HALL CONDUCTIVITY AS THE TOPOLOGICAL INVARIANT IN PHASE SPACE IN THE PRESENCE OF INTERACTIONS AND NON-UNIFORM MAGNETIC FIELD

2019 ◽  
Vol 110 (7-8 (10)) ◽  
pp. 480-481 ◽  
Author(s):  
C.X. ZHANG ◽  
M.A. ZUBKOV
Keyword(s):  
Magnetic Field ◽  
Phase Space ◽  
Uniform Magnetic Field ◽  
Topological Invariant ◽  
Hall Conductivity

scholarly journals Coherent State Quantization and Moment Problem

10.14311/1185 ◽  
2010 ◽  
Vol 50 (3) ◽  
Author(s):  
J. P. Gazeau ◽  
M. C. Baldiotti ◽  
D. M. Gitman
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Energy Spectrum ◽  
Phase Space ◽  
Coherent State ◽  
Moment Problem ◽  
Coherent States ◽  
Uniform Magnetic Field ◽  
Classical Motion ◽  
Negative Numbers

Berezin-Klauder-Toeplitz (“anti-Wick”) or “coherent state” quantization of the complex plane, viewed as the phase space of a particle moving on the line, is derived from the resolution of the unity provided by the standard (or gaussian) coherent states. The construction of these states and their attractive properties are essentially based on the energy spectrum of the harmonic oscillator, that is on natural numbers. We follow in this work the same path by considering sequences of non-negative numbers and their associated “non-linear” coherent states. We illustrate our approach with the 2-d motion of a charged particle in a uniform magnetic field. By solving the involved Stieltjes moment problem we construct a family of coherent states for this model. We then proceed with the corresponding coherent state quantization and we show that this procedure takes into account the circle topology of the classical motion.

scholarly journals Hall conductivity as topological invariant in phase space

2020 ◽  
Vol 95 (6) ◽  
pp. 064003
Author(s):  
I V Fialkovsky ◽  
M Suleymanov ◽  
Xi Wu ◽  
C X Zhang ◽  
M A Zubkov
Keyword(s):  
Phase Space ◽  
Topological Invariant ◽  
Hall Conductivity

scholarly journals Hall conductivity of strained ℤ 2 crystals

2021 ◽  
pp. 2044034
Author(s):  
I. V. Fialkovsky ◽  
M. A. Zubkov
Keyword(s):  
Magnetic Field ◽  
Mechanical Stress ◽  
Topological Invariant ◽  
Hall Conductivity ◽  
Spatially Varying ◽  
2D And 3D

We establish topological nature of Hall conductivity of graphene and other [Formula: see text] crystals in 2D and 3D in the presence of inhomogeneous perturbations. To this end the lattice Weyl–Wigner formalism is employed. The nonuniform mechanical stress is considered, along with the spatially varying magnetic field. The relation of the obtained topological invariant to level counting is clarified.

scholarly journals WIGNER FUNCTIONS FOR THE LANDAU PROBLEM IN NONCOMMUTATIVE SPACES

2002 ◽  
Vol 17 (29) ◽  
pp. 1937-1944 ◽  
Author(s):  
ÖMER F. DAYI ◽  
LARA T. KELLEYANE
Keyword(s):  
Magnetic Field ◽  
Phase Space ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Uniform Magnetic Field ◽  
Effective Hamiltonian ◽  
Wigner Functions ◽  
Noncommutative Spaces

An electron moving on plane in a uniform magnetic field orthogonal to the plane is known as the Landau problem. Wigner functions for the Landau problem when the plane is noncommutative are found employing solutions of the Schrödinger equation as well as solving the ordinary ⋆-genvalue equation in terms of an effective Hamiltonian. Then, we let momenta and coordinates of the phase space be noncommutative and introduce a generalized ⋆-genvalue equation. We solve this equation to find the related Wigner functions and show that under an appropriate choice of noncommutativity relations they are independent of noncommutativity parameter.

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