scholarly journals Construction of various soliton solutions via the simplified extended sinh-Gordon equation expansion method

2018 ◽  
Vol 22 ◽  
pp. 01062
Author(s):  
Tukur Abdulkadir Sulaiman ◽  
Hasan Bulut ◽  
Haci Mehmet Baskonus
Keyword(s):  
Gordon Equation ◽  
Quantum Hall ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Travelling Wave ◽  
Wave Transformation ◽  
Edge States ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
2D And 3D

In this paper, we present the simplified version of the extended sinh-Gordon equation expansion method. The newly proposed approach is based on the well-known sinh-Gordon equation and a travelling wave transformation. We successfully employed this approach to the (2+1)-dimensional nonlinear Chiral Schrodinger's and various solitary wave solutions to the studied nonlinear model are successfully constructed. The (2+1)-dimensional nonlinear Chiral Schrodinger's equation describes the edge states of the fractional quantum hall effect. The 2D and 3D surfaces of some of the obtained solutions are plotted.

Topological Aspects of Quantum Hall Fluid and Berry Phase

1998 ◽  
Vol 12 (26) ◽  
pp. 2649-2707 ◽  
Author(s):  
Banasri Basu ◽  
P. Bandyopadhyay
Keyword(s):  
Quantum Hall Effect ◽  
Berry Phase ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Chiral Anomaly ◽  
Edge States ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Quantum Hall Systems ◽  
Characteristic Features

We have analyzed here the recent development towards our understanding of the Integral and Fractional Quantum Hall effect. It has been pointed out that the chiral anomaly and Berry phase approach embraces in a unified way the whole spectrum of quantum Hall systems with their various characteristic features. This formalism also helps us to understand the edge states observed in Hall fluids. It is argued that Hall fluids with even denominator filling factor leads to the non-Abelian Berry phase.

scholarly journals Quantum dot dephasing by fractional quantum Hall edge states

2006 ◽  
Vol 74 (15) ◽  
Author(s):  
T. K. T. Nguyen ◽  
A. Crépieux ◽  
T. Jonckheere ◽  
A. V. Nguyen ◽  
Y. Levinson ◽  
...  
Keyword(s):  
Quantum Dot ◽  
Quantum Hall ◽  
Edge States ◽  
Fractional Quantum ◽  
Fractional Quantum Hall

scholarly journals MULTIPLE EDGE PARTITION FUNCTIONS FOR FRACTIONAL QUANTUM HALL STATES

1999 ◽  
Vol 14 (23) ◽  
pp. 3745-3759
Author(s):  
KAZUSUMI INO
Keyword(s):  
Quantum Hall ◽  
Multiple Edge ◽  
Partition Functions ◽  
Edge States ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Conformal Field ◽  
Verlinde Formula ◽  
Quantum Hall States ◽  
Edge Partition

We consider the multiple edge states of the Laughlin state and the Pfaffian state. These edge states are globally constrained through the operator algebra of conformal field theory in the bulk. We analyze these constraints by introducing an expression of quantum Hall state by chiral vertex operators and obtain the multiple edge partition functions by using the Verlinde formula.

scholarly journals Helical edge states and fractional quantum Hall effect in a graphene electron–hole bilayer

2016 ◽  
Vol 12 (2) ◽  
pp. 118-122 ◽  
Author(s):  
Javier D. Sanchez-Yamagishi ◽  
Jason Y. Luo ◽  
Andrea F. Young ◽  
Benjamin M. Hunt ◽  
Kenji Watanabe ◽  
...  
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Edge States ◽  
Electron Hole ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Graphene Electron
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