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We consider a free fermion formulation of a statistical model exhibiting a limit shape phenomenon. The model is shown to have a phase transition that can be visualized as the merger of two liquid regions - arctic circles. We show that the merging arctic circles provide a space-time resolved picture of the phase transition in lattice QCD known as Gross-Witten-Wadia transition. The latter is a continuous phase transition of the third order. We argue that this transition is universal and is not spoiled by interactions if parity and time-reversal symmetries are preserved. We refer to this universal transition as the Merger Transition., Comment: 23 pages, 6 figures

We analyse the breathing-mode oscillations of a harmonically quenched Tonks-Giradeau (TG) gas using an exact finite-temperature dynamical theory. We predict a striking collective manifestation of impenetrability---a collective many-body bounce effect. The effect, while being invisible in the evolution of the in-situ density profile of the gas, can be revealed through a nontrivial periodic narrowing of its momentum distribution, taking place at twice the rate of the fundamental breathing-mode frequency. We identify physical regimes for observing the many-body bounce and construct the respective nonequilibrium phase diagram as a function of the quench strength and the initial temperature of the gas. We also develop a finite-temperature hydrodynamic theory of the TG gas, wherein the many-body bounce is explained by an increased thermodynamic pressure of the gas during the isentropic compression, which acts as a potential barrier at the inner turning points of the breathing cycle., Comment: 5 pages, 4 figures, and Supplemental Material. arXiv admin note: substantial text overlap with arXiv:1608.08720

Describing finite-temperature nonequilibrium dynamics of interacting many-particle systems is a notoriously challenging problem in quantum many-body physics. Here we provide an exact solution to this problem for a system of strongly interacting bosons in one dimension in the Tonks-Girardeau regime of infinitely strong repulsive interactions. Using the Fredholm determinant approach and the Bose-Fermi mapping we show how the problem can be reduced to a single-particle basis, wherein the finite-temperature effects enter the solution via an effective "dressing" of the single-particle wavefunctions by the Fermi-Dirac occupation factors. We demonstrate the utility of our approach and its computational efficiency in two nontrivial out-of-equilibrium scenarios: collective breathing mode oscillations in a harmonic trap and collisional dynamics in the Newton's cradle setting involving real-time evolution in a periodic Bragg potential., Comment: Final published version in PRA style; moved Supplemental Material into main text; 6 pages, 3 figures

We study the behaviour of ultracold bosonic gas in the critical region above the Bose-Einstein condensation in the presence of an artificial magnetic field, $B_\mathrm{art}$. We show that the condensate fluctuations above the critical temperature $T_c$ cause the fluctuational susceptibility, $\chi _\mathrm{fl}$, of a uniform gas to have a stronger power-law divergence than in an analogous superconducting system. Measuring such a divergence opens new ways of exploring critical properties of the ultracold gas and an opportunity of an accurate determination of $T_c$. We describe a method of measuring $\chi _\mathrm{fl}$ which requires a constant gradient in $B_\mathrm{art}$ and suggest a way of creating such a field in experiment., Comment: 5 pages, 3 figures, 5 pages of Supplement; the text is rewritten and rearranged, and the figures are modified

We analyze free expansion of a trapped one-dimensional Bose gas after a sudden release from the confining trap potential. By using the stationary phase and local density approximations, we show that the long-time asymptotic density profile and the momentum distribution of the gas are determined by the initial distribution of Bethe rapidities (quasimomenta) and hence can be obtained from the solutions to the Lieb-Liniger equations in the thermodynamic limit. For expansion from a harmonic trap, and in the limits of very weak and very strong interactions, we recover the self-similar scaling solutions known from the hydrodynamic approach. For all other power-law traps and arbitrary interaction strengths, the expansion is not self-similar and shows strong dependence of the density profile evolution on the trap anharmonicity. We also characterize dynamical fermionization of the expanding cloud in terms of correlation functions describing phase and density fluctuations., Comment: Final published version with modified title and a couple of other minor changes. 5 pages, 2 figures, and Supplemental Material

We study a flow of ultracold bosonic atoms through a one-dimensional channel that connects two macroscopic three-dimensional reservoirs of Bose-condensed atoms via weak links implemented as potential barriers between each of the reservoirs and the channel. We consider reservoirs at equal chemical potentials so that a superflow of the quasi-condensate through the channel is driven purely by a phase difference, $2\Phi$, imprinted between the reservoirs. We find that the superflow never has the standard Josephson form $\sim \sin 2\Phi $. Instead, the superflow discontinuously flips direction at $2\Phi =\pm\pi$ and has metastable branches. We show that these features are robust and not smeared by fluctuations or phase slips. We describe a possible experimental setup for observing these phenomena., Comment: Final version, as published (a slightly extended discussion on p.3; misprints corrected); 5 pages, 5 figures + Supplemental material

We scrutinize the hydrodynamic approach for calculating dynamical correlations in one-dimensional superfluids near integrability and calculate the characteristic time scale {\tau} beyond which this approach is valid. For time scales shorter than {\tau} hydrodynamics fails and we develop an approach based on kinetics of fermionic quasiparticles described as mobile impurities. New universal results for the dynamical structure factor relevant to experiments in ultracold atomic gases are obtained., Comment: 5 pages, 2 figures. Supplemental material included. Version 3: Minor typos corrected

We analyze the two-body momentum correlation function for a uniform weakly interacting one-dimensional Bose gas. We show that the strong positive correlation between opposite momenta, expected in a Bose-Einstein condensate with a true long-range order, almost vanishes in a phase-fluctuating quasicondensate where the long-range order is destroyed. Using the Luttinger liquid approach, we derive an analytic expression for the momentum correlation function in the quasicondensate regime, showing (i) the reduction and broadening of the opposite-momentum correlations (compared to the singular behavior in a true condensate) and (ii) an emergence of anticorrelations at small momenta. We also numerically investigate the momentum correlations in the crossover between the quasicondensate and the ideal Bose-gas regimes using a classical field approach and show how the anticorrelations gradually disappear in the ideal-gas limit., Comment: Final published version

Decay of a high-energy double occupancy state, doublon, in a narrow-band lattice requires creation of a coherent many-particle excitation. This leads to an exponentially long relaxation time of such a state. We show that, if the average occupation number is sufficiently small, the corresponding exponent may be evaluated exactly. To this end we develop the quasiclassical approach to calculation of the high-order tree-level decay amplitudes., Comment: 4 pages, 1 figure

Unless protected by the exact integrability, solitons are subject to dissipative forces, originating from a thermally fluctuating background. At low enough temperatures $T$ background fluctuations should be considered as being quantized which enables us to calculate finite lifetime of the solitons $\tau\sim T^{-4}$. We also find that the coherent nature of the quantum fluctuations leads to long-range interactions between the solitons mediated by the superradiation. Our results are of relevance to current experiments with ultracold atoms, while the approach may be extended to solitons in other media., Comment: 5 pages, 1 figure. Accepted for publication in PRL.

The behavior of the spatial two-particle correlation function is surveyed in detail for a uniform 1D Bose gas with repulsive contact interactions at finite temperatures. Both long-, medium-, and short-range effects are investigated. The results span the entire range of physical regimes, from ideal gas, to strongly interacting, and from zero temperature to high temperature. We present perturbative analytic methods, available at strong and weak coupling, and first-principle numerical results using imaginary time simulations with the gauge-P representation in regimes where perturbative methods are invalid. Nontrivial effects are observed from the interplay of thermally induced bunching behavior versus interaction induced antibunching., Comment: 22 pages, 13 figures

A force applied to a spin-flipped particle in a one-dimensional spinor gas may lead to Bloch oscillations of particle's position and velocity. The existence of Bloch oscillations crucially depends on the viscous friction force exerted by the rest of the gas on the spin excitation. We evaluate the friction in terms of the quantum fluid parameters. In particular, we show that the friction is absent for integrable cases, such as SU(2) symmetric gas of bosons or fermions. For small deviations from the exact integrability the friction is very weak, opening the possibility to observe Bloch oscillations., Comment: 4 pages, 2 figures

We analytically calculate the spatial nonlocal pair correlation function for an interacting uniform 1D Bose gas at finite temperature and propose an experimental method to measure nonlocal correlations. Our results span six different physical realms, including the weakly and strongly interacting regimes. We show explicitly that the characteristic correlation lengths are given by one of four length scales: the thermal de Broglie wavelength, the mean interparticle separation, the healing length, or the phase coherence length. In all regimes, we identify the profound role of interactions and find that under certain conditions the pair correlation may develop a global maximum at a finite interparticle separation due to the competition between repulsive interactions and thermal effects., Comment: Final published version, modified title

We consider a longitudinal expansion of a one-dimensional gas of hard-core bosons suddenly released from a trap. We show that the broken translational invariance in the initial state of the system is encoded in correlations between the bosonic occupation numbers in the momentum space. The correlations are protected by the integrability and exhibit no relaxation during the expansion.

We consider wetting of a one-dimensional random walk on a half-line $x\ge 0$ in a short-ranged potential located at the origin $x=0$. We demonstrate explicitly how the presence of a quenched chemical disorder affects the pinning-depinning transition point. For small disorders we develop a perturbative technique which enables us to compute explicitly the averaged temperature (energy) of the pinning transition. For strong disorder we compute the transition point both numerically and using the renormalization group approach. Our consideration is based on the following idea: the random potential can be viewed as a periodic potential with the period $n$ in the limit $n\to\infty$. The advantage of our approach stems from the ability to integrate exactly over all spatial degrees of freedoms in the model and to reduce the initial problem to the analysis of eigenvalues and eigenfunctions of some special non-Hermitian random matrix with disorder--dependent diagonal and constant off-diagonal coefficients. We show that even for strong disorder the shift of the averaged pinning point of the random walk in the ensemble of random realizations of substrate disorder is indistinguishable from the pinning point of the system with preaveraged (i.e. annealed) Boltzmann weight., Comment: 16 pages, 5 figures

We consider off-diagonal correlation functions of impenetrable bosons on a lattice. By using the Jordan-Wigner transformation the one-body density matrix is represented as (Toeplitz) determinant of a matrix of fermionic Green functions. Using the replica method we calculate exactly the full long-range asymptotic behaviour of the one-body density matrix. We discuss how subleading oscillating terms, originating from short-range correlations give rise to interesting features in the momentum distribution., Comment: 10 pages. Submitted to the Focus Issue on 'Cold Atoms in Optical Lattices' of New Journal of Physics

We study correlation functions of the Calogero-Sutherland model in the whole range of the interaction parameter. Using the replica method we obtain analytical expressions for the long-distance asymptotics of the one-body density matrix in addition to the previously derived asymptotics of the pair-distribution function [D.M. Gangardt and A. Kamenev, Nucl. Phys. B, 610, 578 (2001)]. The leading analytic and non-analytic terms in the short-distance expansion of the one-body density matrix are discussed. Exact numerical results for these correlation functions are obtained using Monte Carlo techniques for all distances. The momentum distribution and static structure factor are calculated. The potential and kinetic energies are obtained using the Hellmann-Feynman theorem. Perfect agreement is found between the analytical expressions and numerical data. These results allow for the description of physical regimes of the Calogero-Sutherland model. The zero temperature phase diagram is found to be of a crossover type and includes quasi-condensation, quasi-crystallization and quasi-supersolid regimes., Comment: 17 pages, 7 figures

We study a one-dimensional (iso)spin 1/2 Bose gas with repulsive delta-function interaction by the Bethe Ansatz method and discuss the excitations above the polarized ground state. In addition to phonons the system features spin waves with a quadratic dispersion. We compute analytically and numerically the effective mass of the spin wave and show that the spin transport is greatly suppressed in the strong coupling regime, where the isospin-density (or ``spin-charge'') separation is maximal. Using a hydrodynamic approach, we study spin excitations in a harmonically trapped system and discuss prospects for future studies of two-component ultracold atomic gases., Comment: 4 pages, 1 figure

Using a scaling transformation we exactly determine the dynamics of an harmonically confined Tonks-Girardeau gas under arbitrary time variations of the trap frequency. We show how during a one-dimensional expansion a ``dynamical fermionization'' occurs as the momentum distribution rapidly approaches an ideal Fermi gas distribution, and that under a sudden change of the trap frequency the gas undergoes undamped breathing oscillations displaying alternating bosonic and fermionic character in momentum space. The absence of damping in the oscillations is a peculiarity of the truly Tonks regime., Comment: 4 pages, 2 figures, published version

We calculate the density profiles and density correlation functions of the one-dimensional Bose gas in a harmonic trap, using the exact finite-temperature solutions for the uniform case, and applying a local density approximation. The results are valid for a trapping potential which is slowly varying relative to a correlation length. They allow a direct experimental test of the transition from the weak coupling Gross-Pitaevskii regime to the strong coupling, 'fermionic' Tonks-Girardeau regime. We also calculate the average two-particle correlation which characterizes the bulk properties of the sample, and find that it can be well approximated by the value of the local pair correlation in the trap center., Comment: Final published version; updated references; 19 pages, 12 figures

We discuss the 2D Mott insulator (MI) state of a 2D array of coupled finite size 1D Bose gases. It is shown that the momentum distribution in the lattice plane is very sensitive to the interaction regime in the 1D tubes. In particular, we find that the disappearance of the interference pattern in time of flight experiments will not be a signature of the MI phase, but a clear consequence of the strongly interacting Tonks-Girardeau regime along the tubes., Comment: 4 pages, 3 figures

We discuss the theory of spin waves in non-degenerate ultra-cold gases, and compare various methods which can be used to obtain appropriate kinetic equations. We then study non-hydrodynamic situations, where the amplitude of spin waves is sufficiently large to bring the system far from local equilibrium. In the first part of the article, we compare two general methods which can be used to derive a kinetic equation for a dilute gas of atoms (bosons or fermions) with two internal states (treated as a pseudo-spin 1/2). The collisional methods are in the spirit of Boltzmann's original derivation of his kinetic equation where, at each point of space, the effects of all sorts of possible binary collisions are added. We discuss two different versions of collisional methods, the Yvon-Snider approach and the S matrix approach. The second method uses the notion of mean field, which modifies the drift term of the kinetic equation, in the line of the Landau theory of transport in quantum liquids. For a dilute cold gas, it turns out that all these derivations lead to the same drift terms in the transport equation, but differ in the precise expression of the collision integral and in higher order gradient terms. In the second part of the article, the kinetic equation is applied to spin waves in trapped ultra-cold gases. Numerical simulations are used to illustrate the strongly non-hydrodynamic character of the spin waves recently observed with trapped Rb87 atoms. The decay of the phenomenon, which takes place when the system relaxes back towards equilibrium, is also discussed, with a short comment on decoherence., Comment: To appear in Eur. Phys. J. D

We develop an analytical method for calculating local correlations in strongly interacting 1D Bose gases, based on the exactly solvable Lieb-Liniger model. The results are obtained at zero and finite temperatures. They describe the interaction-induced reduction of local many-body correlation functions and can be used for achieving and identifying the strong-coupling Tonks-Girardeau regime in experiments with cold Bose gases in the 1D regime., Comment: 8 pages, REVTeX4, published in the New Journal of Physics

We calculate the two-particle local correlation for an interacting 1D Bose gas at finite temperature and classify various physical regimes. We present the exact numerical solution by using the Yang-Yang equations and Hellmann-Feynman theorem and develop analytical approaches. Our results draw prospects for identifying the regimes of coherent output of an atom laser, and of finite-temperature ''fermionization'' through the measurement of the rates of two-body inelastic processes, such as photo-association., Comment: Final published version; minor technical changes

We consider a trapped ultra-cold gas of (non-condensed) bosons with two internal states (described by a pseudo spin) and study the stability of a longitudinal pseudo spin polarization gradient. For this purpose, we numerically solve a kinetic equation corresponding to a situation close to an experiment at JILA. It shows the presence of Castaing's instability of transverse spin polarization fluctuations at long wavelengths. This phenomenon could be used to create spontaneous transverse spin waves., Comment: 5 pages, 3 figures; equation (8) corrected; submitted to EPJ D

We discuss stability and phase coherence of 1D trapped Bose gases and find that inelastic decay processes, such as 3-body recombination, are suppressed in the strongly interacting (Tonks-Girardeau) and intermediate regimes. This is promising for achieving these regimes with a large number of particles. "Fermionization" of the system reduces the phase coherence length, and at T=0 the gas is fully phase coherent only deeply in the weakly interacting (Gross-Pitaevskii) regime., Comment: published version

We consider an ultracold gas of (non-condensed) bosons or fermions with two internal states, and study the effect of a gradient of the transition frequency between these states. When a $\pi/2$ RF pulse is applied to the sample, exchange effects during collisions transfer the atoms into internal states which depend on the direction of their velocity. This results, after a short time, in a spatial separation between the two states. A kinetic equation is solved analytically and numerically; the results agree well with the recent observations of Lewandowski et al., Comment: Accepted version, to appear in PRL

We present a study of the behaviour of metastable vortex states in mesoscopic superconductors. Our analysis relies on the London limit within which it is possible to derive closed analytical expressions for the magnetic field and the Gibbs free energy. We consider in particular the situation where the vortices are symmetrically distributed along a closed ring. There, we obtain expressions for the confining Bean-Livingston barrier and for the magnetization which turns out to be paramagnetic away from thermodynamic equilibrium. At low temperature, the barrier is high enough for this regime to be observable. We propose also a local description of both thermodynamic and metastable states based on elementary topological considerations; we find structural phase transitions of vortex patterns between these metastable states and we calculate the corresponding critical fields., Comment: 24 pages, 20 figures

We present an analysis of the magnetic response of a mesoscopic superconductor, i.e. a system of sizes comparable to the coherence length and to the London penetration depth. Our approach is based on special properties of the two dimensional Ginzburg-Landau equations, satisfied at the dual point $(\kappa = \frac{1}{\sqrt{2}}).$ Closed expressions for the free energy and the magnetization of the superconductor are derived. A perturbative analysis in the vicinity of the dual point allows us to take into account vortex interactions, using a new scaling result for the free energy. In order to characterize the vortex/current interactions, we study vortex configurations that are out of thermodynamical equilibrium. Our predictions agree with the results of recent experiments performed on mesoscopic aluminium disks., Comment: revtex, 20 pages, 9 figures