FLUID DYNAMICS, CHERN-SIMONS THEORY, AND THE QUANTUM HALL EFFECT

1991 ◽  
Vol 05 (16n17) ◽  
pp. 2735-2749 ◽  
Author(s):  
SAFI BAHCALL ◽  
LEONARD SUSSKIND
Keyword(s):  
Magnetic Field ◽  
Fluid Dynamics ◽  
Gauge Theory ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Simons Theory ◽  
Quantum Hall System ◽  
Chern Simons ◽  
Chern Simons Theory

In this paper we show that classical fluid dynamics in a plane is a gauge theory useful for studying aspects of the quantum Hall system. When the fluid is charged and placed in a magnetic field, Chern-Simons fields appear naturally and the fractional statistics of vortex excitations can be understood qualitatively. Applying the fluid picture to a gas of anyons shows that it superconducts.

scholarly journals HIERARCHICAL WAVE FUNCTIONS OF FRACTIONAL QUANTUM HALL EFFECT ON THE TORUS

1993 ◽  
Vol 07 (14) ◽  
pp. 2655-2665 ◽  
Author(s):  
DINGPING LI
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Wave Functions ◽  
Simons Theory ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Chern Simons ◽  
Chern Simons Theory

One kind of hierarchical wave functions of Fractional Quantum Hall Effect on the torus is constructed. We find that the wave functions are closely related to the wave functions of generalized Abelian Chern-Simons theory.

scholarly journals AREA-PRESERVING DIFFEOMORPHISMS, W∞ AND ${\mathcal U}_q [{\rm sl}(2)]$ IN CHERN–SIMONS THEORY AND THE QUANTUM HALL SYSTEM

1994 ◽  
Vol 09 (21) ◽  
pp. 3887-3911 ◽  
Author(s):  
IAN I. KOGAN
Keyword(s):  
Gauge Theory ◽  
Quantum Hall ◽  
Simons Theory ◽  
Two Dimensional ◽  
Canonical Transformations ◽  
Dimensional Phase Space ◽  
Quantum Hall System ◽  
Chern Simons ◽  
Area Preserving ◽  
Chern Simons Theory

We discuss a quantum [Formula: see text] symmetry in the Landau problem, which naturally arises due to the relation between [Formula: see text] and the group of magnetic translations. The latter is connected with W∞ and area-preserving (symplectic) diffeomorphisms which are the canonical transformations in the two-dimensional phase space. We shall discuss the hidden quantum symmetry in a 2 + 1 gauge theory with the Chern–Simons term and in a quantum Hall system, which are both connected with the Landau problem.

scholarly journals Solitons in Chern–Simons Theories of Nonrelativistic CPN-1 Models: Spin Textures in the Quantum Hall Effect

1997 ◽  
Vol 12 (30) ◽  
pp. 2243-2260 ◽  
Author(s):  
Ikuo Ichinose ◽  
Akira Sekiguchi
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Degrees Of Freedom ◽  
Quantum Hall ◽  
Simons Theory ◽  
Electron Systems ◽  
Effective Theories ◽  
Chern Simons ◽  
Internal Degrees Of Freedom ◽  
Chern Simons Theory

Topological solitons in CP N-1 models coupled with a Chern–Simons gauge field and a Hopf term are studied both analytically and numerically. These models are low-energy effective theories for the quantum Hall effect (QHE) with internal degrees of freedom, like the QHE in double-layer electron systems. These solitons correspond to skyrmions and merons which are charged quasi-excitations in the QHE. We explicitly show that the CP N-1 models can be used to represent (pseudo-)spin textures in the original Chern–Simons theory of bosonized electrons.

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