Related papers: The partition function for "composite particles"
A mathematical method for constructing fractal curves and surfaces, termed the $p\lambda n$ fractal decomposition, is presented. It allows any function to be split into a finite set of fractal discontinuous functions whose sum is equal…
In this paper, we introduce a natural geometric extension of the partition function. More precisely, we investigate the problem of counting partitions of a rectangle into rectangular blocks with integer sides. Here, two partitions of a…
The completeness of quantum state space, is usually expressed as \sum_{m=0}^{\infty}|m><m|=1, where {|m>} is selected set of quantum states (basis). Density matrix |m><m| describes a pure quantum state. In this paper, by virtue of the…
A formula which only involves a partition number and elementary functions is derived by applying Burnside's Lemma to the set of idempotent maps from a set to itself. One side involves a summation over a set closely related to the partition…
We study partitions of complex numbers as sums of non-negative powers of a fixed algebraic number $\beta$. We prove that if $\beta$ is real quadratic, then the number of partitions is always finite if and only if some conjugate of $\beta$…
The statistical physics approach to the number partioning problem, a classical NP-hard problem, is both simple and rewarding. Very basic notions and methods from statistical mechanics are enough to obtain analytical results for the phase…
We have calculated the quantum correction(QC) in the vibrational partition function and thermodynamic state functions, e.g., internal energy, specific heat, free energy and entropy by using improved Manning-Rosen(MR) potential for Li_2,…
In this paper, we derive an expression for the grand canonical partition function for a fluid of hot, rotating massless scalar field particles in the Einstein universe. We consider the number of states with a given energy as one increases…
The aggregation of particles in the free molecular regime is determined approximately for situations with a high degree of translational energy equilibration. The mean particle sizes develop linearly in time. Scaling relations are used to…
We study the number $p(n,t)$ of partitions of $n$ with difference $t$ between largest and smallest parts. Our main result is an explicit formula for the generating function $P_t(q) := \sum_{n \ge 1} p(n,t) \, q^n$. Somewhat surprisingly,…
This paper, about a fluid-like system of spatially confined particles, reveals the analytic structure for both, the canonical and grand canonical partition functions. The studied system is inhomogeneously distributed in a region whose…
Starting from the general Lindhard theory describing the partition of particles energy in materials between ionisation and displacements, analytical approximate solutions have been derived, for media containing one and more atomic species,…
Using previous work by Merca, we show the partition function involving parts of k different magnitudes, shifted by the triangular numbers, equals the self convolution of the unrestricted partition function. We also provide a combinatorial…
We have improved the procedure for calculating distribution functions and the thermal equation of state for real gases by introducing modified functions of probability distributions into the gas phase state sum. Calculation of real gas…
This article introduces recursive relations allowing the calculation of the number of partitions with constraints on the minimum and/or on the maximum fragment size.
We describe a general methods to localize any sort of k-separability and therefore also the corresponding partial entanglement in genuinely multipartite mixed quantum states. Our methods are based exclusively on the known twopartite methods…
The two-dimensional one-component plasma ---2dOCP--- is a system composed by $n$ mobile particles with charge $q$ over a neutralizing background in a two-dimensional surface. The Boltzmann factor of this system, at temperature $T$, takes…
We study fragmentation numerically using a simple model in which an object is taken to be a set of particles that interact pairwisely via a Lennard-Jones potential while the effect of the fragmentation-induced forces is represented by some…
In the paper we give consecutive description of functional methods of quantum field theory for systems of interacting q-particles. These particles obey exotic statistics and appear in many problems of condensed matter physics, magnetism and…
We consider a refined version of the string-net model which assigns a different energy cost to each plaquette excitation. Using recent exact calculations of the energy-level degeneracies we compute the partition function of this model and…