Non-Gibbs states on a Bose-Hubbard lattice

We study the equilibrium properties of the repulsive quantum Bose-Hubbard model at high temperatures in arbitrary dimensions, with and without disorder. In its microcanonical setting the model conserves energy and particle number. The microcanonical dynamics is characterized by a pair of two densities: energy density $\varepsilon$ and particle number density $n$. The macrocanonical Gibbs distribution also depends on two parameters: the inverse nonnegative temperature $\beta$ and the chemical potential $\mu$. We prove the existence of non-Gibbs states, that is, pairs $(\varepsilon,n)$ which cannot be mapped onto $(\beta,\mu)$. The separation line in the density control parameter space between Gibbs and non-Gibbs states $\varepsilon \sim n^2$ corresponds to infinite temperature $\beta=0$. The non-Gibbs phase cannot be cured into a Gibbs one within the standard Gibbs formalism using negative temperatures.Comment: 8 pages, 1 figure, misprints correcte

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

Friction and diffusion of matter-wave bright solitons

We consider the motion of a matter-wave bright soliton under the influence of a cloud of thermal particles. In the ideal one-dimensional system, the scattering process of the quasiparticles with the soliton is reflectionless, however, the quasiparticles acquire a phase shift. In the realistic system of a Bose-Einstein condensate confined in a tight waveguide trap, the transverse degrees of freedom generate an extra but small nonlinearity in the system which gives rise to finite reflection and leads to dissipative motion of the soliton. We calculate the velocity and temperature-dependent frictional force and diffusion coefficient of a matter wave bright soliton immersed in a thermal cloud

Decay of superfluid currents in the interacting one-dimensional Bose gas

We examine the superfluid properties of a 1D Bose gas in a ring trap based on the model of Lieb and Liniger. While the 1D Bose gas has nonclassical rotational inertia and exhibits quantization of velocities, the metastability of currents depends sensitively on the strength of interactions in the gas: the stronger the interactions, the faster the current decays. It is shown that the Landau critical velocity is zero in the thermodynamic limit due to the first supercurrent state, which has zero energy and finite probability of excitation. We calculate the energy dissipation rate of ring currents in the presence of weak defects, which should be observable on experimental time scales.Comment: 5 pages, 4 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

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