scholarly journals Study Zitterbewegung effect in a quasi one-dimensional relativistic quantum plasma by Dirac-Heisenberg-Wigner formalization

2021 ◽  
Vol 2021 (09) ◽  
pp. 002
Author(s):  
Safura Nematizadeh Juneghani ◽  
Mehran Bagheri ◽  
Babak Shokri
Keyword(s):  
Relativistic Quantum ◽  
Quantum Plasma ◽  
One Dimensional

Modulation instability and soliton formation in the interaction of X-ray laser beam with relativistic quantum plasma

2019 ◽  
Vol 26 (6) ◽  
pp. 062112 ◽  
Author(s):  
R. Roozehdar Mogaddam ◽  
N. Sepehri Javan ◽  
K. Javidan ◽  
H. Mohammadzadeh
Keyword(s):  
Laser Beam ◽  
Modulation Instability ◽  
Relativistic Quantum ◽  
Quantum Plasma ◽  
X Ray

SCHRÖDINGER EQUATION FOR QUANTUM FRACTAL SPACE–TIME OF ORDER n VIA THE COMPLEX-VALUED FRACTIONAL BROWNIAN MOTION

2001 ◽  
Vol 16 (31) ◽  
pp. 5061-5084 ◽  
Author(s):  
GUY JUMARIE
Keyword(s):  
Brownian Motion ◽  
Schrödinger Equation ◽  
Fractional Order ◽  
Schrodinger Equation ◽  
Relativistic Quantum ◽  
Relativistic Quantum Mechanics ◽  
Dimensional System ◽  
One Dimensional ◽  
Klein Gordon ◽  
Complex Valued

First remark: Feynman's discovery in accordance of which quantum trajectories are of fractal nature (continuous everywhere but nowhere differentiable) suggests describing the dynamics of such systems by explicitly introducing the Brownian motion of fractional order in their equations. The second remark is that, apparently, it is only in the complex plane that the Brownian motion of fractional order with independent increments can be generated, by using random walks defined with the complex roots of the unity; in such a manner that, as a result, the use of complex variables would be compulsory to describe quantum systems. Here one proposes a very simple set of axioms in order to expand the consequences of these remarks. Loosely speaking, a one-dimensional system with real-valued coordinate is in fact the average observation of a one-dimensional system with complex-valued coordinate: It is a strip modeling. Assuming that the system is governed by a stochastic differential equation driven by a complex valued fractional Brownian of order n, one can then obtain the explicit expression of the corresponding covariant stochastic derivative with respect to time, whereby we switch to the extension of Lagrangian mechanics. One can then derive a Schrödinger equation of order n in quite a direct way. The extension to relativistic quantum mechanics is outlined, and a generalized Klein–Gordon equation of order n is obtained. As a by-product, one so obtains a new proof of the Schrödinger equation.

On the similarity of particle and photon tunneling and multiple internal reflections in one-dimensional, two-dimensional and three-dimensional photon tunneling

2014 ◽  
Vol 23 (06) ◽  
pp. 1460006 ◽  
Author(s):  
V. S. Olkhovsky
Keyword(s):  
Quantum Electrodynamics ◽  
Electromagnetic Waves ◽  
Relativistic Quantum ◽  
Three Dimensional ◽  
Time Dependent ◽  
Two Dimensional ◽  
Relativistic Quantum Field Theory ◽  
One Dimensional ◽  
Quantum Equation ◽  
Photon Tunneling

The formal mathematical analogy between time-dependent quantum equation for the nonrelativistic particles and time-dependent equation for the propagation of electromagnetic waves had been studied in [A. I. Akhiezer and V. B. Berestezki, Quantum Electrodynamics (FM, Moscow, 1959) [in Russian] and S. Schweber, An Introduction to Relativistic Quantum Field Theory, Chap. 5.3 (Row, Peterson & Co, Ill, 1961)]. Here, we deal with the time-dependent Schrödinger equation for nonrelativistic particles and with time-dependent Helmholtz equation for electromagnetic waves. Then, using this similarity, the tunneling and multiple internal reflections in one-dimensional (1D), two-dimensional (2D) and three-dimensional (3D) particle and photon tunneling are studied. Finally, some conclusions and future perspectives for further investigations are presented.

scholarly journals Relativistic quantum plasma dispersion functions

2006 ◽  
Vol 39 (27) ◽  
pp. 8727-8740 ◽  
Author(s):  
D B Melrose ◽  
J I Weise ◽  
J McOrist
Keyword(s):  
Relativistic Quantum ◽  
Quantum Plasma ◽  
Plasma Dispersion
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