THERMODYNAMICAL PROPERTIES OF HALL SYSTEMS

We study quantum Hall effect within the framework of a newly proposed approach, which captures the principal results of some proposals. This can be established by considering a system of particles living on the noncommutative plane in the presence of an electromagnetic field and quantum statistical mechanically investigate its basic features. Solving the eigenvalue equation, we analytically derive the energy levels and the corresponding wavefunctions. These will be used, at low temperature and weak electric field, to determine the thermodynamical potential Ω nc and related physical quantities. Varying Ω nc with respect to the noncommutativity parameter θ, we define a new function that can be interpreted as a Ω nc density. Evaluating the particle number, we show that the Hall conductivity of the system is θ-dependent. This allows us to make contact with the quantum Hall effect by offering different interpretations. We study the high temperature regime and discuss the magnetism of the system. We finally show that at [Formula: see text], the system is sharing some common features with the Laughlin theory.

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Quantum Hall effect in bilayer systems and the noncommutative plane: A toy model approach

Physics Letters A ◽

10.1016/j.physleta.2005.07.061 ◽

2005 ◽

Vol 346 (1-3) ◽

pp. 133-140 ◽

Cited By ~ 25

Author(s):

B. Basu ◽

Subir Ghosh

Keyword(s):

Hall Effect ◽

Quantum Hall Effect ◽

Quantum Hall ◽

Noncommutative Plane ◽

Model Approach

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QUANTUM HALL EFFECT ON THE FLAG MANIFOLD F2

International Journal of Modern Physics A ◽

10.1142/s0217751x08040524 ◽

2008 ◽

Vol 23 (20) ◽

pp. 3129-3154 ◽

Cited By ~ 10

Author(s):

MOHAMMED DAOUD ◽

AHMED JELLAL

Keyword(s):

Hall Effect ◽

Quantum Hall Effect ◽

Particle Density ◽

Energy Levels ◽

Quantum Hall ◽

Flag Manifold ◽

Point Of View ◽

Wave Functions ◽

Geometrical Structures ◽

Algebraic Point

The Landau problem on the flag manifold F2 = SU (3)/ U (1)× U (1) is analyzed from an algebraic point of view. The involved magnetic background is induced by two U(1) Abelian connections. In quantizing the theory, we show that the wave functions, of a nonrelativistic particle living on F2, are the SU(3) Wigner [Formula: see text]-functions satisfying two constraints. Using the F2 algebraic and geometrical structures, we derive the Landau Hamiltonian as well as its energy levels. The lowest Landau level (LLL) wave functions coincide with the coherent states for the mixed SU(3) representations. We discuss the quantum Hall effect for a filling factor ν = 1, where the obtained particle density is constant and finite for a strong magnetic field. In this limit, we also show that the system behaves like an incompressible fluid. We study the semiclassical properties of the system confined in LLL. These will be used to discuss the edge excitations and construct the corresponding Wess–Zumino–Witten action.

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SPIN AND STATISTICS ON THE GROENEWOLD–MOYAL PLANE: PAULI-FORBIDDEN LEVELS AND TRANSITIONS

International Journal of Modern Physics A ◽

10.1142/s0217751x06031764 ◽

2006 ◽

Vol 21 (15) ◽

pp. 3111-3126 ◽

Cited By ~ 104

Author(s):

A. P. BALACHANDRAN ◽

G. MANGANO ◽

A. PINZUL ◽

S. VAIDYA

Keyword(s):

Hall Effect ◽

Quantum Hall Effect ◽

Energy Levels ◽

Quantum Hall ◽

Prior Work ◽

Commutation Relations ◽

Commutator Formula ◽

Potential Applications ◽

Moyal Plane ◽

Spin And Statistics

The Groenewold–Moyal plane is the algebra [Formula: see text] of functions on ℝd+1 with the *-product as the multiplication law, and the commutator [Formula: see text] between the coordinate functions. Chaichian et al.1 and Aschieri et al.2 have proved that the Poincaré group acts as automorphisms on [Formula: see text] if the coproduct is deformed. (See also the prior work of Majid,3 Oeckl4 and Grosse et al.5) In fact, the diffeomorphism group with a deformed coproduct also does so according to the results of Ref. 2. In this paper we show that for this new action, the Bose and Fermi commutation relations are deformed as well. Their potential applications to the quantum Hall effect are pointed out. Very striking consequences of these deformations are the occurrence of Pauli-forbidden energy levels and transitions. Such new effects are discussed in simple cases.

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Quantum Hall effect and von Klitzing constant

Izmeritel`naya Tekhnika ◽

10.32446/0368-1025it.2021-1-9-13 ◽

2021 ◽

pp. 9-13

Author(s):

Sergey G. Semenchinskiy

Keyword(s):

Hall Effect ◽

Quantum Hall Effect ◽

Current Problem ◽

International System ◽

Quantum Hall ◽

Constant Independent ◽

Electrical Measurements ◽

Weights And Measures ◽

System Of Units ◽

Physical Quantities

The current problem in the field of electrical measurements is considered in connection with the new definitions of SI units of physical quantities adopted by the 26th General Conference on Weights and Measures in November 2018 (France, Versailles), namely, the reproduction of an ohm based on the quantum Hall effect. The reasons for the introduction in 1988 of the Klitzing constant independent of the international system of units and its cancellation in 2018 are explained. The physical foundations of the quantum Hall effect are outlined. The main indirect and direct experiments that led to the creation of an ohm standard based on the quantum Hall effect, including those carried out at VNIIMS in 1982–1986, are analyzed. Using the example of these experiments, the identity of the values of the quantized resistance for samples prepared on the basis of inversion layers in silicon, gallium arsenide and in samples of a fundamentally new substance graphene is shown. Results on the use of graphene to create standards based on the quantum Hall effect for various industries and science based on the latest advances in its production are presented.

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FIELD-THEORETIC FOUNDATION OF NO-FIELD QUANTUM HALL EFFECT

Modern Physics Letters B ◽

10.1142/s0217984902004196 ◽

2002 ◽

Vol 16 (18) ◽

pp. 645-659 ◽

Cited By ~ 2

Author(s):

MASANORI SUGAHARA ◽

NIKOLAI N. BOGOLUBOV

Keyword(s):

Hall Effect ◽

Quantum State ◽

Quantum Hall Effect ◽

Particle Number ◽

Quantum Hall ◽

Electron System ◽

Gauge Potential ◽

Hole Doping ◽

Macroscopic Quantum ◽

Chern Simons

Recently, the authors discussed the possibility of the macroscopic quantum state similar to the Quantum Hall Effect in a semi-localized 2D electron system with a toroidal electron-wave amplitude in the absence of any magnetic field. In order to give the concrete statistical foundation of the study, the fermion-boson statistical transformation of the 2D electron system is made using a Chern–Simons gauge potential. Based on the solution of the resultant boson-type Hamiltonian, we construct the fermion-type solution via a unitary transformation. It is shown that the solution in the form of Laughlin function is stable when electrons form pairs. In the presence of hole doping, the pair Laughlin function leads to a representation of a superconducting state when the phase-coherence length λΘ exceeds the incompressibility length λQ, but when λΘ< λQ, it leads to a macroscopic quantum state characterized by particle-number definiteness.

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