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).

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.

Effects of Landau Level Coupling on the Magnetic Band Structure for Electrons in a Two-Dimensional Hexagonal Lattice

1994 ◽  
Vol 358 ◽  
Author(s):  
O. Kühn ◽  
V. Fessatidis ◽  
H.L. Cui ◽  
N.J.M. Horing
Keyword(s):  
Landau Level ◽  
Uniform Magnetic Field ◽  
Periodic Potential ◽  
Hexagonal Lattice ◽  
Particle Energy ◽  
Landau Levels ◽  
Two Dimensional ◽  
Single Particle Energy ◽  
Hexagonal Symmetry ◽  
Cyclotron Energy

ABSTRACTThe single-particle energy spectrum of two-dimensional electrons in a lateral surface superlattice of hexagonal symmetry, subject to a normal uniform magnetic field is investigated. Special attention is focused on the coupling of different Landau levels due to the periodic potential. It is shown that the inclusion of this coupling causes strong modifications of the spectrum compared with the limit of no coupling investigated previously. It is found that the importance of Landau level coupling is mainly determined by the relation between the potential amplitude and the cyclotron energy, as well as the Landau level index.

scholarly journals VARIATIONAL WAVE FUNCTIONS OF A VORTEX IN CYCLOTRON MOTION

2001 ◽  
Vol 15 (10n11) ◽  
pp. 1601-1604 ◽  
Author(s):  
JIAN-MING TANG
Keyword(s):  
Uniform Magnetic Field ◽  
Energy Levels ◽  
Microscopic Theory ◽  
Two Dimensions ◽  
Wave Functions ◽  
Landau Levels ◽  
Cyclotron Motion ◽  
Rotational States ◽  
Variational Wave Functions ◽  
Variational Wave

In two dimensions the microscopic theory, which provides a basis for the naive analogy between a quantized vortex in a superfluid and an electron in an uniform magnetic field, is presented. A one-to-one correspondence between the rotational states of a vortex in a cylinder and the cyclotron states of an electron in the central gauge is found. Like the Landau levels of an electron, the energy levels of a vortex are highly degenerate. However, the gap between two adjacent energy levels does not only depend on the quantized circulation, but also increases with the energy, and scales with the size of the vortex.

CHARGE-FLUX DENSITY WAVES: ANYONS IN A PERIODIC POTENTIAL

1991 ◽  
Vol 05 (21) ◽  
pp. 1431-1438
Author(s):  
D. M. Gaitonde ◽  
Sumathi Rao
Keyword(s):  
Flux Density ◽  
Periodic Potential ◽  
Mean Field Theory ◽  
Density Wave ◽  
Mean Field ◽  
Landau Levels ◽  
Filling Fraction ◽  
Lattice Periodicity ◽  
Magnetic Length ◽  
A Charge

We show that the lattice periodicity which causes a modulation of the charge density by a wave vector q also leads to a modulation of the flux density if the charged particles are anyons. Within mean field theory, we obtain a charge and flux density wave (CFDW) where the degenerate Landau levels of a constant magnetic field split into bands. For a weak periodic flux superimposed on a strong constant flux, anyon superconductivity at integer filling of Landau levels (corresponding to a statistics parameter of θ = π(1 − 1/ν) with ν = n = integer ) is not affected. However, at statistics corresponding to non-integer filling of Landau levels, for certain commensurability conditions between the lattice length (a), the magnetic length (l) and the filling fraction (ν), gaps open up at the Fermi level and convert an anyon metal into an anyon insulator.

WEAKLY INTERACTING SYMMETRIC AND ANTI-SYMMETRIC STATES IN THE BILAYER SYSTEMS

2007 ◽  
Vol 21 (08n09) ◽  
pp. 1511-1518 ◽  
Author(s):  
M. MARCHEWKA ◽  
E. M. SHEREGII ◽  
I. TRALLE ◽  
G. TOMAKA ◽  
D. PLOCH
Keyword(s):  
Experimental Data ◽  
Wave Functions ◽  
Charge Carriers ◽  
Landau Levels ◽  
Quantum Beats ◽  
Weakly Interacting ◽  
Symmetric Wave ◽  
Sdh Oscillations ◽  
Magnetic Filed ◽  
Symmetric States

We have studied the parallel magneto-transport in DQW-structures of two different potential shapes: quasi-rectangular and quasi-triangular. The quantum beats effect was observed in Shubnikov-de Haas (SdH) oscillations for both types of the DQW structures in perpendicular magnetic filed arrangement. We developed a special scheme for the Landau levels energies calculation by means of which we carried out the necessary simulations of beating effect. In order to obtain the agreement between our experimental data and the results of simulations, we introduced two different quasi-Fermi levels which characterize symmetric and anti-symmetric states in DQWs. The existence of two different quasi Fermi-Levels simply means, that one can treat two sub-systems (charge carriers characterized by symmetric and anti-symmetric wave functions) as weakly interacting and having their own rate of establishing the equilibrium state.

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.

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