scholarly journals Dirac Equation-Based Formulation for the Quantum Conductivity in 2D-Nanomaterials

2021 ◽  
Vol 11 (5) ◽  
pp. 2398
Author(s):  
Luca Pierantoni ◽  
Nicola Pelagalli ◽  
Davide Mencarelli ◽  
Andrea Di Donato ◽  
Matteo Orlandini ◽  
...  
Keyword(s):  
Dirac Equation ◽  
Applied Field ◽  
Quantum Mechanical ◽  
Sample Length ◽  
Finite Mass ◽  
Linear Dispersion ◽  
Polarization Effects ◽  
Basic Model ◽  
Scalar Quantum ◽  
2D Nanomaterials

Starting from the four component-Dirac equation for free, ballistic electrons with finite mass, driven by a constant d.c. field, we derive a basic model of scalar quantum conductivity, capable of yielding simple analytic forms, also in the presence of magnetic and polarization effects. The classical Drude conductivity is recovered as a limit case. A quantum-mechanical evaluation is provided for parabolic and linear dispersion, as in graphene, recovering currently used expressions as particular cases. Numerical values are compared with the ones from the literature in the case of graphene under d.c. applied field. In particular, the effect of the sample length and field strength on the conductivity are highlighted.

On the electrical conductivity of semiclassical two-component plasmas

2002 ◽  
Vol 68 (2) ◽  
pp. 81-86 ◽  
Author(s):  
YU. V. ARKHIPOV ◽  
F. B. BAIMBETOV ◽  
A. E. DAVLETOV ◽  
K. V. STARIKOV
Keyword(s):  
Electrical Conductivity ◽  
Hydrogen Plasma ◽  
Memory Function ◽  
Analytical Formula ◽  
Approximate Expression ◽  
Quantum Mechanical ◽  
Kubo Formula ◽  
Polarization Effects ◽  
Physical Evidence ◽  
Coulomb Logarithm

Starting from a memory-function formalism coupled with the Green– Kubo formula and an approximate expression for the generalized Coulomb logarithm, the electric conductivity of a dense high-temperature hydrogen plasma is studied. A pseudopotential model, taking account of short-range quantum effects and long-range screening-field effects, is employed to include quantum mechanical and polarization effects. An analytical formula for the Coulomb logarithm is proposed when the thermal de Broglie wavelengths are rather smaller than the Debye radius. A minimum in the curve of electrical conductivity is found and some physical evidence for its appearance is produced.

Electric field perturbed electron tunnelling in nonpolar organic glasses

1977 ◽  
Vol 55 (11) ◽  
pp. 2065-2079 ◽  
Author(s):  
A. J. Doheny ◽  
A. C. Albrecht
Keyword(s):  
Angular Distribution ◽  
Time Scale ◽  
Applied Field ◽  
Kinetic Equations ◽  
Quantum Mechanical ◽  
Recombination Rates ◽  
Qualitative And Quantitative ◽  
Organic Glasses ◽  
Trap Ionization ◽  
Nonpolar Organic

Isothermoluminescence (ITL) and electrophotoluminescence (EPL) resulting from electron–cation recombination are measured in a 2-methylpentane–methylcyclohexane glass. The ITL is more characteristic of quantum-mechanical tunnelling and the EPL signal is markedly stronger in this new glass than previous measurements in 3-methylpentane. Quantum-mechanical tunnelling theory is used to predict recombination rates of electrons in the potential field of a cation plus an applied field. Numerical integration of the nonhomogeneous kinetic equations resulting from a distribution of cation–electron separations leads to qualitative and quantitative predictions of the EPL signal that are observed experimentally. Fitting of the theory to experiment supports the conclusions that the angular distribution of the photoelectrons about the cations is close to isotropic, that the electrons active in ITL and EPL on the time scale of minutes are separated about 50 Å from their parent cation, and that the trap ionization potential in this nonpolar hydrocarbon glass is in the range of 0.5 to 0.7 eV.

Explanation of the Quantum-Mechanical Particle-Wave Duality through the Emission of Watt-Less Gravitational Waves by the Dirac Equation

2016 ◽  
Vol 71 (1) ◽  
pp. 53-57 ◽  
Author(s):  
Friedwardt Winterberg
Keyword(s):  
Gravitational Field ◽  
Dirac Equation ◽  
Gravitational Wave ◽  
Gravitational Waves ◽  
Negative Energy ◽  
Quantum Mechanical ◽  
Field Equations ◽  
Negative Mass ◽  
Pilot Wave ◽  
Extended Theories Of Gravity

AbstractAn explanation of the quantum-mechanical particle-wave duality is given by the watt-less emission of gravitational waves from a particle described by the Dirac equation. This explanation is possible through the existence of negative energy, and hence negative mass solutions of Einstein’s gravitational field equations. They permit to understand the Dirac equation as the equation for a gravitationally bound positive–negative mass (pole–dipole particle) two-body configuration, with the mass of the Dirac particle equal to the positive mass of the gravitational field binding the positive with the negative mass particle, and with the mass particles making a luminal “Zitterbewegung” (quivering motion), emitting a watt-less oscillating positive–negative space curvature wave. It is shown that this thusly produced “Zitterbewegung” reproduces the quantum potential of the Madelung-transformed Schrödinger equation. The watt-less gravitational wave emitted by the quivering particles is conjectured to be de Broglie’s pilot wave. The hypothesised connection of the Dirac equation to gravitational wave physics could, with the failure to detect gravitational waves by the LIGO antennas and pulsar timing arrays, give a clue to extended theories of gravity, or a correction of astrophysical models for the generation of such waves.

THE SOLUTION OF DIRAC EQUATION IN QUASI-EXTREME REISSNER–NORDSTRÖM DE SITTER SPACE

2009 ◽  
Vol 24 (30) ◽  
pp. 2433-2443 ◽  
Author(s):  
YAN LYU ◽  
SONG CUI ◽  
LING LIU
Keyword(s):  
Dirac Equation ◽  
Inverse Function ◽  
Quantum Mechanical ◽  
De Sitter ◽  
Mechanical Method ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
First Case ◽  
Quantum Mechanical Method ◽  
Tortoise Coordinate

The radial parts of Dirac equation between the outer black hole horizon and the cosmological horizon in quasi-extreme Reissner–Nordström de Sitter (RNdS) geometry is solved numerically. We use an accurate polynomial approximation to mimic the modified tortoise coordinate [Formula: see text], for obtaining the inverse function [Formula: see text] and [Formula: see text]. We then use a quantum mechanical method to solve the wave equation and give the reflection and transmission coefficients. We concentrate on two limiting cases. The first case is when the two horizons are close to each other, and the second case is when the horizons are far apart.

Sign in / Sign up

Export Citation Format

Share Document