Modulated Amplitude Waves in Collisionally Inhomogeneous Bose-Einstein Condensates

We investigate the dynamics of an effectively one-dimensional Bose-Einstein condensate (BEC) with scattering length $a$ subjected to a spatially periodic modulation, $a=a(x)=a(x+L)$. This "collisionally inhomogeneous" BEC is described by a Gross-Pitaevskii (GP) equation whose nonlinearity coefficient is a periodic function of $x$. We transform this equation into a GP equation with constant coefficient $a$ and an additional effective potential and study a class of extended wave solutions of the transformed equation. For weak underlying inhomogeneity, the effective potential takes a form resembling a superlattice, and the amplitude dynamics of the solutions of the constant-coefficient GP equation obey a nonlinear generalization of the Ince equation. In the small-amplitude limit, we use averaging to construct analytical solutions for modulated amplitude waves (MAWs), whose stability we subsequently examine using both numerical simulations of the original GP equation and fixed-point computations with the MAWs as numerically exact solutions. We show that "on-site" solutions, whose maxima correspond to maxima of $a(x)$, are significantly more stable than their "off-site" counterparts.Comment: 25 pages, 10 figures (many with several parts), to appear in Physica D; higher resolution versions of some figures are available at http://www.its.caltech.edu/~mason/paper

Static and rotating domain-wall crosses in Bose-Einstein condensates

For a Bose-Einstein condensate (BEC) in a two-dimensional (2D) trap, we introduce cross patterns, which are generated by intersection of two domain walls (DWs) separating immiscible species, with opposite signs of the wave functions in each pair of sectors filled by the same species. The cross pattern remains stable up to the zero value of the immiscibility parameter $|\Delta |$, while simpler rectilinear (quasi-1D) DWs exist only for values of $|\Delta |$ essentially exceeding those in BEC mixtures (two spin states of the same isotope) currently available to the experiment. Both symmetric and asymmetric cross configurations are investigated, with equal or different numbers $N_{1,2}$ of atoms in the two species. In rotating traps, ``propellers'' (stable revolving crosses) are found too. A full stability region for of the crosses and propellers in the system's parameter space is identified, unstable crosses evolving into arrays of vortex-antivortex pairs. Stable rotating rectilinear DWs are found too, at larger vlues of $|\Delta |$. All the patterns produced by the intersection of three or more DWs are unstable, rearranging themselves into ones with two DWs. Optical propellers are also predicted in a twisted nonlinear photonic-crystal fiber carrying two different wavelengths or circular polarizations, which can be used for applications to switching and routing.Comment: 9 pages, 10 figures, Phys. Rev. A (in press

Fermi-Polaron: Diagrammatic Monte Carlo for Divergent Sign-Alternating Series

Diagrammatic Monte Carlo approach is applied to a problem of a single spin-down fermion resonantly interacting with the sea of ideal spin-up fermions. On one hand, we develop a generic, sign-problem tolerant, method of exact numerical solution of polaron-type models. On the other hand, our solution is important for understanding the phase diagram and properties of the BCS-BEC crossover in the strongly imbalanced regime. This is the first, and possibly characteristic, example of how the Monte Carlo approach can be applied to a divergent sign-alternating diagrammatic series.Comment: 4 pages, 7 figure

Families of Matter-Waves for Two-Component Bose-Einstein Condensates

We produce several families of solutions for two-component nonlinear Schr\"{o}dinger/Gross-Pitaevskii equations. These include domain walls and the first example of an antidark or gray soliton in the one component, bound to a bright or dark soliton in the other. Most of these solutions are linearly stable in their entire domain of existence. Some of them are relevant to nonlinear optics, and all to Bose-Einstein condensates (BECs). In the latter context, we demonstrate robustness of the structures in the presence of parabolic and periodic potentials (corresponding, respectively, to the magnetic trap and optical lattices in BECs).Comment: 6 pages, 4 figures, EPJD in pres

Unstaggered-staggered solitons in two-component discrete nonlinear Schr\"{o}dinger lattices

We present stable bright solitons built of coupled unstaggered and staggered components in a symmetric system of two discrete nonlinear Schr\"{o}dinger (DNLS) equations with the attractive self-phase-modulation (SPM) nonlinearity, coupled by the repulsive cross-phase-modulation (XPM) interaction. These mixed modes are of a "symbiotic" type, as each component in isolation may only carry ordinary unstaggered solitons. The results are obtained in an analytical form, using the variational and Thomas-Fermi approximations (VA and TFA), and the generalized Vakhitov-Kolokolov (VK) criterion for the evaluation of the stability. The analytical predictions are verified against numerical results. Almost all the symbiotic solitons are predicted by the VA quite accurately, and are stable. Close to a boundary of the existence region of the solitons (which may feature several connected branches), there are broad solitons which are not well approximated by the VA, and are unstable

Effective Confinement as Origin of the Equivalence of Kinetic Temperature and Fluctuation-Dissipation Ratio in a Dense Shear Driven Suspension

We study response and velocity autocorrelation functions for a tagged particle in a shear driven suspension governed by underdamped stochastic dynamics. We follow the idea of an effective confinement in dense suspensions and exploit a time-scale separation between particle reorganization and vibrational motion. This allows us to approximately derive the fluctuation-dissipation theorem in a "hybrid" form involving the kinetic temperature as an effective temperature and an additive correction term. We show numerically that even in a moderately dense suspension the latter is negligible. We discuss similarities and differences with a simple toy model, a single trapped particle in shear flow

Interpretation of the in-plane infrared response of the high-Tc cuprate superconductors involving spin fluctuations revisited

The in-plane infrared response of the high-Tc cuprate superconductors was studied using the spin-fermion model, where charged quasiparticles of the copper-oxygen planes are coupled to spin fluctuations. First, we analyzed structures of the superconducting-state conductivity reflecting the coupling of the quasiparticles to the resonance mode observed by neutron scattering. The conductivity computed with the input spin susceptibility in the simple form of the mode exhibits two prominent features: an onset of the real part of the conductivity starting around the frequency of the mode omega_{0} and a maximum of a related function W(omega), roughly proportional to the second derivative of the scattering rate, centered approximately at omega=omega_{0}+Delta_{0}/hbar, where Delta_{0} is the maximum value of the superconducting gap. The two structures are well known from earlier studies. Their physical meaning, however, has not been sufficiently elucidated thus far. Our analysis involving quasiparticle spectral functions provides a clear interpretation. Second, we explored the role played by the spin-fluctuation continuum. Third, we investigated the temperature dependence of the conductivity, of the intraband spectral weight, and of the effective kinetic energy. The changes of the latter two quantities below Tc are determined by the formation of the gap, by a feedback effect of the spin fluctuations on the quasiparticles, and by a significant shift of the chemical potential.Comment: 20 pages, 18 figures, submitted to Physical Review

Helical vs. fundamental solitons in optical fibers

We consider solitons in a nonlinear optical fiber with a single polarization in a region of parameters where it carries exactly two distinct modes, the fundamental one and the first-order helical mode. From the viewpoint of applications to dense-WDM communication systems, this opens way to double the number of channels carried by the fiber. Aside from that, experimental observation of helical (spinning) solitons and collisions between them and with fundamental solitons are issues of fundamental interest. We introduce a system of coupled nonlinear Schroedinger equations for fundamental and helical modes, which have nonstandard values of the cross-phase-modulation coupling constants, and investigate, analytically and numerically, results of "complete" and "incomplete" collisions between solitons carried by the two modes. We conclude that the collision-induced crosstalk is partly attenuated in comparison with the usual WDM system, which sometimes may be crucially important, preventing merger of the colliding solitons into a breather. The interaction between the two modes is found to be additionally strongly suppressed in comparison with that in the WDM system in the case when a dispersion-shifted or dispersion-compensated fiber is used.Comment: a plain latex file with the text and two ps files with figures. Physica Scripta, in pres

Influence of a temperature-dependent shear viscosity on the azimuthal asymmetries of transverse momentum spectra in ultrarelativistic heavy-ion collisions

We study the influence of a temperature-dependent shear viscosity over entropy density ratio $\eta/s$, different shear relaxation times $\tau_\pi$, as well as different initial conditions on the transverse momentum spectra of charged hadrons and identified particles. We investigate the azimuthal flow asymmetries as a function of both collision energy and centrality. The elliptic flow coefficient turns out to be dominated by the hadronic viscosity at RHIC energies. Only at higher collision energies the impact of the viscosity in the QGP phase is visible in the flow asymmetries. Nevertheless, the shear viscosity near the QCD transition region has the largest impact on the collective flow of the system. We also find that the centrality dependence of the elliptic flow is sensitive to the temperature dependence of $\eta/s$.Comment: 13 pages, 20 figure

Transfer and scattering of wave packets by a nonlinear trap

In the framework of a one-dimensional model with a tightly localized self-attractive nonlinearity, we study the formation and transfer (dragging) of a trapped mode by "nonlinear tweezers", as well as the scattering of coherent linear wave packets on the stationary localized nonlinearity. The use of the nonlinear trap for the dragging allows one to pick up and transfer the relevant structures without grabbing surrounding "garbage". A stability border for the dragged modes is identified by means of of analytical estimates and systematic simulations. In the framework of the scattering problem, the shares of trapped, reflected, and transmitted wave fields are found. Quasi-Airy stationary modes with a divergent norm, that may be dragged by the nonlinear trap moving at a constant acceleration, are briefly considered too.Comment: Phys. Rev. E in pres