Approximate expression for the dynamic structure factor in the Lieb-Liniger model

Recently, Imambekov and Glazman [Phys. Rev. Lett. 100, 206805 (2008)] showed that the dynamic structure factor (DSF) of the 1D Bose gas demonstrates power-law behaviour along the limiting dispersion curve of the collective modes and calculated the corresponding exponents exactly. Combining these recent results with a previously obtained strong-coupling expansion we present an interpolation formula for the DSF of the 1D Bose gas. The obtained expression is further consistent with exact low energy exponents from Luttinger liquid theory and shows nice agreement with recent numerical results.Comment: 4 pages, 3 figure

The Dynamic Structure Factor of the 1D Bose Gas near the Tonks-Girardeau Limit

While the 1D Bose gas appears to exhibit superfluid response under certain conditions, it fails the Landau criterion according to the elementary excitation spectrum calculated by Lieb. The apparent riddle is solved by calculating the dynamic structure factor of the Lieb-Liniger 1D Bose gas. A pseudopotential Hamiltonian in the fermionic representation is used to derive a Hartree-Fock operator, which turns out to be well-behaved and local. The Random-Phase approximation for the dynamic structure factor based on this derivation is calculated analytically and is expected to be valid at least up to first order in $1/\gamma$, where $\gamma$ is the dimensionless interaction strength of the model. The dynamic structure factor in this approximation clearly indicates a crossover behavior from the non-superfluid Tonks to the superfluid weakly-interacting regime, which should be observable by Bragg scattering in current experiments.Comment: 4 pages, 2 figures misprints in formulas correcte

Proof of Bose-Einstein Condensation for Dilute Trapped Gases

The ground state of bosonic atoms in a trap has been shown experimentally to display Bose-Einstein condensation (BEC). We prove this fact theoretically for bosons with two-body repulsive interaction potentials in the dilute limit, starting from the basic Schroedinger equation; the condensation is 100% into the state that minimizes the Gross-Pitaevskii energy functional. This is the first rigorous proof of BEC in a physically realistic, continuum model.Comment: Revised version with some simplifications and clarifications. To appear in Phys. Rev. Let

Polarizability and dynamic structure factor of the one-dimensional Bose gas near the Tonks-Girardeau limit at finite temperatures

Correlation functions related to the dynamic density response of the one-dimensional Bose gas in the model of Lieb and Liniger are calculated. An exact Bose-Fermi mapping is used to work in a fermionic representation with a pseudopotential Hamiltonian. The Hartree-Fock and generalized random phase approximations are derived and the dynamic polarizability is calculated. The results are valid to first order in 1/\gamma where \gamma is Lieb-Liniger coupling parameter. Approximations for the dynamic and static structure factor at finite temperature are presented. The results preclude superfluidity at any finite temperature in the large-\gamma regime due to the Landau criterion. Due to the exact Bose-Fermi duality, the results apply for spinless fermions with weak p-wave interactions as well as for strongly interacting bosons.Comment: 13 pages, 5 figures, the journal versio

Dilute Fermi gas: kinetic and interaction energies

A dilute homogeneous 3D Fermi gas in the ground state is considered for the case of a repulsive pairwise interaction. The low-density (dilution) expansions for the kinetic and interaction energies of the system in question are calculated up to the third order in the dilution parameter. Similar to the recent results for a Bose gas, the calculated quantities turn out to depend on a pairwise interaction through the two characteristic lengths: the former, $a$, is the well-known s-wave scattering length, and the latter, $b$, is related to $a$ by $b=a-m (\partial a/\partial m)$, where $m$ stands for the fermion mass. To take control of the results, calculations are fulfilled in two independent ways. The first involves the Hellmann-Feynman theorem, taken in conjunction with a helpful variational theorem for the scattering length. This way is used to derive the kinetic and interaction energies from the familiar low-density expansion of the total system energy first found by Huang and Yang. The second way operates with the in-medium pair wave functions. It allows one to derive the quantities of interest``from the scratch'', with no use of the total energy. An important result of the present investigation is that the pairwise interaction of fermions makes an essential contribution to their kinetic energy. Moreover, there is a complicated and interesting interplay of these quantities

Three Courses of Tianjiu Therapy in Sanfu Days for Chronic Asthma: A Clinic Efficacy Observation Trail

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Genetic study of congenital bile-duct dilatation identifies de novo and inherited variants in functionally related genes

Background: Congenital dilatation of the bile-duct (CDD) is a rare, mostly sporadic, disorder that results in bile retention with severe associated complications. CDD affects mainly Asians. To our knowledge, no genetic study has ever been conducted. Methods: We aim to identify genetic risk factors by a “trio-based” exome-sequencing approach, whereby 31 CDD probands and their unaffected parents were exome-sequenced. Seven-hundred controls from the local population were used to detect gene-sets significantly enriched with rare variants in CDD patients. Results: Twenty-one predicted damaging de novo variants (DNVs; 4 protein truncating and 17 missense) were identified in several evolutionarily constrained genes (p < 0.01). Six genes carrying DNVs were associated with human developmental disorders involving epithelial, connective or bone morphologies (PXDN, RTEL1, ANKRD11, MAP2K1, CYLD, ACAN) and four linked with cholangio- and hepatocellular carcinomas (PIK3CA, TLN1 CYLD, MAP2K1). Importantly, CDD patients have an excess of DNVs in cancer-related genes (p < 0.025). Thirteen genes were recurrently mutated at different sites, forming compound heterozygotes or functionally related complexes within patients. Conclusions: Our data supports a strong genetic basis for CDD and show that CDD is not only genetically heterogeneous but also non-monogenic, requiring mutations in more than one genes for the disease to develop. The data is consistent with the rarity and sporadic presentation of CDD

Self-consistent calculation of the coupling constant in the Gross-Pitaevskii equation

A method is proposed for a self-consistent evaluation of the coupling constant in the Gross-Pitaevskii equation without involving a pseudopotential replacement. A renormalization of the coupling constant occurs due to medium effects and the trapping potential, e.g. in quasi-1D or quasi-2D systems. It is shown that a simplified version of the Hartree-Fock-Bogoliubov approximation leads to a variational problem for both the condensate and a two-body wave function describing the behaviour of a pair of bosons in the Bose-Einstein condensate. The resulting coupled equations are free of unphysical divergences. Particular cases of this scheme that admit analytical estimations are considered and compared to the literature. In addition to the well-known cases of low-dimensional trapping, cross-over regimes can be studied. The values of the kinetic, interaction, external, and release energies in low dimensions are also evaluated and contributions due to short-range correlations are found to be substantial.Comment: 15 pages, ReVTEX, no figure

Theory of superfluidity and drag force in the one-dimensional Bose gas

The one-dimensional Bose gas is an unusual superfluid. In contrast to higher spatial dimensions, the existence of non-classical rotational inertia is not directly linked to the dissipationless motion of infinitesimal impurities. Recently, experimental tests with ultracold atoms have begun and quantitative predictions for the drag force experienced by moving obstacles have become available. This topical review discusses the drag force obtained from linear response theory in relation to Landau's criterion of superfluidity. Based upon improved analytical and numerical understanding of the dynamical structure factor, results for different obstacle potentials are obtained, including single impurities, optical lattices and random potentials generated from speckle patterns. The dynamical breakdown of superfluidity in random potentials is discussed in relation to Anderson localization and the predicted superfluid-insulator transition in these systems.Comment: 17 pages, 12 figures, mini-review prepared for the special issue of Frontiers of Physics "Recent Progresses on Quantum Dynamics of Ultracold Atoms and Future Quantum Technologies", edited by Profs. Lee, Ueda, and Drummon

Genetic determinants of common epilepsies: a meta-analysis of genome-wide association studies

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