arXiv subjects

P. G. Kevrekidis

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

At least 73 records · Page 4Linked to original sources

arXiv2023

Two-Component 3D Atomic Bose-Einstein Condensates Support Complex Stable Patterns

We report the computational discovery of complex, topologically charged, and spectrally stable states in three-dimensional multi-component nonlinear wave systems of nonlinear Schr{ö}dinger type. While our computations relate to two-component atomic Bose-Einstein condensates in parabolic traps, our methods can be broadly applied to high-dimensional, nonlinear systems of partial differential equations. The combination of the so-called deflation technique with a careful selection of initial guesses enables the computation of an unprecedented breadth of patterns, including ones combining vortex lines, rings, stars, and ``vortex labyrinths''. Despite their complexity, they may be dynamically robust and amenable to experimental observation, as confirmed by Bogolyubov-de Gennes spectral analysis and numerical evolution simulations.

nlin.PS↗

arXiv2023

Efficient Manipulation of Bose-Einstein Condensates in a Double-Well Potential

We pose the problem of transferring a Bose-Einstein Condensate (BEC) from one side of a double-well potential to the other as an optimal control problem for determining the time-dependent form of the potential. We derive a reduced dynamical system using a Galerkin truncation onto a finite set of eigenfunctions and find that including three modes suffices to effectively control the full dynamics, described by the Gross-Pitaevskii model of BEC. The functional form of the control is reduced to finite dimensions by using another Galerkin-type method called the chopped random basis (CRAB) method, which is then optimized by a genetic algorithm called differential evolution (DE). Finally, we discuss the extent to which the reduction-based optimal control strategy can be refined by means of including more modes in the Galerkin reduction.

nlin.PS↗

arXiv2022

Schwarzschild-Finsler-Randers spacetime: Dynamical analysis, Geodesics and Deflection Angle

In this work, we extend the study of Schwarzschild-Finsler-Randers (SFR) spacetime previously investigated by a subset of the present authors (Triantafyllopoulos et al. in Eur Phys J C 80(12):1200, 2020; Kapsabelis et al. in Eur Phys J C 81(11):990, 2021). We will examine the dynamical analysis of geodesics which provides the derivation of the energy and the angular momentum of a particle moving along a geodesic of SFR spacetime. This study allows us to compare our model with the corresponding of general relativity (GR). In addition, the effective potential of SFR model is examined and it is compared with the effective potential of GR. The phase portraits generated by these effective potentials are also compared. Finally we deal with the derivation of the deflection angle of the SFR spacetime and we find that there is a small perturbation from the deflection angle of GR. We also derive an interesting relation between the deflection angles of SFR model and the corresponding result in the work of Shapiro et al (Phys Rev Lett 92(12):121101, 2004). These small differences are attributed to the anisotropic metric structure of the model and especially to a Randers term which provides a small deviation from the GR.

gr-qc↗

arXiv2022

Kink-Antikink Interaction Forces and Bound States in a nonlinear Schr{ö}dinger Model with Quadratic and Quartic dispersion

In the present work we explore the competition of quadratic and quartic dispersion in producing kink-like solitary waves in a model of the nonlinear Schr{ö}dinger type bearing cubic nonlinearity. We present the first 6 families of multikink solutions and explore their bifurcations as the strength of the quadratic dispersion is varied. We reveal a rich bifurcation structure for the system, connecting two-kink states with states involving 4-, as well as 6-kinks. The stability of all of these states is explored. For each family, we discuss a ``lower branch'' adhering to the energy landscape of the 2-kink states. We also, however, study in detail the ``upper branches'' bearing higher numbers of kinks. In addition to computing the stationary states and analyzing their stability within the partial differential equation model, we develop an effective particle ordinary differential equation theory that is shown to be surprisingly efficient in capturing the kink equilibria and normal (as well as unstable) modes. Finally, the results of the bifurcation analysis are corroborated by means of direct numerical simulations involving the excitation of the states in a targeted way in order to explore their instability-induced dynamics.

nlin.PS↗

arXiv2022

Asymptotic dynamics of higher-order lumps in the Davey-Stewartson II equation

A family of higher-order rational lumps on non-zero constant background of Davey-Stewartson (DS) II equation are investigated. These solutions have multiple peaks whose heights and trajectories are approximately given by asymptotical analysis. It is found that the heights are time-dependent and for large time they approach the same constant height value of the first-order fundamental lump. The resulting trajectories are considered and it is found that the scattering angle can assume arbitrary values in the interval of $(\fracπ{2}, π)$ which is markedly distinct from the necessary orthogonal scattering for the higher-order lumps on zero background. Additionally, it is illustrated that the higher-order lumps containing multi-peaked $n$-lumps can be regarded as a nonlinear superposition of $n$ first-order ones as $|t|\rightarrow\infty$.

nlin.SI↗

arXiv2022

Stability and dynamics across magnetic phases of vortex-bright type excitations in spinor Bose-Einstein condensates

The static properties, i.e., existence and stability, as well as the quench-induced dynamics of vortex-bright type excitations in two-dimensional harmonically confined spin-1 Bose-Einstein condensates are investigated. Linearly stable vortex-bright-vortex and bright-vortex-bright solutions arise in both antiferromagnetic and ferromagnetic spinor gases upon quadratic Zeeman energy shift variations. Their deformations across the relevant transitions are exposed and discussed in detail evincing also that emergent instabilities can lead to pattern formation. Spatial elongations, precessional motion and spiraling of the nonlinear excitations when exposed to finite temperatures and upon crossing the distinct phase boundaries, via quenching of the quadratic Zeeman coefficient, are unveiled. Spin-mixing processes triggered by the quench lead, among others, to changes in the waveform of the ensuing configurations. Our findings reveal an interplay between pattern formation and spin-mixing processes being accessible in contemporary cold atom experiments.

cond-mat.quant-gas↗

arXiv2022

Revisiting Multi-breathers in the discrete Klein-Gordon equation: A Spatial Dynamics Approach

We consider the existence and spectral stability of multi-breather structures in the discrete Klein-Gordon equation, both for soft and hard symmetric potentials. To obtain analytical results, we project the system onto a finite-dimensional Hilbert space consisting of the first $M$ Fourier modes, for arbitrary $M$. On this approximate system, we then take a spatial dynamics approach and use Lin's method to construct multi-breathers from a sequence of well-separated copies of the primary, single-site breather. We then locate the eigenmodes in the Floquet spectrum associated with the interaction between the individual breathers of such multi-breather states by reducing the spectral problem to a matrix equation. Expressions for these eigenmodes for the approximate, finite-dimensional system are obtained in terms of the primary breather and its kernel eigenfunctions, and these are found to be in very good agreement with the numerical Floquet spectrum results. This is supplemented with results from numerical timestepping experiments, which are interpreted using the spectral computations.

nlin.PS↗

arXiv2022

Dragging A Defect in a Droplet Bose-Einstein Condensate

In the present work we consider models of quantum droplets in the presence of a defect in the form of a laser beam moving through the respective condensates including the Lee-Huang-Yang correction. Our analysis features separately an exploration of the existence, stability, bifurcations and dynamics in 1D, 2D and 3D settings. In the absence of an analytical solution of the problem, we provide an analysis of the speed of sound and observe how the states traveling with the defect may feature a saddle-center bifurcation as the speed or the strength of the defect is modified. Relevant bifurcation diagrams are constructed systematically, and the unstable states, as well as the dynamics past the existence of stable states is monitored. The connection of the resulting states with dark solitonic patterns in 1D, vortical states in 2D and vortex rings in 3D is accordingly elucidated.

nlin.PS↗

arXiv2022

Control of $^{164}$Dy Bose-Einstein condensate phases and dynamics with dipolar anisotropy

We investigate the quench dynamics of quasi-one and two dimensional dipolar Bose-Einstein condensates (dBEC) of $^{164}$Dy atoms under the influence of a fast rotating magnetic field. The magnetic field thus controls both the magnitude and sign of the dipolar potential. We account for quantum fluctuations, critical to formation of exotic quantum droplet and supersolid phases in the extended Gross-Pitaevskii formalism, which includes the so-called Lee-Huang-Yang (LHY) correction. An analytical variational ansatz allows us to obtain the phase diagrams of the superfluid and droplet phases. The crossover from the superfluid to the supersolid phase and to single and droplet arrays is probed with particle number and dipolar interaction. The dipolar strength is tuned by rotating the magnetic field with subsequent effects on phase boundaries. Following interaction quenches across the aforementioned phases, we monitor the dynamical formation of supersolid clusters or droplet lattices. We include losses due to three-body recombination over the crossover regime, where the three-body recombination rate coefficient scales with the fourth power of the scattering length ($a_s$) or the dipole length ($a_{dd}$). For fixed values of the dimensionless parameter, $ε_{dd} = a_{dd}/a_s$, tuning the dipolar anisotropy leads to an enhancement of the droplet lifetimes.

cond-mat.quant-gas↗

arXiv2022

Dynamical Instability of 3d Stationary and Traveling Planar Dark Solitons

Here we revisit the topic of stationary and propagating solitonic excitations in self-repulsive three-dimensional Bose-Einstein condensates by quantitatively comparing theoretical analysis and associated numerical computations with our experimental results. Using fully 3d numerical simulations, we explore the existence, stability, and evolution dynamics of planar dark solitons, as well as their instability-induced decay products including solitonic vortices and vortex rings. In the trapped case and with no adjustable parameters, our numerical findings are in correspondence with experimentally observed coherent structures. Without a longitudinal trap, we identify numerically exact traveling solutions and quantify how their transverse destabilization threshold changes as a function of the solitary wave speed.

cond-mat.quant-gas↗

arXiv2022

Discrete breathers in a mechanical metamaterial

We consider a previously experimentally realized discrete model that describes a mechanical metamaterial consisting of a chain of pairs of rigid units connected by flexible hinges. Upon analyzing the linear band structure of the model, we identify parameter regimes in which this system may possess discrete breather solutions with frequencies inside the gap between optical and acoustic dispersion bands. We compute numerically exact solutions of this type for several different parameter regimes and investigate their properties and stability. Our findings demonstrate that upon appropriate parameter tuning within experimentally tractable ranges, the system exhibits a plethora of discrete breathers, with multiple branches of solutions that feature period-doubling and symmetry-breaking bifurcations, in addition to other mechanisms of stability change such as saddle-center and Hamiltonian Hopf bifurcations. The relevant stability analysis is corroborated by direct numerical computations examining the dynamical properties of the system and paving the way for potential further experimental exploration of this rich nonlinear dynamical lattice setting.

nlin.PS↗

arXiv2022

The role of mobility in the dynamics of the COVID-19 epidemic in Andalusia

Metapopulation models have been a popular tool for the study of epidemic spread over a network of highly populated nodes (cities, provinces, countries) and have been extensively used in the context of the ongoing COVID-19 pandemic. In the present work, we revisit such a model, bearing a particular case example in mind, namely that of the region of Andalusia in Spain during the period of the summer-fall of 2020 (i.e., between the first and second pandemic waves). Our aim is to consider the possibility of incorporation of mobility across the province nodes focusing on mobile-phone time dependent data, but also discussing the comparison for our case example with a gravity model, as well as with the dynamics in the absence of mobility. Our main finding is that mobility is key towards a quantitative understanding of the emergence of the second wave of the pandemic and that the most accurate way to capture it involves dynamic (rather than static) inclusion of time-dependent mobility matrices based on cell-phone data. Alternatives bearing no mobility are unable to capture the trends revealed by the data in the context of the metapopulation model considered herein.

physics.soc-ph↗

arXiv2022

Dispersive Shock Waves in Lattices: A Dimension Reduction Approach

Dispersive shock waves (DSWs), which connect states of different amplitude via a modulated wave train, form generically in nonlinear dispersive media subjected to abrupt changes in state. The primary tool for the analytical study of DSWs is Whitham's modulation theory. While this framework has been successfully employed in many space-continuous settings to describe DSWs, the Whitham modulation equations are virtually intractable in most spatially discrete systems. In this article, we illustrate the relevance of the reduction of the DSW dynamics to a planar ODE in a broad class of lattice examples. Solutions of this low-dimensional ODE accurately describe the orbits of the DSW in self-similar coordinates and the local averages in a manner consistent with the modulation equations. We use data-driven and quasi-continuum approaches within the context of a discrete system of conservation laws to demonstrate how the underlying low dimensional structure of DSWs can be identified and analyzed. The connection of these results to Whitham modulation theory is also discussed.

nlin.PS↗

arXiv2022

Theoretical and numerical evidence for the potential realization of the Peregrine soliton in repulsive two-component Bose-Einstein condensates

The present work is motivated by the recent experimental realization of the Townes soliton in an effective two-component Bose-Einstein condensate by B. Bakkali-Hassan et al. [Phys. Rev. Lett. 127, 023603 (2021)]. Here, we use a similar multicomponent platform to exemplify theoretically and numerically, within the mean-field Gross-Pitaevskii framework, the potential toward the experimental realization of a different fundamental wave structure, namely the Peregrine soliton. Leveraging the effective attractive interaction produced within the mixture's minority species in the immiscible regime, we illustrate how initialization of the condensate with a suitable power-law decaying spatial density pattern yields the robust emergence of the Peregrine wave in the absence and in the presence of a parabolic trap. We then showcase the spontaneous emergence of the Peregrine soliton via a suitably crafted wide Gaussian initialization, again both in the homogeneous case and in the trap scenario. It is also found that narrower wave packets may result in periodic revivals of the Peregrine soliton, while broader ones give rise to a cascade of Peregrine solitons arranged in a so-called Christmas-tree structure. Strikingly, the persistence of these rogue-wave structures is demonstrated in certain temperature regimes as well as in the presence of transversal excitations through three-dimensional computations in a quasi-one-dimensional regime. This proof-of-principle illustration is expected to represent a practically feasible way to generate and observe this rogue wave in realistic current ultracold atom experimental settings.

cond-mat.quant-gas↗

arXiv2022

Mixed dispersion nonlinear Schrödinger equation in higher dimensions: theoretical analysis and numerical computations

In the present work we provide a characterization of the ground states of a higher-dimensional quadratic-quartic model of the nonlinear Schr{ö}dinger class with a combination of a focusing biharmonic operator with either an isotropic or an anisotropic defocusing Laplacian operator (at the linear level) and power-law nonlinearity. Examining principally the prototypical example of dimension $d=2$, we find that instability arises beyond a certain threshold coefficient of the Laplacian between the cubic and quintic cases, while all solutions are stable for powers below the cubic. Above the quintic, and up to a critical nonlinearity exponent $p$, there exists a progressively narrowing range of stable frequencies. Finally, above the critical $p$ all solutions are unstable. The picture is rather similar in the anisotropic case, with the difference that even before the cubic case, the numerical computations suggest an interval of unstable frequencies. Our analysis generalizes the relevant observations for arbitrary combinations of Laplacian prefactor $b$ and nonlinearity power $p$.

nlin.PS↗

arXiv2022

Floquet solitons in square lattices: Existence, Stability and Dynamics

In the present work, we revisit a recently proposed and experimentally realized topological 2D lattice with periodically time-dependent interactions. We identify the fundamental solitons, previously observed in experiments and direct numerical simulations, as exact, exponentially localized, periodic in time solutions. This is done for a variety of phase-shift angles of the central nodes upon a period oscillation of the coupling strength. Subsequently, we perform a systematic Floquet stability analysis of the relevant structures. We analyze both their point and their continuous spectrum and find that the solutions are generically stable, aside from the possible emergence of complex quartets due to the collision of bands of continuous spectrum. The relevant instabilities become weaker as the lattice size gets larger. Finally, we also consider multi-soliton analogues of these Floquet states, inspired by the corresponding discrete nonlinear Schrödinger (DNLS) lattice. When exciting initially multiple sites in phase, we find that the solutions reflect the instability of their DNLS multi-soliton counterparts, while for configurations with multiple excited sites in alternating phases, the Floquet states are spectrally stable, again in analogy to their DNLS counterparts.

nlin.PS↗

arXiv2022

An Ising machine based on networks of subharmonic electrical resonators

We explore a case example of networks of classical electronic oscillators evolving towards the solution of complex optimization problems. We show that when driven into subharmonic response, a network of such nonlinear electrical resonators can minimize the Ising Hamiltonian on non-trivial graphs such as antiferromagnetically coupled rewired-M{ö}bius ladders. In this context, the spin-up and spin-down states of the Ising machine are represented by the oscillators' response at the even or odd driving cycles. Our experimental setting of driven nonlinear oscillators coupled via a programmable switch matrix leads to a unique energy minimizer when one such exists, and probes frustration where appropriate. Theoretical modeling of the electronic oscillators and their couplings allows us to accurately reproduce the qualitative features of the experimental results. This suggests the promise of this setup as a prototypical one for exploring the capabilities and limitations of such an unconventional computing platform.

nlin.PS↗

arXiv2022

Forced symmetry breaking as a mechanism for rogue bursts in a dissipative nonlinear dynamical lattice

We propose an alternative to the standard mechanisms for the formation of rogue waves in a non-conservative, nonlinear lattice dynamical system. We consider an ODE system that features regular periodic bursting arising from forced symmetry breaking. We then connect such potentially exploding units via a diffusive lattice coupling and investigate the resulting spatio-temporal dynamics for different types of initial conditions (localized or extended). We find that in both cases, particular oscillators undergo extremely fast and large amplitude excursions, resembling a rogue wave burst. Furthermore, the probability distribution of different amplitudes exhibits bimodality, with peaks at both vanishing and very large amplitude. While this phenomenology arises over a range of coupling strengths, for large values thereof the system eventually synchronizes and the above phenomenology is suppressed. We use both distributed (such as a synchronization order parameter) and individual oscillator diagnostics to monitor the dynamics and identify potential precursors to large amplitude excursions. We also examine similar behavior with amplitude-dependent diffusive coupling.

nlin.PS↗