scholarly journals Correction: Camiola, V.D., et al. Equilibrium Wigner Function for Fermions and Bosons in the Case of a General Energy Dispersion Relation. Entropy 2020, 22, 1023

Entropy ◽  
2021 ◽  
Vol 23 (4) ◽  
pp. 417
Author(s):  
Vito Dario Camiola ◽  
Liliana Luca ◽  
Vittorio Romano
Keyword(s):  
Dispersion Relation ◽  
Wigner Function ◽  
Energy Dispersion ◽  
General Energy

In Section 5 of Equilibrium Wigner Function for Fermions and Bosons in the Case of a General Energy Dispersion Relation [...]

scholarly journals Equilibrium Wigner Function for Fermions and Bosons in the Case of a General Energy Dispersion Relation

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 1023
Author(s):  
Vito Dario Camiola ◽  
Liliana Luca ◽  
Vittorio Romano
Keyword(s):  
Wigner Function ◽  
Natural Generalization ◽  
Bloch Equation ◽  
Equilibrium Density ◽  
Diagonal Form ◽  
Energy Dispersion ◽  
Unitary Evolution ◽  
Von Neumann ◽  
General Energy

The approach based on the Wigner function is considered as a viable model of quantum transport which allows, in analogy with the semiclassical Boltzmann equation, to restore a description in the phase-space. A crucial point is the determination of the Wigner function at the equilibrium which stems from the equilibrium density function. The latter is obtained by a constrained maximization of the entropy whose formulation in a quantum context is a controversial issue. The standard expression due to Von Neumann, although it looks a natural generalization of the classical Boltzmann one, presents two important drawbacks: it is conserved under unitary evolution time operators, and therefore cannot take into account irreversibility; it does not include neither the Bose nor the Fermi statistics. Recently a diagonal form of the quantum entropy, which incorporates also the correct statistics, has been proposed in Snoke et al. (2012) and Polkovnikov (2011). Here, by adopting such a form of entropy, with an approach based on the Bloch equation, the general condition that must be satisfied by the equilibrium Wigner function is obtained for general energy dispersion relations, both for fermions and bosons. Exact solutions are found in particular cases. They represent a modulation of the solution in the non degenerate situation.

scholarly journals Dispersive Correction to the p+16 0 Optical Montel Potential

2019 ◽  
Vol 3 ◽  
pp. 186
Author(s):  
G. Pantis
Keyword(s):  
Dispersion Relation ◽  
Optical Model ◽  
Model Potential ◽  
Polarization Potential ◽  
Energy Dispersion ◽  
The Real ◽  
Optical Model Potential ◽  
P 16

The optical model potential to p+16 0 scattering is derived by taking into account the polarization potential induced by the energy dispersion relation. The real part of the potential is derived by the RGM-method with the Volkov or Minnesota potential as a basis for the n-n force. It is shown that the polarization potential effects an adjustment of the parameters of the n-n force due to the constraints imposed by the energy dispersion relation.

scholarly journals A hydrodynamical model for covalent semiconductors with a generalized energy dispersion relation

2014 ◽  
Vol 25 (2) ◽  
pp. 255-276 ◽  
Author(s):  
GIUSEPPE ALÌ ◽  
GIOVANNI MASCALI ◽  
VITTORIO ROMANO ◽  
ROSA CLAUDIA TORCASIO
Keyword(s):  
Dispersion Relation ◽  
Charge Transport ◽  
Optical Phonon ◽  
Impurity Scattering ◽  
Compound Semiconductors ◽  
Polar Optical Phonon ◽  
Energy Dispersion ◽  
Conduction Bands ◽  
Ionized Impurity Scattering ◽  
Ellipsoidal Approximations

We present the first macroscopical model for charge transport in compound semiconductors to make use of analytic ellipsoidal approximations for the energy dispersion relationships in the neighbours of the lowest minima of the conduction bands. The model considers the main scattering mechanisms charges undergo in polar semiconductors, that is the acoustic, polar optical, intervalley non-polar optical phonon interactions and the ionized impurity scattering. Simulations are shown for the cases of bulk 4H and 6H-SiC.

Reciprocal Polarizable Embedding with a Transferable H2O Potential Function I: Formulation & Tests on Dimer

2019 ◽  
Author(s):  
Elvar Jónsson ◽  
Asmus Ougaard Dohn ◽  
Hannes Jonsson
Keyword(s):  
Potential Function ◽  
Dft Method ◽  
Multipole Expansion ◽  
Energy Functional ◽  
Real Space ◽  
Functional Formulation ◽  
General Energy ◽  
Projector Augmented Wave ◽  
Grid Based ◽  
Polarizable Embedding

This work describes a general energy functional formulation of a polarizable embedding QM/MM scheme, as well as an implementation where a real-space Grid-based Projector Augmented Wave (GPAW) DFT method is coupled with a potential function for H<sub>2</sub>O based on a Single Center Multipole Expansion (SCME) of the electrostatics, including anisotropic dipole and quadrupole polarizability.

Sign in / Sign up

Export Citation Format

Share Document