1,354,908 research outputs found
Expectation Values in the Lieb-Liniger Bose Gas
No full textTaking advantage of an exact mapping between a relativistic integrable model and the Lieb–Liniger model we present a novel method to compute expectation values in the Lieb–Liniger Bose gas both at zero and finite temperature. These quantities, relevant in the physics of one-dimensional ultracold Bose gases, are expressed by a series that has a remarkable behavior of convergence. Among other results, we show the computation of the three-body expectation value at finite temperature, a quantity that rules the recombination rate of the Bose gas
One-dimensional Lieb-Liniger Bose gas as nonrelativistic limit of the sinh-Gordon model
No full textThe 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. We use this mapping, together with the Thermodynamical Bethe Ansatz equations and the exact form factors of the Sinh–Gordon model, to set up a compact and general formalism for computing the expectation values of the Lieb–Liniger model both at zero and finite temperatures. The computation of one-point correlators is thoroughly detailed and when possible compared with known results in the literature
Lieb-Liniger gas in a constant-force potential
No full textWe 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). The ground-state properties of the gas in the wedgelike trapping potential are calculated in the strongly interacting regime by using Girardeau’s Fermi-Bose mapping and the pseudopotential approach in the 1/c approximation (c denotes the strength of the interaction). We point out that quantum dynamics of Lieb-Liniger wave packets in the linear potential can be calculated by employing an N-dimensional Fourier transform as in the case of free expansion
Une gueguere de cents and dans le golfe de Guinée
No full textA Guiné-Equatorial, um dos países pouco conhecidos do continente africano, é analisado por Max Liniger-Goumaz do ponto de vista das origens e da herança colonial. A máquina do Estado, os responsáveis políticos, os interesses locais e, principalmente, os interesses externos, são analisados segundo conexões com o esquema da autoridade local. O autor mostra ainda que as alterações ocorridas em termos do sistema de poder não correspondem a mudanças reais no plano político econômico.nuloEquatorial Guinea, one of the countries less known on the African Continent, is analyzed by Max Liniger-Goumaz the points of view on origins and heritance the colonial. The state machine, the responsible politicians, local interests and mainly foreign interests, are analyzed according to their connections with the scheme of local authority. The author still shows that chances done in the ruling system do not correspond to the real changes in the political economic plan
Modelo de Lieb-Liniger
No full textEm 1963, Lieb e Liniger resolveram exatamente um modelo de bósons unidimensional interagindo por um potencial repulsivo δ e calcularam seu estado fundamental no limite termodinâmico. Este texto tem como objetivo estudar a definição deste modelo, e demonstrar como fora calculado o estado fundamental no limite termodinâmico usando o método de Bethe-Ansatz. Também se estuda algumas implicações experimentais atuais oriundas da solução deste modelo.In 1963, Lieb and Liniger solved exactly a one dimensional model of bosons interacting by a repulsive δ-potential and calculated the ground state in the thermodynamic limit. This text intends to approach the definition of this model and show how they calculated the ground state in thermodynamic limit using the Bethe-Ansatz method. The text also approaches some experimental implications from the solutions of the model.35
Quantum quenches in the sinh-Gordon and Lieb-Liniger models
No full textThe non-relativistic limit of integrable field theories at equilibrium has
been intensively studied in the previous years; the simplest non-trivial case
relates the sinh-Gordon model to the Lieb-Liniger model. Here we study this
non-relativistic limit out of equilibrium, namely in the time evolution after a
quantum quench. The obtained results agree with the known ones for the
Lieb-Liniger model, thus showing that the non-relativistic limit is applicable
in this out-of-equilibrium setting
Momentum distribution of a freely expanding Lieb-Liniger gas
No full textWe numerically study free expansion of a few Lieb-Liniger bosons, which are initially in the ground state of an infinitely deep hard-wall trap. Numerical calculation is carried out by employing a standard Fourier transform, as follows from the Fermi-Bose transformation for a time-dependent Lieb-Liniger gas. We study the evolution of the momentum distribution, the real-space single-particle density, and the occupancies of natural orbitals. Our numerical calculation allows us to explore the behavior of these observables in the transient regime of the expansion, where they are nontrivially affected by the particle interactions. We derive analytically (by using the stationary phase approximation) the formula which connects the asymptotic shape of the momentum distribution and the initial state. For sufficiently large times, the momentum distribution coincides (up to a simple scaling transformation) with the shape of the real-space single-particle density (the expansion is asymptotically ballistic). Our analytical and numerical results are in good agreement
Non Relativistic Limit of Integrable QFT and Lieb-Liniger Models
No full text46 pages, 19 figuresInternational audienceIn this paper we study a suitable limit of integrable QFT with the aim to identify continuous non-relativistic integrable models with local interactions. This limit amounts to sending to infinity the speed of light c but simultaneously adjusting the coupling constant g of the quantum field theories in such a way to keep finite the energies of the various excitations. The QFT considered here are Toda Field Theories and the O(N) non-linear sigma model. In both cases the resulting non-relativistic integrable models consist only of Lieb-Liniger models, which are fully decoupled for the Toda theories while symmetrically coupled for the O(N) model. These examples provide explicit evidence of the universality and ubiquity of the Lieb-Liniger models and, at the same time, suggest that these models may exhaust the list of possible non-relativistic integrable theories of bosonic particles with local interactions
Dark solitons revealed in Lieb-Liniger eigenstates
No full textWe study how dark solitons, i.e., solutions of one-dimensional, single-particle, nonlinear, time-dependent Schrödinger equation, emerge from eigenstates of a linear many-body model of contact-interacting bosons moving on a ring, the Lieb-Liniger model. This long-standing problem has been addressed by various groups, which presented different, seemingly unrelated, procedures to reveal the solitonic waves directly from the many-body model. Here, we propose a unification of these results using a simple ansatz for the many-body eigenstate of the Lieb-Liniger model, which gives us access to systems of hundreds of atoms. In this approach, mean-field solitons emerge in a single-particle density through repeated measurements of particle positions in the ansatz state. The postmeasurement state turns out to be a wave packet of yrast states of the reduced system
Interaction and external field quantum quenches in the Lieb-Liniger and Gaudin-Yang model
No full textA review of the solution of the Lieb-Liniger is given. Using the wave function, the dynamics after a quench with a time dependent interaction strength is studied. Directly calculating the overlaps of wave functions, an interaction strength linear in time is examined. Furthermore utilizing those overlaps and the so called Yudson representation a time periodic interaction strength is studied. Moreover the dynamics of the Lieb-Liniger model with an external homogenous field is analyzed. After giving a review of the solution of the Gaudin-Yang model, an outlook on how the wave function for the Gaudin-Yang model in an external homogenous field could be obtained is given.M.S.Includes bibliographical referencesby Stefan M. Groh
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