Related papers: Form factors of local operators in a one-dimension…
We investigate the lowest scattering state of one-dimensional Bose gas with attractive interactions trapped in a hard wall trap. By solving the Bethe ansatz equation numerically we determine the full energy spectrum and the exact wave…
Using the recently introduced boundary form factor bootstrap equations, the form factors of boundary exponential operators in the sinh-Gordon model are constructed. The ultraviolet scaling dimension and the normalization of these operators…
I present the exact solution of a family of fragmented Bose-Hubbard models and represent the models as graphs in one-dimension, two-dimensions and three-dimensions with the condensates in the vertices. The models are solved by the algebraic…
We construct a global Hecke-Baxter operator for integrable systems of arithmetic type associated with the group $GL_2$. This is an element of a global Hecke algebra associated with the double coset space $GL_2(\mathbb{Z})\backslash…
Bose systems, subject to the action of external random potentials, are considered. For describing the system properties, under the action of spatially random potentials of arbitrary strength, the stochastic mean-field approximation is…
For a hard-core Bose gas on a one-dimensional lattice we find characteristic oscillations in the density-density correlation function. Their wavelength diverges as the system undergoes a continuous transition from an incommensurate to a…
We study the complex dynamics of a one-dimensional Bose gas subjected to a dissipative local defect which induces one-body atom losses. In experiments these atom losses occur, for example, when a focused electron or light beam or a single…
The properties of Green's functions and various correlation functions of density and spin operators are considered in a homogeneous spin-1 Bose gas in different phases. The dielectric formalism is worked out and the partial coincidence of…
We implement the Bethe anstaz method for the elliptic quantum group $E_{\tau,\eta}(A_2^{(2)})$. The Bethe creation operators are constructed as polynomials of the Lax matrix elements expressed through a recurrence relation. We also give the…
We investigate the exact solution of the q-deformed one-dimensional Bose gas to derive all integrals of motion and their corresponding eigenvalues. As an application, the thermodynamics is given and compared to an effective field theory at…
The relativistic approach to electroweak properties of two-particle composite systems developed in Ref. [A.F.Krutov, V.E.Troitsky, Phys.Rev.C. 65 (2002) 045501] is generalized here to the case of nonzero spin. In developed technique the…
Shell-shaped Bose-Einstein condensate (BEC) is a typical quantum system in curved geometry. Here we propose a new type of shell-shaped BEC with self-bound character, thereby liberating it from stringent conditions such as microgravity or…
We consider a gas of weakly interacting bosons in three dimensions subject to an external potential in the mean field regime. Assuming that the initial state of our system is a product state, we show that in the trace topology of one-body…
We present the thermodynamic Bethe ansatz as a way to factorize the partition function of a 2d field theory, in particular, a conformal field theory and we compare it with another approach to factorization due to K. Schoutens which consists…
Ultracold gases are a versatile platform to simulate condensed matter physics, as virtually any parameter is experimentally tunable. In particular, highly anisotropic traps allow the realization of low-dimensional systems, where the role of…
We present a method of finding approximate analytical solutions for the spectra and eigenvectors of collective modes in a two-dimensional system of interacting bosons subjected to a linear external potential or the potential of a special…
Building on recent advances in reduced density matrix theory, we develop a geometric framework for describing strongly correlated lattice bosons. We first establish that translational symmetry, together with a fixed pair interaction,…
A Bose gas in an external potential is studied by means of the local density approximation. Analytical results are derived for the thermodynamic properties of an ideal Bose gas in a generic power-law trapping potential, and their dependence…
The structure factor for a Bose system with Bose-Einstein condensate is considered in the frame of the self-consistent mean-field approximation. The accomplished analysis demonstrates the principal importance of the following three points:…
Form factors in the sinh-Gordon model are studied semiclassically for small values of the parameter $b\sim\hbar^{1/2}$ in the background of a radial classical solution, which describes a heavy exponential operator placed at the origin. For…