Exact Statistical Mechanics of a One‐Dimensional System with Coulomb Forces. III. Statistics of the Electric Field

1963 ◽  
Vol 4 (4) ◽  
pp. 533-543 ◽  
Author(s):  
Andrew Lenard
Keyword(s):  
Statistical Mechanics ◽  
Electric Field ◽  
Dimensional System ◽  
One Dimensional

scholarly journals Doping two boron atoms in germanene nanoribbons in an external electric field

2021 ◽  
Vol 2070 (1) ◽  
pp. 012130
Author(s):  
Hoang Van Ngoc ◽  
Trieu Quynh Trang ◽  
Air Xayyadeth ◽  
Chu Viet Ha
Keyword(s):  
Electric Field ◽  
External Electric Field ◽  
Energy Band ◽  
Density Functional ◽  
Unit Cell ◽  
Dimensional System ◽  
Hydrogen Atoms ◽  
Functional Theory ◽  
One Dimensional ◽  
Formation Energies

Abstract Germanene is a two-dimensional system made of germanium atoms, its configuration is hexagonal honeycomb. Germanene nanoribbons (GNRs) are one-dimensional systems made from germanene with hydrogen-modified edges. The GNRs configuration studied here consists of 12 germanium atoms and 4 hydrogen atoms per unit cell. This work investigated the doping of two boron atoms into the unit cell of GNRs. Changing the different doping sites produces different configurations, the configurations been studied as meta-configuration, para-configuration, and ortho-configuration. By using density functional theory (DFT), the formation energies, energy band structures, and density of states of the configurations are studied. The ortho-configuration for the formation energy is the smallest, so this configuration is the most stable. The appearance of an external electric field changes the band gap and the energy band structure of the system.

scholarly journals Ergodic properties of a semi-infinite one-dimensional system of statistical mechanics

1985 ◽  
Vol 101 (3) ◽  
pp. 363-382 ◽  
Author(s):  
C. Boldrighini ◽  
A. Pellegrinotti ◽  
E. Presutti ◽  
Ya. G. Sinai ◽  
M. R. Soloveichik
Keyword(s):  
Statistical Mechanics ◽  
Dimensional System ◽  
One Dimensional ◽  
Ergodic Properties

Statistical mechanics of a one-dimensional Coulomb system with a uniform charge background

1963 ◽  
Vol 59 (4) ◽  
pp. 779-787 ◽  
Author(s):  
R. J. Baxter
Keyword(s):  
Statistical Mechanics ◽  
Positive Charge ◽  
Charged Particles ◽  
Real System ◽  
Coulomb System ◽  
Dimensional System ◽  
One Dimensional ◽  
Uniform Background ◽  
Statistical Mechanical ◽  
Exact Description

AbstractThis paper obtains an exact description of the statistical mechanics of a one-dimensional system of charged particles moving in a uniform neutralizing background of positive charge. These results are compared with the behaviour of a one-dimensional system of equal numbers of positive and negative charged particles. Although the thermodynamics of the two systems do differ, the discrepancy is small enough to indicate that the assumption of a uniform background of positive charge, common in statistical mechanical treatments of a plasma in equilibrium, may provide a good approximation to a real system of discrete charges.

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