Effect of flexibility on liquid-vapor coexistence and surface properties of tangent linear vibrating square well chains in two and three dimensions

2013 ◽  
Vol 138 (22) ◽  
pp. 224509 ◽  
Author(s):  
Gustavo A. Chapela ◽  
Enrique Díaz-Herrera ◽  
Julio C. Armas-Pérez ◽  
Jacqueline Quintana-H
Keyword(s):  
Surface Properties ◽  
Three Dimensions ◽  
Square Well ◽  
Liquid Vapor

Perturbative calculation of energy levels for the Dirac equation with generalized momenta

2020 ◽  
Vol 35 (20) ◽  
pp. 2050106
Author(s):  
Marco Maceda ◽  
Jairo Villafuerte-Lara
Keyword(s):  
Dirac Equation ◽  
Uncertainty Principle ◽  
Energy Levels ◽  
Generalized Uncertainty Principle ◽  
Spatial Dimension ◽  
Three Dimensions ◽  
Minimum Length ◽  
Linear Potential ◽  
Perturbative Calculation ◽  
Square Well

We analyze a modified Dirac equation based on a noncommutative structure in phase space originating from a generalized uncertainty principle with a minimum length. The noncommutative structure induces generalized momenta and contributions to the energy levels of the standard Dirac equation. Applying techniques of perturbation theory, we find the lowest-order corrections to the energy levels and eigenfunctions of the Dirac equation in three dimensions for a spherically symmetric linear potential and for a square-well times triangular potential along one spatial dimension. We find that the corrections due to the noncommutative contributions may be of the same order as the relativistic ones, leading to an upper bound on the parameter fixing the minimum length induced by the generalized uncertainty principle.

Perturbation theory and the local compressibility approximation in classical statistical mechanics

1968 ◽  
Vol 46 (15) ◽  
pp. 1725-1727 ◽  
Author(s):  
W. R. Smith ◽  
D. Henderson ◽  
J. A. Barker
Keyword(s):  
Perturbation Theory ◽  
Statistical Mechanics ◽  
Order Term ◽  
Second Order ◽  
Three Dimensions ◽  
First Order ◽  
Classical Statistical Mechanics ◽  
Square Well ◽  
Exact Calculations

The integrals which appear in the first-order term and the local compressibility approximation to the second-order term in the Barker–Henderson perturbation theory of fluids are evaluated analytically for the square-well potential in one and three dimensions and are compared with exact calculations.

Liquid–vapor interface of square-well fluids of variable interaction range

2004 ◽  
Vol 120 (24) ◽  
pp. 11754-11764 ◽  
Author(s):  
Pedro Orea ◽  
Yurko Duda ◽  
Volker C. Weiss ◽  
Wolffram Schröer ◽  
José Alejandre
Keyword(s):  
Interaction Range ◽  
Vapor Interface ◽  
Square Well ◽  
Variable Interaction ◽  
Liquid Vapor

scholarly journals Liquid–vapor coexistence in square-well fluids: an RHNC study

2009 ◽  
Vol 107 (4-6) ◽  
pp. 555-562 ◽  
Author(s):  
Achille Giacometti ◽  
Giorgio Pastore ◽  
Fred Lado
Keyword(s):  
Square Well ◽  
Liquid Vapor

Do attractive scattering potentials concentrate particles at the origin in one, two and three dimensions? I. Potentials finite at the origin

1983 ◽  
Vol 388 (1795) ◽  
pp. 401-418 ◽  
Keyword(s):  
Quantum Mechanics ◽  
Classical Mechanics ◽  
Three Dimensions ◽  
Simple Extension ◽  
Final State ◽  
Central Potential ◽  
Scattering State ◽  
Square Well ◽  
Semiclassical Regime ◽  
High Wavenumbers

Paradoxically, in beta decay, for instance, the final-state Coulomb forces pulling the electron inwards accelerate the emission. Quantum mechanics (q. m. ) makes the rate proportional to α ≡ ρ 0 / ρ ∞ ; ρ 0, ∞ (and v 0, ∞ ) are the particle densities (and speeds) at r = 0 and far upstream in the scattering state which describes the electron. Hence, as regards the effects of finalstate interactions, one must base one’s physical intuition on this ratio α . It is shown that according to (non-relativistic) classical mechanics, if the origin is accessible, then any central potential U(r) where v 0 < ∞ (i. e. where U (0) > -∞) gives in 1, 2 and 3 dimensions, α 1 = v ∞ / v 0 , α 2 = 1, α 3 = v 0 / v ∞ ; the remaining course of U(r) is irrelevant to α . The same results hold also in q. m. in the semiclassical regime, i. e. in the W. K. B. approximation which for such potentials becomes valid at high wavenumbers; in 2D it needs rather careful formulation, and in 3D one must avoid the Langer modification. (The W. K. B. results apply even if d U / d r diverges at r = 0, provided U (0) remains finite; these cases are covered by a simple extension of the argument. ) The square-well and exponential potentials are discussed as examples. Potentials which diverge at the origin are treated in the following paper.

The hard-sphere and square-well models for the surface properties of liquid metals

1979 ◽  
Vol 67 (2-3) ◽  
pp. 397-398 ◽  
Author(s):  
P.K. Chakrabarti ◽  
T. Nammalvar ◽  
R.C. Sastri
Keyword(s):  
Surface Properties ◽  
Hard Sphere ◽  
Liquid Metals ◽  
Square Well ◽  
Well Models
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