Related papers: Dynamical correlation functions for an impenetrabl…
The book contain detailed explanation of Bethe Ansatz, Quantum Inverse Scattering Method and Algebraic Bether Ansatz as well. Main Models are Nonlinear Schrodinger equation (one dimensional Bose gas), Sine-Gordon and Thiring models.…
Two basic correlation functions are calculated for a model of $N$ harmonically interacting identical particles in a parabolic potential well. The density and the pair correlation function of the model are investigated for the boson case.…
We compute all dynamical spin-spin correlation functions for the spin-1/2 $XXZ$ anisotropic Heisenberg model in the gapless antiferromagnetic regime, using numerical sums of exact determinant representations for form factors of spin…
In this paper, we consider the heat-conducting compressible self-gravitating fluids in time-dependent domains, which typically describe the motion of viscous gaseous stars. The flow is governed by the 3-D Navier-Stokes-Fourier-Poisson…
A rigorous methodology for the analysis of initial boundary value problems on the half-line, $0<x<\infty$, $t>0$, for integrable nonlinear evolution PDEs has recently appeared in the literature. As an application of this methodology the…
For a noninteracting Bose gas with a fixed one-body Hamiltonian H^0 independent of the number of particles we derive the inequalities <N_i>_N < <N_i>_{N+1}, <N_i N_j>_N < <N_i>_N <N_j>_N for i\neq j, \partial <N_0>_N/\partial \beta >0 and…
We present a theoretical treatment of coherent light scattering from an interacting 1D Bose gas at finite temperatures. We show how this can provide a nondestructive measurement of the atomic system states. The equilibrium states are…
Matsubara Green's functions for interacting bosons are expressed as classical statistical averages corresponding to a linear imaginary-time stochastic differential equation. This makes direct numerical simulations applicable to the study of…
We develop a form factor approach to the study of dynamical correlation functions of quantum integrable models in the critical regime. As an example, we consider the quantum non-linear Schr\"odinger model. We derive long-distance/long-time…
The foundation for the theory of correlation functions of exactly solvable models is determinant representation. Determinant representation permit to describe correlation functions by classical completely integrable differential equations…
We study the Drude weight $D(T)$ at finite temperatures $T$ of an integrable bosonic model where the particles interact via nearest-neighbour coupling on a chain. At low temperatures, $D(T)$ is shown to be universal in the sense that this…
Functional relations play a key role in the study of integrable models. We argue in this paper that for massless field theories at zero temperature, these relations can in fact be interpreted as monodromy relations. Combined with a recently…
We determine dynamical response functions $<{\cal O}^\dagger(t,x_1){\cal O}(0,x_2)>$ in the scaling limit of the quantum Ising chain on the half line in the presence of a boundary magnetic field. Using a spectral representation in terms of…
A general expression for temperature-dependent magnetic susceptibility of quantum gases composed of particles possessing both charge and spin degrees of freedom has been obtained within the framework of the generalized random-phase…
The N-particle partition function of a one-dimensional $\delta$-function bose gas is calculated explicitly using only the periodic boundary condition (the Bethe ansatz equation). The N-particles cluster integrals are shown to be the same as…
Transport coefficients are typically divergent for quantum integrable systems in one dimension, such as a Bose gas with a two-body contact interaction. However, when a one-dimensional system is realized by confining bosons into a tight…
We propose a versatile variational method to investigate the spatio-temporal dynamics of one-dimensional magnetically-trapped Bose-condensed gases. To this end we employ a \emph{q}-Gaussian trial wave-function that interpolates between the…
The system that describes the dynamics of a Bose-Einstein Condensate (BEC) and the thermal cloud at finite temperature consists of a nonlinear Schrodinger (NLS) and a quantum Boltzmann (QB) equations. In such a system of trapped Bose gases…
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…
A detailed calculation of the real part of the finite temperature dynamic susceptibility of the free Bose gas is presented. After a short discussion on the different ways in which it can be calculated for temperatures above and below the…