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Observation about the Classical Electromagnetic Gauge Transformation and Its Quantum Correspondence

Journal of Modern Physics（现代物理） 2020年第10期

作者： Gustavo V.López jorge a.lizarraga

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Journal of Modern Physics 2024年第4期15卷 474-479页

作者： Gustavo V. López jorge A. lizarraga Departamento de Física Universidad de Guadalajara Guadalajara Mexico

Using the Landau and symmetric gauges for the vector potential of a constant magnetic field and the quantum problem of a charged particle moving on a flat surface, we show the classical electromagnetic gauge transformation does not correspond to a one-dimensional unitary group transformation U(1) of the wave function for the quantum case. In addition, with the re-examination of the relation between the magnetic field B and its vector potential A, we found that, in order to have a consistent formulation of the dynamics of the charged particle with both expressions, we must have that B=∇×A if and only if B≠0.

关键词： Gauge Transformation Harmonic Oscillator Quantum Hall Effect Electromagnetic Potentials

C12- C13Diamond Quantum Computer with Longitudinal rf-Magnetic Field

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Journal of Modern Physics 2020年第8期11卷 1123-1131页

作者： Gustavo V. López jorge lizarraga Departamento de Física CUCEI Universidad de Guadalajara Blvd. Marcelino García Barragan y Calzada Olímpica Guadalajara Jalisco Mexico

In the diamond C12 (nuclear spin zero) structure with a linear chain of C13 (nuclear spin one half) atoms is applied to a transverse static field with respect of this linear chain, having a gradient along the linear chain, and it is also applied to an rf-magnetic field in a plane with a component in the direction of the static field. It is shown that one qubit rotation, the Controlled-Not (CNOT), the Controlled-Controlled-NoT (CCNOT) quantum gates, and teleportation algorithm can be implemented on this structure using integer multiples of electromagnetic π-pulses. Therefore, a quantum computer can be constructed in this form.

关键词： Quantum Computer Diamond Universal Quantum Gates

Dynamics of 1-D Electron Motion under a Periodic Electric Field with Radiation Reaction Effect

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Journal of Applied Mathematics and Physics 2020年第5期8卷 814-820页

作者： Gustavo V. López jorge lizarraga Departamento de Física Universidad de Guadalajara Blvd. Marcelino García Barragan y Calzada Olímpica Guadalajara Jalisco Mexico

We consider the 1-D motion of an electron under a periodic force and take into account the effect of radiation reaction dissipation force on its motion, using the formulation of novel radiation reaction force as a function of the external force expression. Two cases are considered: a simple sinusoidal time depending force, and sinusoidal electromagnetic force with position and time dependence. The purpose of the study of these cases is to bring about a way to find an experimental study to determine the validity of this novel approach for the radiation reaction force. We found that the difference of the normalized (with respect the speed of light) velocities, with and without radiation reaction, is quite small between 10-31 to 10-14 for intensities on the electric field of 10-8 to 1 Dynes/ues, which may represent some concern to measure experimentally.

关键词： Radiation Reaction Force 1-D Electron Motion Damping Motion

Charged Particle in a Flat Box with Static Electromagnetic Field and Landau’s Levels

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Journal of Modern Physics 2020年第10期11卷 1731-1742页

作者： Gustavo V. López jorge A. lizarraga Departamento de Física Universidad de Guadalajara Guadalajara México

We study the quantization of a charged particle motion without spin inside a flat box under a static electromagnetic field. Contrary to Landau’s solution with constant magnetic field transverse to the box and using Fourier transformation, we found a full solution for the wave function which is different from that one given by Landau, and this fact remains when static electric field is added. However, the Landau’s levels appear in all cases.

关键词： Landau’s Levels Quantum Hall Effect Flat Box

Single Charged Particle Motion in a Flat Surface with Static Electromagnetic Field and Quantum Hall Effect

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Journal of Modern Physics 2022年第11期13卷 1324-1330页

作者： Gustavo V. López jorge A. lizarraga Departamento de Física Universidad de Guadalajara Guadalajara México

Taking into account the non separable solution for the quantum problem of the motion of a charged particle in a flat surface of lengths Lx and Ly with transversal static magnetic field B and longitudinal static electric field E, the quantum current, the transverse (Hall) and longitudinal resistivities are calculated for the state n = 0 and j = 0. We found that the transverse resistivity is proportional to an integer number, due to the quantization of the magnetic flux, and longitudinal resistivity can be zero for times t >> LxB/cE. In addition, using a modified periodicity of the solution, a modified quantization of the magnetic flux is found which allows to have IQHE and FQHE of any filling factor of the form v = k/l, with k, l ∈Z.

关键词： Landau’s Gauge Quantum Hall Effect Degeneration

About Degeneration of Landau’s Levels

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Journal of Modern Physics 2022年第2期13卷 122-126页

作者： jorge A. lizarraga Gustavo V. López Departamento de Física Universidad de Guadalajara Blvd. Marcelino García Barragan y Calzada Olímpica CP 44200 Guadalajara Jalisco México

Through the non separable solution of the eigenvalue problem associated to the problem of a charged particle in a flat box and a constant transversal magnetic field, with Landau and symmetric gauges, it is found that the Landau’s levels are numerably degenerated in both cases. A mathematical proposition is proven to carry out this statement.

关键词： Landau’s Gauge Symmetric Gauge Quantum Hall Effect Degeneration

Quantum Charged Particle in a Flat Box under Static Electromagnetic Field with Landau’s Gauge and Special Case with Symmetric Gauge

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Journal of Modern Physics 2021年第10期12卷 1464-1474页

作者： Gustavo V. López jorge A. lizarraga Omar J. P. Bravo Departamento de Física Universidad de Guadalajara Guadalajara México

We summarize our results about the quantization of a charged particle motion without spin inside a flat box under a static electromagnetic field with Landau’s gauge for the magnetic field, where Fourier’s transformation was used to analyze the problem, to point out that there exists a wave function which is different to that one given by Landau with the same Landau’s levels. The quantization of the magnetic flux is deduced differently to previous one, and a new solution is presented for the case of symmetric gauge of the magnetic field, and having the same Landau’s levels.

关键词： Landau’s Gauge Symmetric Gauge Quantum Hall Effect Flat Box

C12 - C13 Diamond Quantum Computer with Longitudinal rf-Magnetic Field

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Single Charged Particle Motion in a Flat Surface with Static Electromagnetic Field and Quantum Hall Effect

Journal of Modern Physics（现代物理） 2020年第8期

作者： Gustavo V.López jorge lizarraga

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