Related papers: The Partition Function of Multicomponent Log-Gases
Two roads are presently being followed in order to establish the existence of a liquid-gas phase transition in finite nuclear systems from nuclear reactions at high energy. The clean experiment of observing the thermodynamic properties of a…
The asymptotic partition function for quantized Abelian Higgs vortices at high temperature $T$ is found to leading and subleading order, and from this the equation of state of the vortex gas is derived, including the first quantum…
We consider a two-dimensional bi-layered loop model with a certain interlayer coupling and study its spectrum on a torus. Each layer consists of an $O(n)$ model on a honeycomb lattice with periodic boundary conditions; these layers are…
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…
For a system of bosons that interact through a class of general memory kernels, a recurrence relation for the partition function is derived within the path-integral formalism. This approach provides a generalization to previously known…
Exact expressions for the partition functions of the rigid string and membrane at any temperature are obtained in terms of hypergeometric functions. By using zeta function regularization methods, the results are analytically continued and…
The non-uniform (or inhomogeneous) electron gas has received much attention in many-body quantum mechanics and quantum chemistry in the early days of density functional theory, mainly as a theoretical device to construct gradient…
To simulate indistinguishable particles, recent studies of path-integral molecular dynamics formulated their partition function $Z$ as a recurrence relation involving a variable $\xi$, with $\xi=1$(-1) for bosons (fermions). Inspired by…
For the space $Lat_n$ of all the lattices in a $p$-adic $n$-dimensional linear space we obtain an analog of matrix beta-functions; this beta-function has a degeneration to the Tamagawa zeta-function. We propose an analog of Berezin kernels…
With use of the nonlinear Schr{\"o}dinger (or Gross-Pitaevskii) equation with strong repulsive cubic nonlinearity, dynamics of multi-component Bose-Einstein condensates (BECs) with a harmonic trap in 2 dimensions is investigated beyond the…
I derive a loop representation for the canonical and grand-canonical partition functions for an interacting four-component Fermi gas in one spatial dimension and an arbitrary external potential. The representation is free of the "sign…
Bimetallic catalysts can undergo segregation or redistribution of the metals driven by oxidizing and reducing environments. Bragg coherent diffraction imaging (BCDI) was used to relate displacement fields to compositional distributions in…
The expansion of the partition function for large coordination number $Z$ is a long standing method and has formerly been used to describe the Ising model at finite temperatures. We extend this approach and study the interacting Bose gas at…
Dynamics of attractive ultra-cold bosonic clouds in one dimension are studied by solving the many-particle time-dependent Schr\"odinger equation. The initially coherent wave-packet can dynamically dissociate into two parts when its energy…
We consider the Ising model on an $M\times N$ rectangular lattice with an asymmetric self-dual boundary condition, and derive a closed-form expression for its partition function. We show that zeroes of the partition function are given by…
At finite temperatures below the phase transition point, the Bose-Einstein condensation, the macroscopic occupation of a single quantum state by particles of integer spin, is not complete. In the language of superfluid helium, this means…
We show that the partition function for a scalar field in a static spacetime background can be expressed as a functional integral in the corresponding optical space, and point out that the difference between this and the functional integral…
We apply a path integral variational approach to obtain analytical expressions for condensate wave functions of an ultracold, interacting trapped Bose gases. As in many recent experiments, the particles are confined in a 1D or 3D harmonic…
The excitation spectrum of a two-component Bose-Einstein condensate has been discussed by Ref \cite{alex2comp} using the Bogoliubov equations. Here we make the additional contributions of the linear response function and dielectric function…
The existence of stationary distributions in a multicomponent Boltzmann equation using a non-additive kinetic energy composition rule for binary collisions is discussed. It is found that detailed balance is not achieved when -- in contrast…