Related papers: The Partition Function of Log-Gases with Multiple …
We present a new algorithm for computing integral bases in algebraic function fields of one variable, or equivalently for constructing the normalization of a plane curve. Our basic strategy makes use of the concepts of localization and…
Numerical evaluation of functional integrals usually involves a finite (L-slice) discretization of the imaginary-time axis. In the auxiliary-field method, the L-slice approximant to the density matrix can be evaluated as a function of…
In this paper a spectral-Lagrangian method for the Boltzmann equation for a multi-energy level gas is proposed. Internal energy levels are treated as separate species and inelastic collisions (leading to internal energy excitation and…
We derive an exact recursion formula for the calculation of thermodynamic functions of finite systems obeying Bose-Einstein statistics. The formula is applicable for canonical systems where the particles can be treated as noninteracting in…
With the integral representation of Bose functions, the Bose-Einstein condensation of non-interacting bosons in a three-dimensional harmonic trap was studied. The relation between the particle number and its phase transition temperature was…
Solving the Gross--Pitaevskii (GP) equation describing a Bose--Einstein condensate (BEC) immersed in an optical lattice potential can be a numerically demanding task. We present a variational technique for providing fast, accurate solutions…
We present a method aimed at sampling charge density fluctuations in Coulomb systems. The derivation follows from a functional integral representation of the partition function in terms of charge density fluctuations. Starting from the…
We compute the partition function for the $N=1$ spinning particle, including pictures and the large Hilbert space, and show that it counts the dimension of the BRST cohomology in two- and four-dimensional target space. We also construct a…
We calculate the partition function of a harmonic oscillator with quasi-periodic boundary conditions using the zeta-function method. This work generalizes a previous one by Gibbons and contains the usual bosonic and fermionic oscillators as…
We study integration over functions on superspaces. These functions are invariant under a transformation which maps the whole superspace onto the part of the superspace which only comprises purely commuting variables. We get a compact…
Charged particle transport is an important energy transport mode in the combustion process of inertial confinement fusion plasma. On the one hand, charged particles inside the hot spot have a strong non-equilibrium effect, so it is…
We summarize recent developments in the field of higher dimensional bosonization made by the authors and collaborators and propose a general formula for the field operator in terms of currents and densities in one dimension using a new…
The possibility of Bloch oscillations for a degenerate and superfluid Fermi gas of atoms in an optical lattice is considered. For a one-component degenerate gas the oscillations are suppressed for high temperatures and band fillings. For a…
Let $\mathrm{pod}_{-3}(n)$ denote the number of partition triples of $n$ where the odd parts in each partition are distinct. We find many arithmetic properties of $\mathrm{pod}_{-3}(n)$ involving the following infinite family of…
In this paper we develop a gapless theory of BEC which can be applied to both trapped and homogeneous gases at zero and finite temperature. The many-body Hamiltonian for the system is written in a form which is approximately quadratic with…
We develop a new closed-form arithmetic and recursive formula for the partition function and a generalization of Andrews' smallest parts (spt) function. Using the inclusion-exclusion principle, we additionally develop a formula for the…
A semi-infinite crack loaded by a general asymmetric system of forces in an infinite bi-material plane is considered. A boundary integral formulation is derived using the fundamental reciprocal identity (Betti formula). The resulting…
We find necessary and sufficient conditions for the Law of Large Numbers for random discrete $N$-particle systems with the deformation (inverse temperature) parameter $\theta$, as their size $N$ tends to infinity simultaneously with the…
Bragg coherent diffraction imaging (BCDI), the well-established technique for imaging internal strain of nanoparticles, was used to image the internal compositional distribution of binary alloys in thermal equilibrium. The images…
In present work a calculation of transfer coefficients for many-component dense gases for charged and non-charged hard spheres is carried out using the Enskog-Landau kinetic equation which takes into account realistic particle sizes.