Related papers: A generalized Lieb-Liniger model
We consider the integrable one-dimensional delta-function interacting Bose gas in a hard wall box which is exactly solved via the coordinate Bethe Ansatz. The ground state energy, including the surface energy, is derived from the…
We review the physics of one-dimensional interacting bosonic systems. Beginning with results from exactly solvable models and computational approaches, we introduce the concept of bosonic Tomonaga-Luttinger Liquids relevant for…
We derive explicit expressions for dynamical correlations of the field and density operators in the Lieb-Liniger model, within an arbitrary eigenstate with a small particle density ${\cal D}$. They are valid for all space and time and any…
The Bethe roots describing the ground state energy of the integrable 1D model of interacting bosons with weakly repulsive two-body delta interactions are seen to satisfy the set of Richardson equations appearing in the strong coupling limit…
We present a comprehensive review on the state-of-the-art of the approximate analytic approaches describing the finite-temperature thermodynamic quantities of the Lieb-Liniger model of the one-dimensional (1D) Bose gas with contact…
We consider a system of $N$ bosons where the particles experience a short range two-body interaction given by $N^{-1}v_N(x)=N^{3\beta-1}v(N^\beta x)$ where $v \in C^\infty_c(\mathbb{R}^3)$, without a definite sign on $v$. We extend the…
We investigate the possible existence of the bound state in the system of three bosons interacting with each other via zero-radius potentials in two dimensions (it can be atoms confined in two dimensions or tri-exciton states in…
We use Gaudin's Fermi-Bose mapping operator to calculate exact solutions for the Lieb-Liniger model in a linear (constant force) potential (the constructed exact stationary solutions are referred to as the Lieb-Liniger-Airy wave functions).…
We have investigated S-wave bound states composed of three identical bosons interacting via regulated delta function potentials in non-relativistic quantum mechanics. For low-energy systems, these short-range potentials serve as an…
We study the ground state energy of a gas of 1D bosons with density $\rho$, interacting through a general, repulsive 2-body potential with scattering length $a$, in the dilute limit $\rho |a|\ll1$. The first terms in the expansion of the…
Equation of state of uncharged bosonic matter is studied within a field-theoretical approach in the mean-field approximation. Interaction of bosons is described by a scalar field $\sigma$ with a Skyrme-like potential which contains both…
We define an infinite class of ``frustration-free'' interacting lattice quantum Hamiltonians for bosons, constructed such that their exact ground states have a density distribution specified by the Boltzmann weight of a corresponding…
It is proved that the Lieb-Liniger (LL) cusp condition implementing the delta function interaction in one-dimensional Bose gases is dynamically conserved under phase imprinting by pulses of arbitrary spatial form and the subsequent…
Motivated by recent experiments we derive an exact expression for the correlation function entering the three-body recombination rate for a one-dimensional gas of interacting bosons. The answer, given in terms of two thermodynamic…
The repulsive Lieb-Liniger model can be obtained as the non-relativistic limit of the Sinh-Gordon model: all physical quantities of the latter model (S-matrix, Lagrangian and operators) can be put in correspondence with those of the former.…
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…
The theory of ultracold, dilute Bose gases is the subject of intensive studies, driven by new experimental applications, which also motivate the study of Bose-Einstein condensation (BEC) in low dimensions. From the theoretical point of view…
The quantum kicked rotor is well-known to display dynamical localization in the non-interacting limit. In the interacting case, while the mean-field (Gross-Pitaevskii) approximation displays a destruction of dynamical localization, its fate…
Exactly solved models provide rigorous understanding of many-body phenomena in strongly correlated systems. In this article, we report a breakthrough in uncovering universal many-body correlated properties of quantum integrable Lieb-Liniger…
The Lieb-Liniger equation of state accurately describes the zero-temperature universal properties of a dilute one-dimensional Bose gas in terms of the s-wave scattering length. For weakly-interacting bosons we derive non-universal…