Ground-state energy and excitation spectrum of the Lieb-Liniger model : accurate analytical results and conjectures about the exact solution

We study the ground-state properties and excitation spectrum of the Lieb-Liniger model, i.e. the one-dimensional Bose gas with repulsive contact interactions. We solve the Bethe-Ansatz equations in the thermodynamic limit by using an analytic method based on a series expansion on orthogonal polynomials developed in \cite{Ristivojevic} and push the expansion to an unprecedented order. By a careful analysis of the mathematical structure of the series expansion, we make a conjecture for the analytic exact result at zero temperature and show that the partially resummed expressions thereby obtained compete with accurate numerical calculations. This allows us to evaluate the density of quasi-momenta, the ground-state energy, the local two-body correlation function and Tan's contact. Then, we study the two branches of the excitation spectrum. Using a general analysis of their properties and symmetries, we obtain novel analytical expressions at arbitrary interaction strength which are found to be extremely accurate in a wide range of intermediate to strong interactions

Tan's contact of a harmonically trapped one-dimensional Bose gas: strong-coupling expansion and conjectural approach at arbitrary interactions

We study Tan's contact, i.e. the coefficient of the high-momentum tails of the momentum distribution at leading order, for an interacting one-dimensional Bose gas subjected to a harmonic confinement. Using a strong-coupling systematic expansion of the ground-state energy of the homogeneous system stemming from the Bethe-Ansatz solution, together with the local-density approximation, we obtain the strong-coupling expansion for Tan's contact of the harmonically trapped gas. Also, we use a very accurate conjecture for the ground-state energy of the homogeneous system to obtain an approximate expression for Tan's contact for arbitrary interaction strength, thus estimating the accuracy of the strong-coupling expansion. Our results are relevant for ongoing experiments with ultracold atomic gases

Dynamic structure factor and drag force in a one-dimensional strongly-interacting Bose gas at finite temperature

We study the effect of thermal and quantum fluctuations on the dynamical response of a one-dimensional strongly-interacting Bose gas in a tight atomic waveguide. We combine the Luttinger liquid theory at arbitrary interactions and the exact Bose-Fermi mapping in the Tonks-Girardeau-impenetrable-boson limit to obtain the dynamic structure factor of the strongly-interacting fluid at finite temperature. Then, we determine the drag force felt by a potential barrier moving along the fluid in the experimentally realistic situation of finite barrier width and temperature.Comment: 13 pages, 11 figure

Visual motion processing and human tracking behavior

The accurate visual tracking of a moving object is a human fundamental skill that allows to reduce the relative slip and instability of the object's image on the retina, thus granting a stable, high-quality vision. In order to optimize tracking performance across time, a quick estimate of the object's global motion properties needs to be fed to the oculomotor system and dynamically updated. Concurrently, performance can be greatly improved in terms of latency and accuracy by taking into account predictive cues, especially under variable conditions of visibility and in presence of ambiguous retinal information. Here, we review several recent studies focusing on the integration of retinal and extra-retinal information for the control of human smooth pursuit.By dynamically probing the tracking performance with well established paradigms in the visual perception and oculomotor literature we provide the basis to test theoretical hypotheses within the framework of dynamic probabilistic inference. We will in particular present the applications of these results in light of state-of-the-art computer vision algorithms

A connection between non-local one-body and local three-body correlations of the Lieb-Liniger model

We derive a connection between the fourth coefficient of the short-distance Taylor expansion of the one-body correlation function, and the local three-body correlation function of the Lieb-Liniger model of $\delta$-interacting spinless bosons in one dimension. This connection, valid at arbitrary interaction strength, involves the fourth moment of the density of quasi-momenta. Generalizing recent conjectures, we propose approximate analytical expressions for the fourth coefficient covering the whole range of repulsive interactions, validated by comparison with accurate numerics. In particular, we find that the fourth coefficient changes sign at interaction strength $\gamma_c\simeq 3.816$, while the first three coefficients of the Taylor expansion of the one-body correlation function retain the same sign throughout the whole range of interaction strengths

On a singular variety associated to a polynomial mapping

In the paper "Geometry of polynomial mapping at infinity via intersection homology" the second and third authors associated to a given polynomial mapping F : \C^2 \to \C^2 with nonvanishing jacobian a variety whose homology or intersection homology describes the geometry of singularities at infinity of the mapping. We generalize this result.Comment: 1 figur

Neutral low-dimensional assemblies of a Mn(III) schiff base complex and octacyanotungstate(V) : synthesis, characterization, and magnetic properties

International audienceTwo novel low-dimensional molecular magnetic materials were prepared by the self-assembly of 3d- and 5d-metal complexes. These are the first neutral heterobimetallic cyanobridged compounds involving one anisotropic Mn(III) Schiff base complex and one octacyanotungstate(V) per molecular unit. A slow diffusion of the constituents’ solutions leads to the formation of the 0D crystalline complex 1, due to coordination of a water molecule to the Mn center, which prevents polymer formation. A rapid mixing of reagents results in the precipitation of the microcrystalline powder of complex 2, which based on the totality of experimental data, possesses a 1D polymeric structure. The magnetic studies have shown that antiferromagnetic exchange interactions prevail in 1 (J/kB = −13.1(7) K, D = −3.0(1.3) K, zJ' = −0.16(20) K and gav = 2.00(1)); while the presence of the significant intramolecular Mn(III)–W(V) ferromagnetic coupling through cyanide bridge is characteristic for 2 (J/kB = 46.1(5) K, gMn = 2.11(3), fixed gW = 2.0). Due to the weak interchain interactions, zJ′/kB = −0.8(2) K, and compound 2 is a metamagnet with the Néel temperature of 9.5 K undergoing a spin-flip transition at 2 kOe. The slow magnetization dynamics of 2 were investigated at a DC field of 0 and 2 kOe, giving the values of τ0 32(15) and 36(15) ps, respectively, well within the range typical for single-chain magnets (SCMs). The respective ∆τ/kB values were 48.4(1.2) and 44.9(1.0) K