Remarks on eigenvalues and eigenvectors of Hermitian matrices, berry phase, adiabatic connections and quantum Hall effect

1995 ◽  
Vol 1 (1) ◽  
pp. 1-19 ◽  
Author(s):  
V. I. Arnold
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Berry Phase ◽  
Quantum Hall ◽  
Hermitian Matrices ◽  
Eigenvalues And Eigenvectors

QUANTUM HALL EFFECT AND BERRY PHASE

1994 ◽  
Vol 08 (26) ◽  
pp. 1643-1653 ◽  
Author(s):  
DIPTI BANERJEE ◽  
PRATUL BANDYOPADHYAY
Keyword(s):  
Magnetic Field ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Berry Phase ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Intense Magnetic Field ◽  
Topological Features

It is shown here that a particle in an intense magnetic field may acquire the Berry phase and the topological features associated with this phase may be taken to be responsible for both the integrally and fractionally quantized Hall effect. The two different manifestations of quantum Hall effect have been realized in a unified scheme where the electrons associated with the fractional quantum Hall effect are found to be in an excited state having higher angular momentum.

scholarly journals TOPOLOGICAL ASPECTS OF HIGH-Tc SUPERCONDUCTIVITY, FRACTIONAL QUANTUM HALL EFFECT AND BERRY PHASE

1999 ◽  
Vol 13 (28) ◽  
pp. 3393-3404 ◽  
Author(s):  
B. BASU ◽  
D. PAL ◽  
P. BANDYOPADHYAY
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Berry Phase ◽  
Quantum Hall ◽  
Three Dimensional ◽  
Fractional Quantum Hall Effect ◽  
Chiral Anomaly ◽  
Fractional Quantum ◽  
High Tc ◽  
Fractional Quantum Hall

We have analysed here the equivalence of RVB states with ν=1/2 FQH states in terms of the Berry Phase which is associated with the chiral anomaly in 3+1 dimensions. It is observed that the three-dimensional spinons and holons are chracterised by the non-Abelian Berry phase and these reduce to 1/2 fractional statistics when the motion is confined to the equatorial planes. The topological mechanism of superconductivity is analogous to the topological aspects of fractional quantum Hall effect with ν=1/2.

scholarly journals QUANTUM HALL EFFECT AND BERRY PHASE FACTOR

1991 ◽  
Vol 40 (3) ◽  
pp. 345
Author(s):  
CHEN CHENG-MING ◽  
ZHANG QUAN
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Berry Phase ◽  
Quantum Hall ◽  
Phase Factor

The Hierarchy of Fractional Quantum Hall States and Berry Phase

1998 ◽  
Vol 12 (01) ◽  
pp. 49-62 ◽  
Author(s):  
B. Basu ◽  
P. Bandyopadhyay
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Filling Factor ◽  
Berry Phase ◽  
Quantum Hall ◽  
Chiral Anomaly ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Dynamical Phase ◽  
Integer Quantum Hall Effect

The Hierarchy of Fractional Quantum Hall (FQH) states have been studied here in the framework of chiral anomaly and Berry Phase. It is shown that the unambiguously observed FQH states with filling factor ν=p/q with p even or odd and q an odd integer can be considered from the viewpoint that the Berry phase associated with even number of vortices can be removed to the dynamical phase and the corresponding fermionic state attains a higher Landau level. This also leads to the fact that FQH states with even denominator filling factor can arise when we have pairs of degenerate electrons giving rise to the non-Abelian Berry phase which suggests that these FQH states correspond to non-Abelian Hall fluid. In this framework Integer Quantum Hall Effect (IQHE) as well as Fractional Quantum Hall Effect (FQHE) with filling factor ν=p/q with q odd or even can be studied in a unified way.

The tube diameter in polymer melts, its existence. and its relation to the quantum Hall effect

1994 ◽  
Vol 4 (6) ◽  
pp. 843-862 ◽  
Author(s):  
Arkady L. Kholodenko ◽  
Thomas A. Vilgis
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Polymer Melts ◽  
Quantum Hall ◽  
Tube Diameter
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