Number density, entropy density, and energy density of statistical mechanics for D‐dimensional grand canonical ensembles

1995 ◽  
Vol 36 (2) ◽  
pp. 750-755 ◽  
Author(s):  
M. D. Kostin
Keyword(s):  
Energy Density ◽  
Statistical Mechanics ◽  
Entropy Density ◽  
Number Density ◽  
Canonical Ensembles ◽  
Grand Canonical

Statistical mechanics

2017 ◽  
Author(s):  
Michael P. Allen ◽  
Dominic J. Tildesley
Keyword(s):  
Statistical Mechanics ◽  
Potential Model ◽  
Quantum Corrections ◽  
Inhomogeneous Systems ◽  
Hard Constraints ◽  
Complex Liquids ◽  
Fluid Membranes ◽  
Dynamical Properties ◽  
Canonical Ensembles ◽  
Grand Canonical

This chapter contains the essential statistical mechanics required to understand the inner workings of, and interpretation of results from, computer simulations. The microcanonical, canonical, isothermal–isobaric, semigrand and grand canonical ensembles are defined. Thermodynamic, structural, and dynamical properties of simple and complex liquids are related to appropriate functions of molecular positions and velocities. A number of important thermodynamic properties are defined in terms of fluctuations in these ensembles. The effect of the inclusion of hard constraints in the underlying potential model on the calculated properties is considered, and the addition of long-range and quantum corrections to classical simulations is presented. The extension of statistical mechanics to describe inhomogeneous systems such as the planar gas–liquid interface, fluid membranes, and liquid crystals, and its application in the simulation of these systems, are discussed.

Coherent alloy phase separation: Differences in canonical and grand canonical ensembles

1997 ◽  
Vol 55 (21) ◽  
pp. 14222-14229 ◽  
Author(s):  
E. M. Vandeworp ◽  
Kathie E. Newman
Keyword(s):  
Phase Separation ◽  
Canonical Ensembles ◽  
Grand Canonical

Canonical and Grand–Canonical Ensembles for Trapped Bose Gases

2010 ◽  
pp. 3-14
Author(s):  
Abel Camacho ◽  
Alfredo Macías ◽  
Abel Camacho–Galván
Keyword(s):  
Bose Gases ◽  
Canonical Ensembles ◽  
Grand Canonical

scholarly journals GROSS–PITAEVSKII MODEL FOR NONZERO TEMPERATURE BOSE–EINSTEIN CONDENSATES

2006 ◽  
Vol 16 (09) ◽  
pp. 2713-2719 ◽  
Author(s):  
KESTUTIS STALIUNAS
Keyword(s):  
Power Spectra ◽  
Pitaevskii Equation ◽  
Nonzero Temperature ◽  
Ginzburg Landau ◽  
Long Wavelength ◽  
Occupation Numbers ◽  
Ginzburg Landau Equations ◽  
Bose Einstein ◽  
Canonical Ensembles ◽  
Grand Canonical

Momentum distributions and temporal power spectra of nonzero temperature Bose–Einstein condensates are calculated using a Gross–Pitaevskii model. The distributions are obtained for micro-canonical ensembles (conservative Gross–Pitaevskii equation) and for grand-canonical ensembles (Gross–Pitaevskii equation with fluctuations and dissipation terms). Use is made of equivalence between statistics of the solutions of conservative Gross–Pitaevskii and dissipative complex Ginzburg–Landau equations. In all cases the occupation numbers of modes follow a 〈Nk〉 ∝ k-2 dependence, which corresponds in the long wavelength limit (k → 0) to Bose–Einstein distributions. The temporal power spectra are of 1/fα form, where: α = 2 - D/2 with D the dimension of space.

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