Exact Statistical Mechanics of a One‐Dimensional System with Coulomb Forces

1961 ◽  
Vol 2 (5) ◽  
pp. 682-693 ◽  
Author(s):  
A. Lenard
Keyword(s):  
Statistical Mechanics ◽  
Dimensional System ◽  
One Dimensional

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.

Stabilization of Dominant Structures in an Ionic Reaction-Diffusion System

1998 ◽  
Vol 63 (6) ◽  
pp. 761-769 ◽  
Author(s):  
Roland Krämer ◽  
Arno F. Münster
Keyword(s):  
Reaction Diffusion ◽  
Dominant Mode ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Local Perturbation ◽  
Dimensional System ◽  
One Dimensional ◽  
Brusselator Model ◽  
The One ◽  
Dominant Structure

We describe a method of stabilizing the dominant structure in a chaotic reaction-diffusion system, where the underlying nonlinear dynamics needs not to be known. The dominant mode is identified by the Karhunen-Loeve decomposition, also known as orthogonal decomposition. Using a ionic version of the Brusselator model in a spatially one-dimensional system, our control strategy is based on perturbations derived from the amplitude function of the dominant spatial mode. The perturbation is used in two different ways: A global perturbation is realized by forcing an electric current through the one-dimensional system, whereas the local perturbation is performed by modulating concentrations of the autocatalyst at the boundaries. Only the global method enhances the contribution of the dominant mode to the total fluctuation energy. On the other hand, the local method leads to simple bulk oscillation of the entire system.

scholarly journals Topological phase transition between a normal insulator and a topological metal state in a quasi-one-dimensional system

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Milad Jangjan ◽  
Mir Vahid Hosseini
Keyword(s):  
Phase Transition ◽  
Dimensional System ◽  
Inversion Symmetry ◽  
Topological Phase ◽  
Edge States ◽  
Zero Energy ◽  
One Dimensional ◽  
Topological Phase Transition ◽  
Metal State ◽  
Topological Metal

AbstractWe theoretically report the finding of a new kind of topological phase transition between a normal insulator and a topological metal state where the closing-reopening of bandgap is accompanied by passing the Fermi level through an additional band. The resulting nontrivial topological metal phase is characterized by stable zero-energy localized edge states that exist within the full gapless bulk states. Such states living on a quasi-one-dimensional system with three sublattices per unit cell are protected by hidden inversion symmetry. While other required symmetries such as chiral, particle-hole, or full inversion symmetry are absent in the system.

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