scholarly journals Statistical Mechanics of Simple Dense Fluids Using Functional Integration

1969 ◽  
Vol 22 (6) ◽  
pp. 747 ◽  
Author(s):  
RG Storer
Keyword(s):  
Partition Function ◽  
Statistical Mechanics ◽  
Short Range ◽  
Equations Of State ◽  
Functional Integration ◽  
Functional Integral ◽  
Grand Partition Function ◽  
Dense Fluids ◽  
Approximate Equations

The use of functional integration in developing approximate equations of state for simple dense fluids is outlined. The repulsive (short range) and attraotive parts of the potential are treated separately and the grand partition function is expressed in terms of a functional integral which involves knowledge of the thermodynamio properties of the "short.range system". Two separate prooedures are outlined to obtain approximate equations of state for dense fluids from this exact functional integral.

THERMODYNAMICS OF q-MODIFIED BOSONS

1996 ◽  
Vol 10 (06) ◽  
pp. 683-699 ◽  
Author(s):  
P. NARAYANA SWAMY
Keyword(s):  
Mechanical Properties ◽  
Phase Transition ◽  
Equation Of State ◽  
Partition Function ◽  
Statistical Mechanics ◽  
Specific Heat ◽  
Thermodynamic Functions ◽  
Bose Condensation ◽  
Grand Partition Function ◽  
Statistical Mechanical

Based on a recent study of the statistical mechanical properties of the q-modified boson oscillators, we develop the statistical mechanics of the q-modified boson gas, in particular the Grand Partition Function. We derive the various thermodynamic functions for the q-boson gas including the entropy, pressure and specific heat. We demonstrate that the gas exhibits a phase transition analogous to ordinary bose condensation. We derive the equation of state and develop the virial expansion for the equation of state. Several interesting properties of the q-boson gas are derived and compared with those of the ordinary boson which may point to the physical relevance of such systems.

SHEAF COHOMOLOGY AND FUNCTIONAL INTEGRATION

1989 ◽  
Vol 04 (18) ◽  
pp. 4919-4928
Author(s):  
CHARLES NASH
Keyword(s):  
Functional Integration ◽  
Functional Integral ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Topological Properties ◽  
Sheaf Cohomology

Various analytic and topological properties of the spaces of functions arising in the functional integral are derived. It is shown that these spaces can possess attractive properties such as continuity, smoothness, and complex analyticity. We provide illustrations of the results with examples taken from several quantum field theories in varying dimensions.

A non-perturbative path-integral based thermal cluster expansion approach for grand partition function of quantum systems

2002 ◽  
Vol 352 (1-2) ◽  
pp. 63-69 ◽  
Author(s):  
Sheikh Hannan Mandal ◽  
Rathindranath Ghosh ◽  
Goutam Sanyal ◽  
Debashis Mukherjee
Keyword(s):  
Partition Function ◽  
Path Integral ◽  
Cluster Expansion ◽  
Quantum Systems ◽  
Grand Partition Function

A non-perturbative cumulant expansion method for the grand partition function of quantum systems

2001 ◽  
Vol 335 (3-4) ◽  
pp. 281-288 ◽  
Author(s):  
Sheikh Hannan Mandal ◽  
Rathindranath Ghosh ◽  
Debashis Mukherjee
Keyword(s):  
Partition Function ◽  
Expansion Method ◽  
Quantum Systems ◽  
Grand Partition Function ◽  
Cumulant Expansion

scholarly journals Hard Squares with Negative Activity and Rhombus Tilings of the Plane

10.37236/1093 ◽  
2006 ◽  
Vol 13 (1) ◽  
Author(s):  
Jakob Jonsson
Keyword(s):  
Partition Function ◽  
Statistical Mechanics ◽  
Simplicial Complex ◽  
Transfer Matrix ◽  
Euler Characteristic ◽  
Independent Sets ◽  
Roots Of Unity ◽  
Hard Squares ◽  
Vertex Set

Let $S_{m,n}$ be the graph on the vertex set ${\Bbb Z}_m \times {\Bbb Z}_n$ in which there is an edge between $(a,b)$ and $(c,d)$ if and only if either $(a,b) = (c,d\pm 1)$ or $(a,b) = (c \pm 1,d)$ modulo $(m,n)$. We present a formula for the Euler characteristic of the simplicial complex $\Sigma_{m,n}$ of independent sets in $S_{m,n}$. In particular, we show that the unreduced Euler characteristic of $\Sigma_{m,n}$ vanishes whenever $m$ and $n$ are coprime, thereby settling a conjecture in statistical mechanics due to Fendley, Schoutens and van Eerten. For general $m$ and $n$, we relate the Euler characteristic of $\Sigma_{m,n}$ to certain periodic rhombus tilings of the plane. Using this correspondence, we settle another conjecture due to Fendley et al., which states that all roots of $\det (xI-T_m)$ are roots of unity, where $T_m$ is a certain transfer matrix associated to $\{\Sigma_{m,n} : n \ge 1\}$. In the language of statistical mechanics, the reduced Euler characteristic of $\Sigma_{m,n}$ coincides with minus the partition function of the corresponding hard square model with activity $-1$.

The theory of rubber elasticity

1976 ◽  
Vol 351 (1666) ◽  
pp. 397-406 ◽  
Keyword(s):  
Equation Of State ◽  
Statistical Mechanics ◽  
Equations Of State ◽  
Rubber Elasticity ◽  
Elastic Behaviour ◽  
Excluded Volume ◽  
Simple Pattern ◽  
Dynamical Approach ◽  
Equilibrium Approach ◽  
The Future

It is argued that since statistical mechanics has developed in two ways, the dynamical approach of Boltzmann and the equilibrium approach of Gibbs, both should be valuable in rubber elasticity. It is shown that this is indeed the case, and the generality of these approaches allows one to study the problem in greater depth than hitherto. In particular, damping terms in the elastic behaviour of rubber can be calculated, and also the effect of entanglements and excluded volume on the equation of state. It is noticeable that although the calculated equations of state are quite complex, they do not fit into a simple pattern of invariants. The future for these developments is briefly discussed.

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