Modified Kuramoto-Sivashinsky equation: stability of stationary solutions and the consequent dynamics

We study the effect of a higher-order nonlinearity in the standard Kuramoto-Sivashinsky equation: \partial_x \tilde G(H_x). We find that the stability of steady states depends on dv/dq, the derivative of the interface velocity on the wavevector q of the steady state. If the standard nonlinearity vanishes, coarsening is possible, in principle, only if \tilde G is an odd function of H_x. In this case, the equation falls in the category of the generalized Cahn-Hilliard equation, whose dynamical behavior was recently studied by the same authors. Instead, if \tilde G is an even function of H_x, we show that steady-state solutions are not permissible.Comment: 4 page

Infrared behavior and spectral function of a Bose superfluid at zero temperature

In a Bose superfluid, the coupling between transverse (phase) and longitudinal fluctuations leads to a divergence of the longitudinal correlation function, which is responsible for the occurrence of infrared divergences in the perturbation theory and the breakdown of the Bogoliubov approximation. We report a non-perturbative renormalization-group (NPRG) calculation of the one-particle Green function of an interacting boson system at zero temperature. We find two regimes separated by a characteristic momentum scale $k_G$ ("Ginzburg" scale). While the Bogoliubov approximation is valid at large momenta and energies, |\p|,|\w|/c\gg k_G (with $c$ the velocity of the Bogoliubov sound mode), in the infrared (hydrodynamic) regime |\p|,|\w|/c\ll k_G the normal and anomalous self-energies exhibit singularities reflecting the divergence of the longitudinal correlation function. In particular, we find that the anomalous self-energy agrees with the Bogoliubov result \Sigan(\p,\w)\simeq\const at high-energies and behaves as \Sigan(\p,\w)\sim (c^2\p^2-\w^2)^{(d-3)/2} in the infrared regime (with $d$ the space dimension), in agreement with the Nepomnyashchii identity \Sigan(0,0)=0 and the predictions of Popov's hydrodynamic theory. We argue that the hydrodynamic limit of the one-particle Green function is fully determined by the knowledge of the exponent $3-d$ characterizing the divergence of the longitudinal susceptibility and the Ward identities associated to gauge and Galilean invariances. The infrared singularity of \Sigan(\p,\w) leads to a continuum of excitations (coexisting with the sound mode) which shows up in the one-particle spectral function.Comment: v1) 23 pages, 11 figures. v2) Changes following referee's comments. To appear in Phys. Rev.A. v3) Typos correcte

Non-perturbative renormalization-group approach to zero-temperature Bose systems

We use a non-perturbative renormalization-group technique to study interacting bosons at zero temperature. Our approach reveals the instability of the Bogoliubov fixed point when $d\leq 3$ and yields the exact infrared behavior in all dimensions $d>1$ within a rather simple theoretical framework. It also enables to compute the low-energy properties in terms of the parameters of a microscopic model. In one-dimension and for not too strong interactions, it yields a good picture of the Luttinger-liquid behavior of the superfluid phase.Comment: v1) 6 pages, 8 figures; v2) added references; v3) corrected typo

Unified picture of superfluidity: From Bogoliubov's approximation to Popov's hydrodynamic theory

Using a non-perturbative renormalization-group technique, we compute the momentum and frequency dependence of the anomalous self-energy and the one-particle spectral function of two-dimensional interacting bosons at zero temperature. Below a characteristic momentum scale $k_G$, where the Bogoliubov approximation breaks down, the anomalous self-energy develops a square root singularity and the Goldstone mode of the superfluid phase (Bogoliubov sound mode) coexists with a continuum of excitations, in agreement with the predictions of Popov's hydrodynamic theory. Thus our results provide a unified picture of superfluidity in interacting boson systems and connect Bogoliubov's theory (valid for momenta larger than $k_G$) to Popov's hydrodynamic approach.Comment: v2) 4 pages, 4 figures v3) Revised title + minor change

Binary Quantum Turbulence Arising from Countersuperflow Instability in Two-Component Bose-Einstein Condensates

We theoretically study the development of quantum turbulence from two counter-propagating superfluids of miscible Bose-Einstein condensates by numerically solving the coupled Gross-Pitaevskii equations. When the relative velocity exceeds a critical value, the counter-superflow becomes unstable and quantized vortices are nucleated, which leads to isotropic quantum turbulence consisting of two superflows. It is shown that the binary turbulence can be realized experimentally in a trapped system.Comment: 5 pages, 3 figure

Asymmetric Fermion Superfluid with Inter- and Intra-Species Pairings

We investigate the phase structure of an asymmetric fermion superfluid with inter- and intra-species pairings. The introduction of the intra-species pairing mechanism in canonical ensemble changes significantly the phase diagram and brings in a new state with coexisting inter- and intra-species pairings. Different from the case with only inter-species pairing, all the fermion excitations are fully gapped in the region with intra-species pairing.Comment: 5 pages, 4 figure

Infrared behavior of interacting bosons at zero temperature

We review the infrared behavior of interacting bosons at zero temperature. After a brief discussion of the Bogoliubov approximation and the breakdown of perturbation theory due to infrared divergences, we present two approaches that are free of infrared divergences -- Popov's hydrodynamic theory and the non-perturbative renormalization group -- and allow us to obtain the exact infrared behavior of the correlation functions. We also point out the connection between the infrared behavior in the superfluid phase and the critical behavior at the superfluid--Mott-insulator transition in the Bose-Hubbard model.Comment: 8 pages, 4 figures. Proceedings of the 19th International Laser Physics Workshop, LPHYS'10 (Foz do Iguacu, Brazil, July 5-9, 2010

Theory of Bose-Einstein condensation for trapped atoms

We outline the general features of the conventional mean-field theory for the description of Bose-Einstein condensates at near zero temperatures. This approach, based on a phenomenological model, appears to give excellent agreement with experimental data. We argue, however, that such an approach is not rigorous and cannot contain the full effect of collisional dynamics due to the presence of the mean-field. We thus discuss an alternative microscopic approach and explain, within our new formalism, the physical origin of these effects. Furthermore, we discuss the potential formulation of a consistent finite-temperature mean-field theory, which we claim necessiates an analysis beyond the conventional treatment.Comment: 12 pages. To appear in Phil. Trans. R. Soc. Lond. A 355 (1997

Thermodynamics of a Bose-Einstein Condensate with Weak Disorder

We consider the thermodynamics of a homogeneous superfluid dilute Bose gas in the presence of weak quenched disorder. Following the zero-temperature approach of Huang and Meng, we diagonalize the Hamiltonian of a dilute Bose gas in an external random delta-correlated potential by means of a Bogoliubov transformation. We extend this approach to finite temperature by combining the Popov and the many-body T-matrix approximations. This approach permits us to include the quasi-particle interactions within this temperature range. We derive the disorder-induced shifts of the Bose-Einstein critical temperature and of the temperature for the onset of superfluidity by approaching the transition points from below, i.e., from the superfluid phase. Our results lead to a phase diagram consistent with that of the finite-temperature theory of Lopatin and Vinokur which was based on the replica method, and in which the transition points were approached from above.Comment: 11 pages, 5 figure

Countersuperflow instability in miscible two-component Bose-Einstein condensates

We study theoretically the instability of countersuperflow, i.e., two counterpropagating miscible superflows, in uniform two-component Bose-Einstein condensates. Countersuperflow instability causes mutual friction between the superfluids, causing a momentum exchange between the two condensates, when the relative velocity of the counterflow exceeds a critical value. The momentum exchange leads to nucleation of vortex rings from characteristic density patterns due to the nonlinear development of the instability. Expansion of the vortex rings drastically accelerates the momentum exchange, leading to a highly nonlinear regime caused by intervortex interaction and vortex reconnection between the rings. For a sufficiently large interaction between the two components, rapid expansion of the vortex rings causes isotropic turbulence and the global relative motion of the two condensates relaxes. The maximum vortex line density in the turbulence is proportional to the square of the relative velocity.Comment: 9 pages, 6 figure