Constants of Motion and Quantum Non-Relativistic Motion of a Charged Particle on a Flat Surface under Constant Magnetic Field | Chapter 5 | Current Research Progress in Physical Science Vol. 7

The motion of a charged particle moving on a flat surface is studied through the constants of motion associated with the system, given the magnetic gauge. The usual Landau’ solution and the non-separable solution for the Landau’s gauge are found, and a new non-separable solution for the symmetric gauge is given. As a consequence of this, the quantization of the magnetic flux results from the invariance of the solutions under the unitary transformations which arise from the operator’s constants of motion.

 

Author (s) Details

 

Gustavo V. Lopez
Department of Physics, University of Guadalajara, Mexico.

 

Jorge A. Lizarraga
Department of Physics, University of Guadalajara, Mexico.

 

Please see the book here:- https://doi.org/10.9734/bpi/crpps/v7/3694

Quantum Hall Effect for a Single Charged Particle in a Flat Surface under an Static Electromagnetic Field | Chapter 2 | New Frontiers in Physical Science Research Vol. 8

 While seeing the non separable answer for the quantum question of the motion of a charged atom in a flat surface of lengths Lx and Ly with transversal motionless magnetic field B and long-term static energetic field E, the quantum current, the transverse (Hall) and lengthwise resistivities are estimated for united states of america n = 0 and j = 0.We noticed that the transverse resistivity is equivalent to an integer number, due to the quantization of the attractive flux, and lengthwise resistivity can be nothing for times t ≫ LxB/cE. Additionally, a reduced quantization of the magnetic flow is discovered handling a modified rhythm of the eigenfunction, allowing for IQHE and FQHE of any contents factor of the form v = k/l, accompanying k, l ∈ z.

Author(s) Details:

Gustavo V. López,
Departamento de Física, Universidad de Guadalajara, Blvd. Marcelino García Barragan y Calzada Olímpica, CP 44200, Guadalajara, Jalisco, México.

Jorge A. Lizarraga,
Departamento de Física, Universidad de Guadalajara, Blvd. Marcelino García Barragan y Calzada Olímpica, CP 44200, Guadalajara, Jalisco, México.

Please see the link here: https://stm.bookpi.org/NFPSR-V8/article/view/9684

Trajectories and Curvatures of Hermitian and Non-Hermitian Random Matrix Eigenvalues| Chapter 2 | New Frontiers in Physical Science Research Vol. 1

 Study is done on the characteristics of the evolution of the eigenvalues of Hermitian and non-Hermitian matrices as a function of a parameter that simulates time. The so-called Olshanetsky-Perelomov Projection Method, which is based on the Lax equation, is applied in the Hermitian case. As a result, the Dyson index, which in the Gaussian ensemble has values of 1, 2, and 3, can take on any real value in the loggas Hamiltonian. As a result, one has a 1D loggas dynamics for the ensemble's tridiagonal matrices' eigenvalues. On the other hand, in the non-Hermitian scenario, a model is built to investigate the statistical characteristics of erroneous log-gas trajectories whose positions correspond to the complex eigenvalues of the unitary Ginibre ensembre.  It is shown that statistical analysis of the trajectories creates a shell structure that makes the eigenvalue departure sites visible. The eigenvalue curvatures are also demonstrated to be the universal distribution for 1D trajectories and a Cauchy distribution for trajectories in the complex plane as a function of the parameter.

Author(s) Details:

M. P. Pato,
Inst´ıtuto de F´ısica, Universidade de S˜ao Paulo CEP 05508-090 S˜ao Paulo, S.P., Brazil.

Please see the link here: https://stm.bookpi.org/NFPSR-V1/article/view/8118