scholarly journals Information Entropy Approach for a Disorderless One-Dimensional Lattice

2020 ◽  
Vol 2 (1) ◽  
pp. 107-113
Author(s):  
Luis Arturo Juárez-Villegas ◽  
Moisés Martínez-Mares
Keyword(s):  
Maximum Entropy ◽  
Information Entropy ◽  
Information Criterion ◽  
System Size ◽  
Reflection Symmetry ◽  
Fixed Size ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Fixed Energy ◽  
Alternative Approach

Dimensionless conductance through a disorderless lattice is studied using an alternative approach. Usually, the conductance of an ordered lattice is studied at a fixed size, either finite or infinite if the crystalline limit is reached. Here, we propose one to consider the set of systems of all sizes from zero to infinite. As a consequence, we find that the conductance presents fluctuations, with respect to system size, at a fixed energy. At the band edge, these fluctuations are described by a statistical distribution satisfied by an ensemble of chaotic cavities with reflection symmetry, which also satisfies a maximum-entropy, or minimum-information, criterion.

HEAT CONDUCTION IN ONE-DIMENSIONAL LATTICE WITH DOUBLE-WELL INTERACTION

2011 ◽  
Vol 25 (06) ◽  
pp. 823-832 ◽  
Author(s):  
HAIBIN LI
Keyword(s):  
Heat Conduction ◽  
Low Temperature ◽  
Interaction Potential ◽  
Temperature Region ◽  
System Size ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Period 2 ◽  
Large System Size ◽  
Anomalous Heat

Heat conduction in one-dimensional lattice with double-well interaction potential is studied numerically in different temperature regions. In the low temperature case, different structures such as order, period-2, and disorder structure phases, lead to different anomalous heat conduction. In a shallow intermediate temperature region, the heat conductivity is finite in a large system size. When temperature increases high enough, the heat conduction is anomalous, as well as FPU-β model.

scholarly journals INVARIANT KINEMATICS ON A ONE-DIMENSIONAL LATTICE IN NONCOMMUTATIVE GEOMETRY

1998 ◽  
Vol 13 (07) ◽  
pp. 1159-1168
Author(s):  
E. ATZMON
Keyword(s):  
Noncommutative Geometry ◽  
Test Particle ◽  
Quantum Particle ◽  
Point Particle ◽  
Translation Invariance ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Alternative Approach ◽  
Dependent Mass ◽  
Classical Point

In a one-dimensional lattice, the induced metric (from a noncommutative geometry calculation) breaks translation invariance. This leads to some inconsistencies among different spectator frames, in the observation of the hoppings of a test particle between lattice sites. To resolve the inconsistencies between the different spectator frames, we replace the test particle's bare mass by an effective locally dependent mass. This effective mass also depends on the lattice constant — i.e. it a scale dependent variable (a "running" mass). We also develop an alternative approach based on a compensating potential. The induced potential between a spectator frame and the test particle is attractive on the average. We then show that the entire formalism holds for a quantum particle represented by a wave function, just as it applies to the mechanics of a classical point particle.

scholarly journals DIFFERENTIAL EQUATION APPROACH FOR ONE- AND TWO-DIMENSIONAL LATTICE GREEN'S FUNCTION

2007 ◽  
Vol 21 (02n03) ◽  
pp. 139-154 ◽  
Author(s):  
J. H. ASAD
Keyword(s):  
Differential Equation ◽  
Green’S Function ◽  
Recurrence Relation ◽  
Green's Function ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
The One ◽  
Lattice Green's Function ◽  
Lattice Green’S Function

A first-order differential equation of Green's function, at the origin G(0), for the one-dimensional lattice is derived by simple recurrence relation. Green's function at site (m) is then calculated in terms of G(0). A simple recurrence relation connecting the lattice Green's function at the site (m, n) and the first derivative of the lattice Green's function at the site (m ± 1, n) is presented for the two-dimensional lattice, a differential equation of second order in G(0, 0) is obtained. By making use of the latter recurrence relation, lattice Green's function at an arbitrary site is obtained in closed form. Finally, the phase shift and scattering cross-section are evaluated analytically and numerically for one- and two-impurities.

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