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Related papers: A generalized Lieb-Liniger model

200 papers

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…

Statistical Mechanics · Physics 2007-05-23 M. T. Batchelor , X. W. Guan , N. Oelkers , C. Lee

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…

Strongly Correlated Electrons · Physics 2011-12-06 M. A. Cazalilla , R. Citro , T. Giamarchi , E. Orignac , M. Rigol

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…

Mathematical Physics · Physics 2021-03-31 Etienne Granet

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…

Statistical Mechanics · Physics 2009-11-10 M. T. Batchelor , X. W. Guan , J. B. McGuire

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…

Quantum Gases · Physics 2024-08-09 M. L. Kerr , G. De Rosi , K. V. Kheruntsyan

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…

Mathematical Physics · Physics 2020-07-30 Jacky Jia Wei Chong

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…

Quantum Gases · Physics 2017-01-10 Tianhao Ren , Igor Aleiner

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).…

Quantum Gases · Physics 2010-08-16 D. Jukić , S. Galić , R. Pezer , H. Buljan

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…

Nuclear Theory · Physics 2007-05-23 R. F. Mohr

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…

Mathematical Physics · Physics 2024-11-08 Johannes Agerskov , Robin Reuvers , Jan Philip Solovej

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…

High Energy Physics - Phenomenology · Physics 2024-12-31 Leonid M. Satarov , Igor N. Mishustin , Horst Stoecker

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…

Superconductivity · Physics 2025-09-11 Zhaoyu Han , Steven A. Kivelson

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…

Soft Condensed Matter · Physics 2009-11-10 M. D. Girardeau

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…

Other Condensed Matter · Physics 2009-11-11 Vadim V. Cheianov , H. Smith , M. B. Zvonarev

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.…

Statistical Mechanics · Physics 2010-05-21 M. Kormos , G. Mussardo , A. Trombettoni

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…

Mathematical Physics · Physics 2016-06-09 Craig A. Tracy , Harold Widom

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…

Mathematical Physics · Physics 2013-01-09 Serena Cenatiempo

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…

Quantum Gases · Physics 2021-04-13 Radu Chicireanu , Adam Rançon

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…

Quantum Gases · Physics 2025-09-24 Song Cheng , Yang-Yang Chen , Xi-Wen Guan , Wen-Li Yang , Rubem Mondaini , Hai-Qing Lin

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…

Quantum Gases · Physics 2017-12-19 A. Cappellaro , L. Salasnich