DISORDERED GROUND STATES OF CLASSICAL LATTICE MODELS

1991 ◽  
Vol 03 (02) ◽  
pp. 125-135 ◽  
Author(s):  
CHARLES RADIN
Keyword(s):  
Dynamical Systems ◽  
Statistical Mechanics ◽  
Continuous Spectrum ◽  
Ground State ◽  
Short Range ◽  
Ground States ◽  
Lattice Models ◽  
Positive Entropy ◽  
Classical Lattice ◽  
Classical Statistical Mechanics

We use strictly ergodic dynamical systems to describe two methods for constructing short range interactions of classical statistical mechanics models with unique ground states and unusual properties of disorder; in particular, these ground states can be mixing under translations (and therefore have purely continuous spectrum), and can have positive entropy. Because of the uniqueness of the ground state the disorder is not of the usual type associated with local degeneracy.

scholarly journals Dynamical Temperature from the Phase Space Trajectory

2017 ◽  
Vol 45 (1) ◽  
pp. 1-3 ◽  
Author(s):  
András Baranyai
Keyword(s):  
System Theory ◽  
Phase Space ◽  
Dynamical Systems ◽  
Hamiltonian System ◽  
Statistical Mechanics ◽  
Chaotic System ◽  
Space Trajectories ◽  
Classical Statistical Mechanics ◽  
Phase Space Trajectory ◽  
Phase Space Trajectories

Abstract In classical statistical mechanics the trajectory in phase space represents the propagation of a classical Hamiltonian system. While trajectories play a key role in chaotic system theory, exploitation of a single trajectory has yet to be considered. This work shows that for ergodic dynamical systems the dynamical temperature can be derived using phase space trajectories.

scholarly journals LATTICE THREE-SPECIES MODELS OF THE SPATIAL SPREAD OF RABIES AMONG FOXES

1999 ◽  
Vol 10 (06) ◽  
pp. 1025-1038 ◽  
Author(s):  
A. BENYOUSSEF ◽  
N. BOCCARA ◽  
H. CHAKIB ◽  
H. EZ-ZAHRAOUY
Keyword(s):  
Carrying Capacity ◽  
Short Range ◽  
Lattice Models ◽  
Infection Process ◽  
Spatial Spread ◽  
One Dimensional ◽  
Sense Of Direction ◽  
Speed Of Propagation ◽  
Automata Network ◽  
And Diffusion

Lattice models describing the spatial spread of rabies among foxes are studied. In these models, the fox population is divided into three-species: susceptible (S), infected or incubating (I), and infectious or rabid (R). They are based on the fact that susceptible and incubating foxes are territorial while rabid foxes have lost their sense of direction and move erratically. Two different models are investigated: a one-dimensional coupled-map lattice model, and a two-dimensional automata network model. Both models take into account the short-range character of the infection process and the diffusive motion of rabid foxes. Numerical simulations show how the spatial distribution of rabies, and the speed of propagation of the epizootic front depend upon the carrying capacity of the environment and diffusion of rabid foxes out of their territory.

scholarly journals Glassy behaviour in short-range lattice models without quenched disorder

2002 ◽  
Vol 82 (5) ◽  
pp. 617-623 ◽  
Author(s):  
Mário J. de Oliveira ◽  
Alberto Petri
Keyword(s):  
Short Range ◽  
Lattice Models ◽  
Quenched Disorder

scholarly journals Introduction to Focus Issue: Statistical mechanics and billiard-type dynamical systems

2012 ◽  
Vol 22 (2) ◽  
pp. 026101 ◽  
Author(s):  
Edson D. Leonel ◽  
Marcus W. Beims ◽  
Leonid A. Bunimovich
Keyword(s):  
Dynamical Systems ◽  
Statistical Mechanics

scholarly journals LOCALIZATION OF THE NUMBER OF PHOTONS OF GROUND STATES IN NONRELATIVISTIC QED

2003 ◽  
Vol 15 (03) ◽  
pp. 271-312 ◽  
Author(s):  
FUMIO HIROSHIMA
Keyword(s):  
Radiation Field ◽  
Ground State ◽  
Fock Space ◽  
Adjoint Operator ◽  
Ground States ◽  
Electron System ◽  
Number Operator ◽  
Position Variable ◽  
Boson Fock Space ◽  
Quantized Radiation Field

One electron system minimally coupled to a quantized radiation field is considered. It is assumed that the quantized radiation field is massless, and no infrared cutoff is imposed. The Hamiltonian, H, of this system is defined as a self-adjoint operator acting on L2 (ℝ3) ⊗ ℱ ≅ L2 (ℝ3; ℱ), where ℱ is the Boson Fock space over L2 (ℝ3 × {1, 2}). It is shown that the ground state, ψg, of H belongs to [Formula: see text], where N denotes the number operator of ℱ. Moreover, it is shown that for almost every electron position variable x ∈ ℝ3 and for arbitrary k ≥ 0, ‖(1 ⊗ Nk/2) ψg (x)‖ℱ ≤ Dk e-δ|x|m+1 with some constants m ≥ 0, Dk > 0, and δ > 0 independent of k. In particular [Formula: see text] for 0 < β < δ/2 is obtained.

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