scholarly journals QUANTUM GROUP SYMMETRY AND QUANTUM HALL WAVE FUNCTIONS ON A TORUS

1994 ◽  
Vol 09 (20) ◽  
pp. 1819-1825 ◽  
Author(s):  
HARU-TADA SATO
Keyword(s):  
Quantum Group ◽  
Uniform Magnetic Field ◽  
Deformation Parameter ◽  
Filling Factor ◽  
Particle System ◽  
Group Structure ◽  
Quantum Hall ◽  
Wave Functions ◽  
Group Symmetry ◽  
Two Dimensional

We generalize the quantum group structure of two-dimensional nonrelativistic electron in a uniform magnetic field into the case of a many-particle system on a torus. We verify the conjecture that the deformation parameter of the quantum algebra is given by the filling factor ν=1/p (p odd) on the basis of the Haldane-Rezayi’s wave functions.

scholarly journals LANDAU LEVELS AND QUANTUM GROUP

1994 ◽  
Vol 09 (05) ◽  
pp. 451-458 ◽  
Author(s):  
HARU-TADA SATO
Keyword(s):  
Quantum Group ◽  
Uniform Magnetic Field ◽  
Periodic Potential ◽  
Group Structure ◽  
Quantum Algebra ◽  
Wave Functions ◽  
Landau Levels ◽  
Group Symmetry ◽  
Factor V ◽  
Level Degeneracy

We find a quantum group structure in two-dimensional motions of a nonrelativistic electron in a uniform magnetic field and in a periodic potential. The representation basis of the quantum algebra is composed of wave functions of the system. The quantum group symmetry commutes with the Hamiltonian and is relevant to the Landau level degeneracy. The deformation parameter q of the quantum algebra turns out to be given by the fractional filling factor v=1/m (m odd integer).

POISSON–LIE GROUPS AND CLASSICAL W-ALGEBRAS

1992 ◽  
Vol 07 (05) ◽  
pp. 853-876 ◽  
Author(s):  
V. A. FATEEV ◽  
S. L. LUKYANOV
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Quantum Group ◽  
Lie Groups ◽  
Group Structure ◽  
Two Dimensional ◽  
Poisson Structures ◽  
Additional Symmetries ◽  
Conformal Field ◽  
Poisson Lie Groups

This is the first part of a paper studying the quantum group structure of two-dimensional conformal field theory with additional symmetries. We discuss the properties of the Poisson structures possessing classical W-invariance. The Darboux variables for these Poisson structures are constructed.

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.

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.

QUANTUM GROUP AND TWO-DIMENSIONAL GRAVITY

1992 ◽  
Vol 06 (11n12) ◽  
pp. 1917-1937 ◽  
Author(s):  
JEAN-LOUP GERVAIS
Keyword(s):  
Quantum Gravity ◽  
Quantum Group ◽  
Group Structure ◽  
Two Dimensional ◽  
Dimensional Gravity ◽  
Conformal Gauge

Current progress in understanding quantum gravity from the operator viewpoint are reviewed. They are based on the Uq(sl(2))-quantum-group structure recently put forward,1,2 for the chiral components of the metric in the conformal gauge.

scholarly journals Fractional statistics in anyon collisions

Science ◽  
2020 ◽  
Vol 368 (6487) ◽  
pp. 173-177 ◽  
Author(s):  
H. Bartolomei ◽  
M. Kumar ◽  
R. Bisognin ◽  
A. Marguerite ◽  
J.-M. Berroir ◽  
...  
Keyword(s):  
Quantum Hall Effect ◽  
Filling Factor ◽  
Quantum Hall ◽  
Theoretical Models ◽  
Fractional Quantum Hall Effect ◽  
Two Dimensional ◽  
Fractional Statistics ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Exotic Particles

Two-dimensional systems can host exotic particles called anyons whose quantum statistics are neither bosonic nor fermionic. For example, the elementary excitations of the fractional quantum Hall effect at filling factor ν = 1/m (where m is an odd integer) have been predicted to obey Abelian fractional statistics, with a phase ϕ associated with the exchange of two particles equal to π/m. However, despite numerous experimental attempts, clear signatures of fractional statistics have remained elusive. We experimentally demonstrate Abelian fractional statistics at filling factor ν = ⅓ by measuring the current correlations resulting from the collision between anyons at a beamsplitter. By analyzing their dependence on the anyon current impinging on the splitter and comparing with recent theoretical models, we extract ϕ = π/3, in agreement with predictions.

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 Hidden U q (sl(2)) $otimes$ U q (sl(2)) Quantum Group Symmetry in Two Dimensional Gravity

1997 ◽  
Vol 183 (3) ◽  
pp. 609-643 ◽  
Author(s):  
Eug&#x000E8;ne Cremmer ◽  
Jean-Loup Gervais ◽  
Jens Schnittger
Keyword(s):  
Quantum Group ◽  
Group Symmetry ◽  
Two Dimensional ◽  
Dimensional Gravity
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