On self-consistent thermal equilibrium structures in two–dimensional negative-temperature systems

1994 ◽  
Vol 72 (9-10) ◽  
pp. 618-624 ◽  
Author(s):  
Nikolay K. Martinov ◽  
Nikolay K. Vitanov
Keyword(s):  
Thermal Equilibrium ◽  
Negative Temperature ◽  
Coulomb Gas ◽  
Elementary Cell ◽  
Positive Temperature ◽  
Two Dimensional ◽  
Thermal Equilibrium State ◽  
Self Consistent ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation

Two-dimensional negative-temperature systems described by means of analytical solutions of the Poisson–Boltzmann equation are investigated. It is shown that two kinds of doubly periodic self-consistent structures can exist. The structures obtained confirm the prediction of equilibrium statistical mechanics that no spatially homogeneous thermal equilibrium state for negative-temperature systems exists. The structures investigated are similar to the two kinds of structures in a two-dimensional, two-component positive-temperature Coulomb gas but the location of the elements of the system within the region of the elementary cell of the structure is different. By means of the approach developed in this paper the parameters of the structures, the self-consistent potential, the corresponding charge density, and the energy of the negative-temperature structures can be calculated.

scholarly journals Negative temperature states for the two-dimensional guiding-centre plasma

1973 ◽  
Vol 10 (1) ◽  
pp. 107-121 ◽  
Author(s):  
Glenn Joyce ◽  
David Montgomery
Keyword(s):  
Numerical Simulation ◽  
Thermal Equilibrium ◽  
Negative Temperature ◽  
Theoretical Development ◽  
Two Dimensional ◽  
Thermal Equilibrium State ◽  
Spatially Inhomogeneous ◽  
Negative Temperatures ◽  
Total Interaction ◽  
Spatially Homogeneous

Theoretical development and numerical simulation of the two-dimensional electrostatic guiding-centre plasma with positive total interaction energy are presented. Equilibrium statistical mechanics predicts that no spatially homogeneous thermal equilibrium state exists for this system. This non-existence is associated with the phenomenon of ‘negative temperatures’. Quasi-stable, spatially inhomogeneous states are shown to form, and are characterized by macroscopic spatially-separated vortex structures.

Thermal Equilibrium Concentrations and Effects of Ga Vacancies in n-TYPE GaAs

1993 ◽  
Vol 300 ◽  
Author(s):  
Teh Y. Tan ◽  
Homg-Ming You ◽  
Ulrich M. Gösele
Keyword(s):  
Temperature Dependence ◽  
Point Defect ◽  
Thermal Equilibrium ◽  
Quantitative Data ◽  
Equilibrium Concentration ◽  
Negative Temperature ◽  
Positive Temperature ◽  
Self Diffusion ◽  
N Doping ◽  
Equilibrium Concentrations

ABSTRACTWe have calculated the thermal equilibrium concentrations of the various Ga vacancy species in GaAs. That of the triply-negatively-charged Ga vacancy, V3Ga has been emphasized, since it dominates Ga self-diffusion and Ga-Al interdiffusion under intrinsic and ndoping conditions, as well as the diffusion of Si donor atoms occupying Ga sites. Under strong n-doping conditions, the thermal equilibrium V3Ga concentration, CeqvGa.3−(n), has been found to exhibit a temperature independence or a negative temperature dependence, in the sense that the CeqvGa.3−(n) value is either unchanged or increases as the temperature is lowered. This is contrary to the normal positive temperature dependence of point defect theerqmal equilibrium concentrations, which decreases as the temperature is lowered. This CeqvGa.3−(n) property provides explanations to a number of outstanding experimental results, either requiring the interpretation thatV3−Ga has attained its thermal equilibrium concentration at the onset of each experiment, or requiring mechanisms involving point defect non-equilibrium phenomena. Furthermore, there exist also a few quantitative data which are in agreement with the presently calculated results.

An Iterative Discontinuous Galerkin Method for Solving the Nonlinear Poisson Boltzmann Equation

2014 ◽  
Vol 16 (2) ◽  
pp. 491-515 ◽  
Author(s):  
Peimeng Yin ◽  
Yunqing Huang ◽  
Hailiang Liu
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Solution Space ◽  
Initial Guess ◽  
Two Dimensional ◽  
Order Of Accuracy ◽  
Dg Method ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation

AbstractAn iterative discontinuous Galerkin (DG) method is proposed to solve the nonlinear Poisson Boltzmann (PB) equation. We first identify a function space in which the solution of the nonlinear PB equation is iteratively approximated through a series of linear PB equations, while an appropriate initial guess and a suitable iterative parameter are selected so that the solutions of linear PB equations are monotone within the identified solution space. For the spatial discretization we apply the direct discontinuous Galerkin method to those linear PB equations. More precisely, we use one initial guess when the Debye parameterλ=(1), and a special initial guess forλ≫1 to ensure convergence. The iterative parameter is carefully chosen to guarantee the existence, uniqueness, and convergence of the iteration. In particular, iteration steps can be reduced for a variable iterative parameter. Both one and two-dimensional numerical results are carried out to demonstrate both accuracy and capacity of the iterative DG method for both cases ofλ=(1) andλ≪ 1. The (m+ 1)th order of accuracy forL2andmth order of accuracy forH1forPmelements are numerically obtained.

Sign in / Sign up

Export Citation Format

Share Document