scholarly journals Thermostatistical analysis for short-range interaction potentials

2020 ◽  
Vol 17 (13) ◽  
pp. 2050193
Author(s):  
M. J. Neves ◽  
Everton M. C. Abreu ◽  
Jorge B. de Oliveira ◽  
Marcelo Kesseles Gonçalves
Keyword(s):  
Density Of States ◽  
Short Range ◽  
Plasma Potential ◽  
Thermal Capacity ◽  
Partition Functions ◽  
Range Interaction ◽  
The Mean ◽  
Gibbs Formalism ◽  
Canonical Ensembles ◽  
Physical Quantities

In this paper, we study the thermodynamics of short-range central potentials, namely, the Lee–Wick (LW) potential, and the Plasma potential. In the first part of the paper, we obtain the numerical solution for the orbits equation for these potentials. Posteriorly, we introduce the thermodynamics through the microcanonical and canonical ensembles formalism defined on the phase space of the system. We calculate the density of states associated with the LW and the Plasma potentials. From density of states, we obtain the thermodynamical physical quantities like entropy and temperature as functions of the energy. We also use the Boltzmann–Gibbs formalism to obtain the partition functions, the mean energy and the thermal capacity for these short-range potentials.

Hamilton-Jacobi Theory

2018 ◽  
Author(s):  
Peter Mann
Keyword(s):  
Phase Space ◽  
Bbgky Hierarchy ◽  
Distribution Functions ◽  
Symplectic Integrators ◽  
Partition Functions ◽  
Von Neumann ◽  
Equipartition Theorem ◽  
Recurrence Theorem ◽  
Phase Amplitude ◽  
Canonical Ensembles

This chapter focuses on Liouville’s theorem and classical statistical mechanics, deriving the classical propagator. The terms ‘phase space volume element’ and ‘Liouville operator’ are defined and an n-particle phase space probability density function is constructed to derive the Liouville equation. This is deconstructed into the BBGKY hierarchy, and radial distribution functions are used to develop n-body correlation functions. Koopman–von Neumann theory is investigated as a classical wavefunction approach. The chapter develops an operatorial mechanics based on classical Hilbert space, and discusses the de Broglie–Bohm formulation of quantum mechanics. Partition functions, ensemble averages and the virial theorem of Clausius are defined and Poincaré’s recurrence theorem, the Gibbs H-theorem and the Gibbs paradox are discussed. The chapter also discusses commuting observables, phase–amplitude decoupling, microcanonical ensembles, canonical ensembles, grand canonical ensembles, the Boltzmann factor, Mayer–Montroll cluster expansion and the equipartition theorem and investigates symplectic integrators, focusing on molecular dynamics.

Static critical behaviors in random-spin systems with short-range interaction

1978 ◽  
Vol 56 (1) ◽  
pp. 139-148 ◽  
Author(s):  
Yoshitake Yamazaki
Keyword(s):  
Short Range ◽  
Spin Systems ◽  
Three Dimensions ◽  
Index Formula ◽  
Spin Component ◽  
Renormalization Group Theory ◽  
Short Range Interaction ◽  
Range Interaction ◽  
The Stability ◽  
Component Models

Critical behaviors in quenched random-spin systems with N-spin component are studied in the limit M → 0 of the non-random MN-component models by means of the renormalization group theory. As the static critical phenomena the stability of the fixed points is investigated and the critical exponents η[~ O(ε3); ε ≡ 4 – d], γ, α, and crossover index [Formula: see text] and the equation of state [~ O(ε)] are obtained. Within the approximation up to the order ε2, even the random-spin systems with N = 2 or 3 are unstable in the three dimensions and the pure systems are stable there.

scholarly journals Short-Range Interaction Impact on Two-Dimensional Dipolar Scattering

2018 ◽  
Vol 173 ◽  
pp. 06008 ◽  
Author(s):  
Eugene A. Koval ◽  
Oksana A. Koval
Keyword(s):  
Cross Section ◽  
Short Range ◽  
Strong Dependence ◽  
Dipolar Interaction ◽  
Two Dimensional ◽  
Short Range Interaction ◽  
Range Interaction ◽  
Interaction Radius ◽  
Ultracold Polar Molecules ◽  
Spatial Dimensions

We report numerical investigation of the short range interaction influence on the two-dimensional quantum scattering of two dipoles. The model simulates two ultracold polar molecules collisions in two spatial dimensions. The used algorithm allows us to quantitatively analyse the scattering of two polarized dipoles with account for strongly anisotropic nature of dipolar interaction. The strong dependence of the scattering total cross section on the short range interaction radius was discovered for threshold collision energies. We also discuss differences of calculated scattering cross section dependencies for different polarisation axis tilt angles.

scholarly journals The state space of short-range Ising spin glasses: the density of states

1998 ◽  
Vol 2 (3) ◽  
pp. 313-317 ◽  
Author(s):  
T. Klotz ◽  
S. Schubert ◽  
K.H. Hoffmann
Keyword(s):  
State Space ◽  
Density Of States ◽  
Spin Glasses ◽  
Short Range ◽  
The State ◽  
Ising Spin

scholarly journals Population dynamics with spatial structure and an Allee effect

2020 ◽  
Author(s):  
Anudeep Surendran ◽  
Michael Plank ◽  
Matthew Simpson
Keyword(s):  
Population Dynamics ◽  
Spatial Structure ◽  
Short Range ◽  
Allee Effect ◽  
Mean Field ◽  
Mean Field Approximation ◽  
Continuum Approximation ◽  
Spatial Moment ◽  
Mean Field Models ◽  
The Mean

AbstractAllee effects describe populations in which long-term survival is only possible if the population density is above some threshold level. A simple mathematical model of an Allee effect is one where initial densities below the threshold lead to population extinction, whereas initial densities above the threshold eventually asymptote to some positive carrying capacity density. Mean field models of population dynamics neglect spatial structure that can arise through short-range interactions, such as short-range competition and dispersal. The influence of such non mean-field effects has not been studied in the presence of an Allee effect. To address this we develop an individual-based model (IBM) that incorporates both short-range interactions and an Allee effect. To explore the role of spatial structure we derive a mathematically tractable continuum approximation of the IBM in terms of the dynamics of spatial moments. In the limit of long-range interactions where the mean-field approximation holds, our modelling framework accurately recovers the mean-field Allee threshold. We show that the Allee threshold is sensitive to spatial structure that mean-field models neglect. For example, we show that there are cases where the mean-field model predicts extinction but the population actually survives and vice versa. Through simulations we show that our new spatial moment dynamics model accurately captures the modified Allee threshold in the presence of spatial structure.

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