Statistical mechanics of partially ionized stellar plasma - The Planck-Larkin partition function, polarization shifts, and simulations of optical spectra

1987 ◽  
Vol 319 ◽  
pp. 195 ◽  
Author(s):  
Werner Dappen ◽  
Lawrence Anderson ◽  
Dimitri Mihalas
Keyword(s):  
Partition Function ◽  
Statistical Mechanics ◽  
Optical Spectra ◽  
Partially Ionized

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 $-1$.

scholarly journals Statistical Mechanics of Discrete Multicomponent Fragmentation

2020 ◽  
Vol 5 (4) ◽  
pp. 64
Author(s):  
Themis Matsoukas
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Partition Function ◽  
Statistical Mechanics ◽  
Closed Form ◽  
Fixed Number ◽  
Arbitrary Degree ◽  
Fragment Distribution ◽  
The Mean ◽  
Fragmentation Event

We formulate the statistics of the discrete multicomponent fragmentation event using a methodology borrowed from statistical mechanics. We generate the ensemble of all feasible distributions that can be formed when a single integer multicomponent mass is broken into fixed number of fragments and calculate the combinatorial multiplicity of all distributions in the set. We define random fragmentation by the condition that the probability of distribution be proportional to its multiplicity, and obtain the partition function and the mean distribution in closed form. We then introduce a functional that biases the probability of distribution to produce in a systematic manner fragment distributions that deviate to any arbitrary degree from the random case. We corroborate the results of the theory by Monte Carlo simulation, and demonstrate examples in which components in sieve cuts of the fragment distribution undergo preferential mixing or segregation relative to the parent particle.

Statistical Mechanics of a Partially Ionized Hydrogen Plasma

1970 ◽  
Vol 1 (3) ◽  
pp. 957-965 ◽  
Author(s):  
O. Theimer ◽  
P. Kepple
Keyword(s):  
Statistical Mechanics ◽  
Hydrogen Plasma ◽  
Partially Ionized

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.

THE SOLUTION OF THE THREE-DIMENSIONAL TWISTED GROUP LATTICES

1992 ◽  
Vol 06 (10) ◽  
pp. 1631-1645 ◽  
Author(s):  
STUART SAMUEL
Keyword(s):  
Partition Function ◽  
Statistical Mechanics ◽  
Three Dimensional ◽  
Group Representations ◽  
Screw Dislocations ◽  
Irreducible Group ◽  
Twisted Group ◽  
Free Propagation

We define new lattices called d-dimensional twisted group lattices. They are similar to ordinary lattices except that abstract screw dislocations are present at the centers of all plaquettes. Some physical aspects are enumerated. We consider the statistical mechanics system of free propagation on the three-dimensional twisted group lattice. For this case, the partition function is explicitly computed by finding the irreducible group representations.

scholarly journals Twisted Conformal Algebra and Quantum Statistics of Harmonic Oscillators

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
J. Naji ◽  
S. Heydari ◽  
R. Darabi
Keyword(s):  
Free Energy ◽  
Partition Function ◽  
Statistical Mechanics ◽  
Quantum Statistics ◽  
Conformal Algebra ◽  
Harmonic Oscillators ◽  
Two Dimensional ◽  
Raising And Lowering Operators ◽  
Lowering Operators

We consider noncommutative two-dimensional quantum harmonic oscillators and extend them to the case of twisted algebra. We obtained modified raising and lowering operators. Also we study statistical mechanics and thermodynamics and calculated partition function which yields the free energy of the system.

Sign in / Sign up

Export Citation Format

Share Document