arXiv subjects

P. G. Kevrekidis

Publications and source records attributed to P. G. Kevrekidis.

At least 343 records · Page 19Linked to original sources

arXiv2012

Characteristics of Two-Dimensional Quantum Turbulence in a Compressible Superfluid

Under suitable forcing a fluid exhibits turbulence, with characteristics strongly affected by the fluid's confining geometry. Here we study two-dimensional quantum turbulence in a highly oblate Bose-Einstein condensate in an annular trap. As a compressible quantum fluid, this system affords a rich phenomenology, allowing coupling between vortex and acoustic energy. Small-scale stirring generates an experimentally observed disordered vortex distribution that evolves into large-scale flow in the form of a persistent current. Numerical simulation of the experiment reveals additional characteristics of two-dimensional quantum turbulence: spontaneous clustering of same-circulation vortices, and an incompressible energy spectrum with $k^{-5/3}$ dependence for low wavenumbers $k$ and $k^{-3}$ dependence for high $k$.

cond-mat.quant-gas↗

arXiv2012

Beating dark-dark solitons in Bose-Einstein condensates

Motivated by recent experimental results, we study beating dark-dark solitons as a prototypical coherent structure that emerges in two-component Bose-Einstein condensates. We showcase their connection to dark- bright solitons via SO(2) rotation, and infer from it both their intrinsic beating frequency and their frequency of oscillation inside a parabolic trap. We identify them as exact periodic orbits in the Manakov limit of equal inter- and intra-species nonlinearity strengths with and without the trap and showcase the persistence of such states upon weak deviations from this limit. We also consider large deviations from the Manakov limit illustrating that this breathing state may be broken apart into dark-antidark soliton states. Finally, we consider the dynamics and interactions of two beating dark-dark solitons in the absence and in the presence of the trap, inferring their typically repulsive interaction.

cond-mat.quant-gas↗

arXiv2012

Spatial solitons under competing linear and nonlinear diffractions

We introduce a general model which augments the one-dimensional nonlinear Schrödinger (NLS) equation by nonlinear-diffraction terms competing with the linear diffraction. The new terms contain two irreducible parameters and admit a Hamiltonian representation in a form natural for optical media. The equation serves as a model for spatial solitons near the supercollimation point in nonlinear photonic crystals. In the framework of this model, a detailed analysis of the fundamental solitary waves is reported, including the variational approximation (VA), exact analytical results, and systematic numerical computations. The Vakhitov-Kolokolov (VK) criterion is used to precisely predict the stability border for the solitons, which is found in an exact analytical form, along with the largest total power (norm) that the waves may possess. Past a critical point, collapse effects are observed, caused by suitable perturbations. Interactions between two identical parallel solitary beams are explored by dint of direct numerical simulations. It is found that in-phase solitons merge into robust or collapsing pulsons, depending on the strength of the nonlinear diffraction.

math-ph↗

arXiv2012

Existence, Stability, and Dynamics of Bright Vortices in the Cubic-Quintic Nonlinear Schrödinger Equation

We revisit the topic of the existence and azimuthal modulational stability of solitary vortices (alias vortex solitons) in the two-dimensional (2D) cubic-quintic nonlinear Schr{ö}dinger equation. We develop a semi-analytical approach, assuming that the vortex soliton is relatively narrow, and thus splitting the full 2D equation into radial and azimuthal 1D equations. A variational approach is used to predict the radial shape of the vortex soliton, using the radial equation, yielding results very close to those obtained from numerical solutions. Previously known existence bounds for the solitary vortices are recovered by means of this approach. The 1D azimuthal equation of motion is used to analyze the modulational instability of the vortex solitons. The semi-analytical predictions -- in particular, that for the critical intrinsic frequency of the vortex soliton at the instability border -- are compared to systematic 2D simulations. We also compare our findings to those reported in earlier works, which featured some discrepancies. We then perform a detailed computational study of collisions between stable vortices with different topological charges. Borders between elastic and destructive collisions are identified.

nlin.PS↗

arXiv2011

Discrete Breathers in a Nonlinear Polarizability Model of Ferroelectrics

We present a family of discrete breathers, which exists in a nonlinear polarizability model of ferroelectric materials. The core-shell model is set up in its non-dimensionalized Hamiltonian form and its linear spectrum is examined. Subsequently, seeking localized solutions in the gap of the linear spectrum, we establish that numerically exact and potentially stable discrete breathers exist for a wide range of frequencies therein. In addition, we present nonlinear normal mode, extended spatial profile solutions from which the breathers bifurcate, as well as other associated phenomena such as the formation of phantom breathers within the model. The full bifurcation picture of the emergence and disappearance of the breathers is complemented by direct numerical simulations of their dynamical instability, when the latter arises.

physics.comp-ph↗

arXiv2011

Statics and dynamics of atomic dark-bright solitons in the presence of delta-like impurities

Adopting a mean-field description for a two-component atomic Bose-Einstein condensate, we study the stat- ics and dynamics of dark-bright solitons in the presence of localized impurities. We use adiabatic perturbation theory to derive an equation of motion for the dark-bright soliton center. We show that, counter-intuitively, an attractive (repulsive) delta-like impurity, acting solely on the bright soliton component, induces an effective localized barrier (well) in the effective potential felt by the soliton; this way, dark-bright solitons are reflected from (transmitted through) attractive (repulsive) impurities. Our analytical results for the small-amplitude oscil- lations of solitons are found to be in good agreement with results obtained via a Bogoliubov-de Gennes analysis and direct numerical simulations.

cond-mat.quant-gas↗

arXiv2011

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.

nlin.PS↗

arXiv2011

Stationary states of a nonlinear Schrödinger lattice with a harmonic trap

We study a discrete nonlinear Schrödinger lattice with a parabolic trapping potential. The model, describing, e.g., an array of repulsive Bose-Einstein condensate droplets confined in the wells of an optical lattice, is analytically and numerically investigated. Starting from the linear limit of the problem, we use global bifurcation theory to rigorously prove that - in the discrete regime - all linear states lead to nonlinear generalizations thereof, which assume the form of a chain of discrete dark solitons (as the density increases). The stability of the ensuing nonlinear states is studied and it is found that the ground state is stable, while the excited states feature a chain of stability/instability bands. We illustrate the mechanisms under which discreteness destabilizes the dark-soliton configurations, which become stable only inside the continuum regime. Continuation from the anti-continuum limit is also considered, and a rich bifurcation structure is revealed.

cond-mat.quant-gas↗

arXiv2011

Dark-bright solitons in Bose-Einstein condensates at finite temperatures

We study the dynamics of dark-bright solitons in binary mixtures of Bose gases at finite temperature using a system of two coupled dissipative Gross-Pitaevskii equations. We develop a perturbation theory for the two-component system to derive an equation of motion for the soliton centers and identify different temperature-dependent damping regimes. We show that the effect of the bright ("filling") soliton component is to partially stabilize "bare" dark solitons against temperature-induced dissipation, thus providing longer lifetimes. We also study analytically thermal effects on dark-bright soliton "molecules" (i.e., two in- and out-of-phase dark-bright solitons), showing that they undergo expanding oscillations while interacting. Our analytical findings are in good agreement with results obtained via a Bogoliubov-de Gennes analysis and direct numerical simulations.

cond-mat.quant-gas↗

arXiv2011

Rabi flopping induces spatial demixing dynamics

We experimentally investigate the mixing/demixing dynamics of Bose-Einstein condensates in the presence of a linear coupling between two internal states. The observed amplitude reduction of the Rabi oscillations can be understood as a result of demixing dynamics of dressed states as experimentally confirmed by reconstructing the spatial profile of dressed state amplitudes. The observations are in quantitative agreement with numerical integration of coupled Gross-Pitaevskii equations without free parameters, which also reveals the criticality of the dynamics on the symmetry of the system. Our observations demonstrate new possibilities for changing effective atomic interactions and studying critical phenomena.

cond-mat.quant-gas↗

arXiv2011

Dark-bright ring solitons in Bose-Einstein condensates

We study dark-bright ring solitons in two-component Bose-Einstein condensates. In the limit of large densities of the dark component, we describe the soliton dynamics by means of an equation of motion for the ring radius. The presence of the bright, "filling" species is demonstrated to have a stabilizing effect on the ring dark soliton. Near the linear limit, we discuss the symmetry-breaking bifurcations of dark-bright soliton stripes and vortex-bright soliton clusters from the dark-bright ring and relate the stabilizing effect of filling to changes in the bifurcation diagram. Finally, we show that stabilization by means of a second component is not limited to the radially symmetric structures, but can also be observed in a cross-like dark-bright soliton configuration.

cond-mat.quant-gas↗

arXiv2011

Guiding-center dynamics of vortex dipoles in Bose-Einstein condensates

A quantized vortex dipole is the simplest vortex molecule, comprising two counter-circulating vortex lines in a superfluid. Although vortex dipoles are endemic in two-dimensional superfluids, the precise details of their dynamics have remained largely unexplored. We present here several striking observations of vortex dipoles in dilute-gas Bose-Einstein condensates, and develop a vortex-particle model that generates vortex line trajectories that are in good agreement with the experimental data. Interestingly, these diverse trajectories exhibit essentially identical quasi-periodic behavior, in which the vortex lines undergo stable epicyclic orbits.

cond-mat.quant-gas↗

arXiv2011

Fluctuating and dissipative dynamics of dark solitons in quasi-condensates

The fluctuating and dissipative dynamics of matter-wave dark solitons within harmonically trapped, partially condensed Bose gases is studied both numerically and analytically. A study of the stochastic Gross-Pitaevskii equation, which correctly accounts for density and phase fluctuations at finite temperatures, reveals dark soliton decay times to be lognormally distributed at each temperature, thereby characterizing the previously predicted long lived soliton trajectories within each ensemble of numerical realizations (S.P. Cockburn {\it et al.}, Phys. Rev. Lett. 104, 174101 (2010)). Expectation values for the average soliton lifetimes extracted from these distributions are found to agree well with both numerical and analytic predictions based upon the dissipative Gross-Pitaevskii model (with the same {\it ab initio} damping). Probing the regime for which $0.8 k_{B}T < μ< 1.6 k_{B}T$, we find average soliton lifetimes to scale with temperature as $τ\sim T^{-4}$, in agreement with predictions previously made for the low-temperature regime $k_{B}T\llμ$. The model is also shown to capture the experimentally-relevant decrease in the visibility of an oscillating soliton due to the presence of background fluctuations.

cond-mat.quant-gas↗

arXiv2011

Dynamics of Vortex Dipoles in Confined Bose-Einstein Condensates

We present a systematic theoretical analysis of the motion of a pair of straight counter-rotating vortex lines within a trapped Bose-Einstein condensate. We introduce the dynamical equations of motion, identify the associated conserved quantities, and illustrate the integrability of the ensuing dynamics. The system possesses a stationary equilibrium as a special case in a class of exact solutions that consist of rotating guiding-center equilibria about which the vortex lines execute periodic motion; thus, the generic two-vortex motion can be classified as quasi-periodic. We conclude with an analysis of the linear and nonlinear stability of these stationary and rotating equilibria.

cond-mat.quant-gas↗

arXiv2011

On the existence of solitary traveling waves for generalized Hertzian chains

We consider the question of existence of "bell-shaped" (i.e. non-increasing for x>0 and non-decreasing for x<0) traveling waves for the strain variable of the generalized Hertzian model describing, in the special case of a p=3/2 exponent, the dynamics of a granular chain. The proof of existence of such waves is based on the English and Pego [Proceedings of the AMS 133, 1763 (2005)] formulation of the problem. More specifically, we construct an appropriate energy functional, for which we show that the constrained minimization problem over bell-shaped entries has a solution. We also provide an alternative proof of the Friesecke-Wattis result [Comm. Math. Phys 161, 394 (1994)], by using the same approach (but where the minimization is not constrained over bell-shaped curves). We briefly discuss and illustrate numerically the implications on the doubly exponential decay properties of the waves, as well as touch upon the modifications of these properties in the presence of a finite precompression force in the model.

nlin.PS↗

arXiv2011

Multiple dark-bright solitons in atomic Bose-Einstein condensates

We present experimental results and a systematic theoretical analysis of dark-br ight soliton interactions and multiple-dark-bright soliton complexes in atomic t wo-component Bose-Einstein condensates. We study analytically the interactions b etween two-dark-bright solitons in a homogeneous condensate and, then, extend ou r considerations to the presence of the trap. An effective equation of motion is derived for the dark-bright soliton center and the existence and stability of stationary two-dark-bright soliton states is illustrated (with the bright components being either in- or out-of-phase). The equation of motion provides the characteristic oscillation frequencies of the solitons, in good agreement with the eigenfrequencies of the anomalous modes of the system.

cond-mat.quant-gas↗

arXiv2011

Discrete breathers in a nonlinear electric line: Modeling, Computation and Experiment

We study experimentally and numerically the existence and stability properties of discrete breathers in a periodic nonlinear electric line. The electric line is composed of single cell nodes, containing a varactor diode and an inductor, coupled together in a periodic ring configuration through inductors and driven uniformly by a harmonic external voltage source. A simple model for each cell is proposed by using a nonlinear form for the varactor characteristics through the current and capacitance dependence on the voltage. For an electrical line composed of 32 elements, we find the regions, in driver voltage and frequency, where $n$-peaked breather solutions exist and characterize their stability. The results are compared to experimental measurements with good quantitative agreement. We also examine the spontaneous formation of $n$-peaked breathers through modulational instability of the homogeneous steady state. The competition between different discrete breathers seeded by the modulational instability eventually leads to stationary $n$-peaked solutions whose precise locations is seen to sensitively depend on the initial conditions.

nlin.PS↗

arXiv2011

Quasi-discrete microwave solitons in a split ring resonator-based left-handed coplanar waveguide

We study the propagation of quasi-discrete microwave solitons in a nonlinear left-handed coplanar waveguide coupled with split ring resonators. By considering the relevant transmission line analogue, we derive a nonlinear lattice model which is studied analytically by means of a quasi-discrete approximation. We derive a nonlinear Schr{ö}dinger equation, and find that the system supports bright envelope soliton solutions in a relatively wide subinterval of the left-handed frequency band. We perform systematic numerical simulations, in the framework of the nonlinear lattice model, to study the propagation properties of the quasi-discrete microwave solitons. Our numerical findings are in good agreement with the analytical predictions, and suggest that the predicted structures are quite robust and may be observed in experiments.

nlin.PS↗