic Field and a Harmonic Potential

1997 ◽  
Vol 11 (06) ◽  
pp. 239-244 ◽  
Author(s):  
Hong-Yi Fan ◽  
Yan Zhang
Keyword(s):  
Magnetic Field ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Uniform Magnetic Field ◽  
Cyclotron Frequency ◽  
Quantum Hall ◽  
Wave Functions ◽  
Harmonic Potential

By virtue of the <λ| representation (Hong-yi Fan and Yong Ren, Mod. Phys. Lett.B10, 523 (1996)), which is useful for studying quantum Hall effect, we reveal that a squeezing mechanism directly corresponding to the variation of electron's cyclotron frequency is involved in the dynamics of an electron in a uniform magnetic field and a harmonic potential. Electron's wave functions are also derived by the squeezing transformation in the <λ| representation.

scholarly journals Two-Dimensional Gases of Generalized Statistics in A Uniform Magnetic Field

1997 ◽  
Vol 11 (11) ◽  
pp. 461-470 ◽  
Author(s):  
Choon-Lin Ho ◽  
Man-Jui Liao
Keyword(s):  
Magnetic Field ◽  
Low Temperature ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Low Temperatures ◽  
Uniform Magnetic Field ◽  
Quantum Hall ◽  
Charge Carriers ◽  
Two Dimensional ◽  
Ideal Gases

We study the low temperature properties of two-dimensional ideal gases of generalized statistics in a uniform magnetic field. The generalized statistics considered here are the parafermion statistics and the exclusion statistics. Similarity in the behaviors of the parafermion gas of finite order p and the gas with exclusion coefficient g=1/p at very low temperatures is noted. These two systems become exactly equivalent at T=0. Quantum Hall effect with these particles as charge carriers is briefly discussed.

scholarly journals HIERARCHICAL WAVE FUNCTIONS AND FRACTIONAL STATISTICS IN FRACTIONAL QUANTUM HALL EFFECT ON THE TORUS

1993 ◽  
Vol 07 (15) ◽  
pp. 2779-2794 ◽  
Author(s):  
DINGPING LI
Keyword(s):  
Magnetic Field ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Braid Group ◽  
Group Analysis ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Wave Functions ◽  
Fractional Quantum ◽  
Fractional Quantum Hall

One kind of hierarchical wave functions of Fractional Quantum Hall Effect (FQHE) on the torus are constructed. The multi-component nature of anyon wave functions and the degeneracy of FQHE on the torus are very clearly reflected in this kind of wave functions. We also calculate the braid statistics of the quasiparticles in FQHE on the torus and show they fit the picture of anyons interacting with magnetic field on the torus obtained from braid group analysis.

scholarly journals The quantum Hall effect in the absence of disorder

2021 ◽  
Vol 6 (1) ◽  
Author(s):  
Kyung-Su Kim ◽  
Steven A. Kivelson
Keyword(s):  
Magnetic Field ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Finite Interval ◽  
Quantum Hall ◽  
Wigner Crystal ◽  
Quasi Particle ◽  
Hall Conductance ◽  
Finite Extent

AbstractIt is widely held that disorder is essential to the existence of a finite interval of magnetic field in which the Hall conductance is quantized, i.e., for the existence of “plateaus” in the quantum Hall effect. Here, we show that the existence of a quasi-particle Wigner crystal (QPWC) results in the persistence of plateaus of finite extent even in the limit of vanishing disorder. Several experimentally detectable features that characterize the behavior in the zero disorder limit are also explored.

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