Related papers: From multiple integrals to Fredholm determinants
We consider the determinantal point process with the confluent hypergeometric kernel. This process is a universal point process in random matrix theory and describes the distribution of eigenvalues of large random Hermitian matrices near…
The six-vertex model with domain wall boundary conditions is considered. A Fredholm determinant representation for the partition function of the model is obtained. The kernel of the corrtesponding integral operator depends on Laguerre…
1d Bose gas interacting through delta, delta' and double-delta function potentials is shown to be equivalent to a delta anyon gas allowing exact Bethe ansatz solution. In the noninteracting limit it describes an ideal gas with generalized…
We prove that Fredholm determinants of the form det(1-K_s), where K_s is the restriction of either the discrete Bessel kernel or the discrete {}_2F_1 kernel to {s,s+1,...}, can be expressed through solutions of discrete Painleve II and V…
The weak coupling asymptotics, to order $(c/\rho)^2$, of the ground state energy of the delta-function Bose gasmis derived. Here $2c\ge 0$ is the delta-function potential amplitude and $\rho$ the density of the gas in the thermodynamic…
We propose a new type of approximation to quantum determinants, ``quantum Fredholm determinant", and conjecture that, compared to the quantum Selberg zeta functions derived from Gutzwiller semiclassical trace formulas, such determinants…
We present a boundary integral formulation of the Helmholtz equation with visco-thermal boundary conditions, in two dimensions. Such boundary conditions allow for the accurate simulation of viscous and thermal losses in the vicinity of the…
We prove a Feynman-Kac-type formula for the relative motion of the two-body delta-Bose gas in two dimensions. The multiplicative functional is not exponential, and the process is a skew-product diffusion uniquely extended in law, in the…
A quantum field-theoretical model, which describes spatially non-homogeneous repulsive Bose gas in an external harmonic potential is considered. Two-point thermal correlation functions of the Bose gas are calculated in the framework of the…
At zero temperature, homogeneous interacting Bose-condensed fluids are entirely superfluid, with remarkable transport properties. A non-superfluid, normal component is induced by finite temperatures and spatial inhomogeneity, the combined…
The paper extends earlier results from \cite{SK}, \cite{SKS} about infinite-volume quantum bosonic states (FK-DLR states) to the case of multi-type particles with non-negative interactions. (An example is a quantum Widom--Rowlinson model.)…
We consider the quantum nonlinear Schr\"odinger equation in one space and one time dimension. We are interested in the non-free-fermionic case. We consider static temperature-dependent correlation functions. The determinant representation…
In this work we explore an instance of the $\tau$-function of vertex type operators, specified in terms of a constant phase shift in a free-fermionic basis. From the physical point of view this $\tau$-function has multiple interpretations:…
The formalism developed in the first paper of the series [arXiv:0901.1060] is applied to two thermodynamic systems: (i) of three global observables (the energy, the total electron number and the spin number), (ii) of one global observable…
We study a Fredholm determinant of the hypergeometric kernel arising in the representation theory of the infinite-dimensional unitary group. It is shown that this determinant coincides with the Palmer-Beatty-Tracy tau function of a Dirac…
The one-loop effective potential for non-relativistic bosons with a delta function repulsive potential is calculated for a given chemical potential using functional methods. After renormalization and at zero temperature it reproduces the…
Expanding upon previous work, using the path-integral formalism we derive expressions for the one-particle reduced density matrix and the two-point correlation function for a quadratic system of bosons that interact through a general class…
Decoherence with recurrences appear in the dynamics of the one-body density matrix of an $F = 1$ spinor Bose-Einstein condensate, initially prepared in coherent states, in the presence of an external uniform magnetic field and within the…
The ideal uniform two-dimensional (2D) Fermi and Bose gases are considered both in the thermodynamic limit and the finite case. We derive May's Theorem, viz. the correspondence between the internal energies of the Fermi and Bose gases in…
We discuss the interaction of a mobile quantum impurity with a Bose-Einstein condensate of atoms at finite temperature. To describe the resulting Bose polaron formation we extend the dynamical variational approach of [Phys.Rev.Lett. 117,…