arXiv subjects

Magnus Johansson

Publications and source records attributed to Magnus Johansson.

At least 19 recordsLinked to original sources

arXiv2025

Thresholdless nonlinearity-induced edge solitons in trimer arrays

We consider a one-dimensional discrete nonlinear Schr\"odinger (DNLS) model with Kerr-type on-site nonlinearity, where the nearest-neighbor coupling constants take two different values ordered in a three-periodic sequence. The existence of localized edge states in the linear limit (Su-Schrieffer-Heeger trimer, SSH3) is known to depend on the precise location of the edge. Here, we show that for a termination that does not support linear edge states, an arbitrarily weak on-site nonlinearity will induce an edge mode with asymptotic exponential localization, bifurcating from a linear band edge. Close to the gap edge, the shape of the mode can be analytically described in a continuum approximation as one half of a standard gap soliton. The linear stability properties of nonlinear edge modes are also discussed.

nlin.PS↗

arXiv2020

Multichannel asymmetric transmission through a dimer defect with saturable inter-site nonlinearity

We consider the asymmetric transmission properties of a Discrete Nonlinear Schr{ö}dinger type dimer with a saturable nonlinear intersite coupling between the dimer sites, in addition to a cubic onsite nonlinearity and asymmetric linear onsite potentials. In contrast to previously studied cases with pure onsite nonlinearities, the transmission coefficient for stationary transmission is shown to be a multivalued function of the transmitted intensity, in regimes of low saturability and small or moderate transmitted intensity. The corresponding backward transfer map is analyzed analytically and numerically, and shown to have either one or three distinct solutions for saturable coupling, and zero or two solutions for the purely cubic nonlinear coupling. As saturation strength is increased, the multi-solution regimes disappear through bifurcations and the single-valued regime of the onsite model is recovered. The existence of multiple solution branches yields novel mechanisms for asymmetric left/right stationary transmission: in addition to shifts of the positions of transmission peaks, peaks for transmission in one direction may correspond to nonexistence of stationary solutions propagating in the opposite direction, at the corresponding branch and transmitted intensity. Moreover, one of these transmission channels behaves as a nearly perfect mirror for incoming signals. The linear stability of the stationary solutions is analyzed, and instabilities are typically observed, and illustrated by direct numerical simulations, in regimes with large transmission coefficient. Intersite nonlinearities are found to prevent the formation of a localized dimer mode in the instability-induced dynamics. Finally, the partial reflection and transmission of a Gaussian excitation is studied, and the asymmetric transmission properties are compared to previously studied onsite models.

nlin.PS↗

arXiv2018

Nonlinear gap modes and compactons in a lattice model for spin-orbit coupled exciton-polaritons in zigzag chains

We consider a system of generalized coupled Discrete Nonlinear Schrödinger (DNLS) equations, derived as a tight-binding model from the Gross-Pitaevskii-type equations describing a zigzag chain of weakly coupled condensates of exciton-polaritons with spin-orbit (TE-TM) coupling. We focus on the simplest case when the angles for the links in the zigzag chain are $\pm π/4$ with respect to the chain axis, and the basis (Wannier) functions are cylindrically symmetric (zero orbital angular momenta). We analyze the properties of the fundamental nonlinear localized solutions, with particular interest in the discrete gap solitons appearing due to the simultaneous presence of spin-orbit coupling and zigzag geometry, opening a gap in the linear dispersion relation. In particular, their linear stability is analyzed. We also find that the linear dispersion relation becomes exactly flat at particular parameter values, and obtain corresponding compact solutions localized on two neighboring sites, with spin-up and spin-down parts $π/2$ out of phase at each site. The continuation of these compact modes into exponentially decaying gap modes for generic parameter values is studied numerically, and regions of stability are found to exist in the lower or upper half of the gap, depending on the type of gap modes.

nlin.PS↗

arXiv2015

Compactification tuning for nonlinear localized modes in sawtooth lattices

We discuss the properties of nonlinear localized modes in sawtooth lattices, in the framework of a discrete nonlinear Schrödinger model with general on-site nonlinearity. Analytic conditions for existence of exact compact three-site solutions are obtained, and explicitly illustrated for the cases of power-law (cubic) and saturable nonlinearities. These nonlinear compact modes appear as continuations of linear compact modes belonging to a flat dispersion band. While for the linear system a compact mode exists only for one specific ratio of the two different coupling constants, nonlinearity may lead to compactification of otherwise non-compact localized modes for a range of coupling ratios, at some specific power. For saturable lattices, the compactification power can be tuned by also varying the nonlinear parameter. Introducing different on-site energies and anisotropic couplings yield further possibilities for compactness tuning. The properties of strongly localized modes are investigated numerically for cubic and saturable nonlinearities, and in particular their stability over large parameter regimes is shown. Since the linear flat band is isolated, its compact modes may be continued into compact nonlinear modes both for focusing and defocusing nonlinearities. Results are discussed in relation to recent realizations of sawtooth photonic lattices.

nlin.PS↗

arXiv2014

Breather mobility and the PN potential: Brief review and recent progress

The question whether a nonlinear localized mode (discrete soliton/breather) can be mobile in a lattice has a standard interpretation in terms of the Peierls-Nabarro (PN) potential barrier. For the most commonly studied cases, the PN barrier for strongly localized solutions becomes large, rendering these essentially immobile. Several ways to improve the mobility by reducing the PN-barrier have been proposed during the last decade, and the first part gives a brief review of such scenarios in 1D and 2D. We then proceed to discuss two recently discovered novel mobility scenarios. The first example is the 2D Kagome lattice, where the existence of a highly degenerate, flat linear band allows for a very small PN-barrier and mobility of highly localized modes in a small-power regime. The second example is a 1D waveguide array in an active medium with intrinsic (saturable) gain and damping, where exponentially localized, travelling discrete dissipative solitons may exist as stable attractors. Finally, using the framework of an extended Bose-Hubbard model, we show that while quantum fluctuations destroy the mobility of slowly moving, strongly localized classical modes, coherent mobility of rapidly moving states survives even in a strongly quantum regime.

nlin.PS↗

arXiv2014

Strongly localized moving discrete dissipative breather-solitons in Kerr nonlinear media supported by intrinsic gain

We investigate the mobility of nonlinear localized modes in a generalized discrete Ginzburg-Landau type model, describing a one-dimensional waveguide array in an active Kerr medium with intrinsic, saturable gain and damping. It is shown that exponentially localized, traveling discrete dissipative breather-solitons may exist as stable attractors supported only by intrinsic properties of the medium, i.e., in absence of any external field or symmetry-breaking perturbations. Through an interplay by the gain and damping effects, the moving soliton may overcome the Peierls-Nabarro barrier, present in the corresponding conservative system, by self-induced time-periodic oscillations of its power (norm) and energy (Hamiltonian), yielding exponential decays to zero with different rates in the forward and backward directions. In certain parameter windows, bistability appears between fast modes with small oscillations, and slower, large-oscillation modes. The velocities and the oscillation periods are typically related by lattice commensurability, and exhibit period-doubling bifurcations to chaotically "walking" modes under parameter variations. If the model is augmented by inter-site Kerr nonlinearity, thereby reducing the Peierls-Nabarro barrier of the conservative system, the existence regime for moving solitons increases considerably, and a richer scenario appears including Hopf-bifurcations to incommensurately moving solutions and phase-locking intervals. Stable moving breathers also survive in presence of weak disorder.

physics.optics↗

arXiv2013

Discrete flat-band solitons in the Kagome lattice

We consider a model for a two-dimensional Kagome-lattice with defocusing nonlinearity, and show that families of localized discrete solitons may bifurcate from localized linear modes of the flat band with zero power threshold. Each family of such fundamental nonlinear modes corresponds to a unique configuration in the strong-nonlinearity limit. By choosing well-tuned dynamical perturbations, small-amplitude, strongly localized solutions from different families may be switched into each other, as well as moved between different lattice positions. In a window of small power, the lowest-energy state is a symmetry-broken localized state, which may appear spontaneously.

nlin.PS↗

arXiv2012

Discrete solitons in coupled active lasing cavities

We examine the existence and stability of discrete spatial solitons in coupled nonlinear lasing cavities (waveguide resonators), addressing the case of active defocusing media, where the gain exceeds damping in the low-amplitude limit. A new family of stable localized structures is found: these are bright and grey cavity solitons representing the connections between homogeneous and inhomogeneous states. Solitons of this type can be controlled by the discrete diffraction and are stable when the bistability of homogenous states is absent.

physics.optics↗

arXiv2011

Psi-calculi: a framework for mobile processes with nominal data and logic

The framework of psi-calculi extends the pi-calculus with nominal datatypes for data structures and for logical assertions and conditions. These can be transmitted between processes and their names can be statically scoped as in the standard pi-calculus. Psi-calculi can capture the same phenomena as other proposed extensions of the pi-calculus such as the applied pi-calculus, the spi-calculus, the fusion calculus, the concurrent constraint pi-calculus, and calculi with polyadic communication channels or pattern matching. Psi-calculi can be even more general, for example by allowing structured channels, higher-order formalisms such as the lambda calculus for data structures, and predicate logic for assertions. We provide ample comparisons to related calculi and discuss a few significant applications. Our labelled operational semantics and definition of bisimulation is straightforward, without a structural congruence. We establish minimal requirements on the nominal data and logic in order to prove general algebraic properties of psi-calculi, all of which have been checked in the interactive theorem prover Isabelle. Expressiveness of psi-calculi significantly exceeds that of other formalisms, while the purity of the semantics is on par with the original pi-calculus.

cs.LO↗

arXiv2011

Peierls-Nabarro energy surfaces and directional mobility of discrete solitons in two-dimensional saturable nonlinear Schrödinger lattices

We address the problem of directional mobility of discrete solitons in two-dimensional rectangular lattices, in the framework of a discrete nonlinear Schrödinger model with saturable on-site nonlinearity. A numerical constrained Newton-Raphson method is used to calculate two-dimensional Peierls-Nabarro energy surfaces, which describe a pseudopotential landscape for the slow mobility of coherent localized excitations, corresponding to continuous phase-space trajectories passing close to stationary modes. Investigating the two-parameter space of the model through independent variations of the nonlinearity constant and the power, we show how parameter regimes and directions of good mobility are connected to existence of smooth surfaces connecting the stationary states. In particular, directions where solutions can move with minimum radiation can be predicted from flatter parts of the surfaces. For such mobile solutions, slight perturbations in the transverse direction yield additional transverse oscillations with frequencies determined by the curvature of the energy surfaces, and with amplitudes that for certain velocities may grow rapidly. We also describe how the mobility properties and surface topologies are affected by inclusion of weak lattice anisotropy.

nlin.PS↗

arXiv2010

KAM tori in 1D random discrete nonlinear Schrödinger model?

We suggest that KAM theory could be extended for certain infinite-dimensional systems with purely discrete linear spectrum. We provide empirical arguments for the existence of square summable infinite-dimensional invariant tori in the random discrete nonlinear Schrödinger equation, appearing with a finite probability for a given initial condition with sufficiently small norm. Numerical support for the existence of a fat Cantor set of initial conditions generating almost-periodic oscillations is obtained by analyzing (i) sets of recurrent trajectories over successively larger time scales, and (ii) finite-time Lyapunov exponents. The norm region where such KAM-like tori may exist shrinks to zero when the disorder strength goes to zero and the localization length diverges.

nlin.PS↗

arXiv2010

A Fully Abstract Symbolic Semantics for Psi-Calculi

We present a symbolic transition system and bisimulation equivalence for psi-calculi, and show that it is fully abstract with respect to bisimulation congruence in the non-symbolic semantics. A psi-calculus is an extension of the pi-calculus with nominal data types for data structures and for logical assertions representing facts about data. These can be transmitted between processes and their names can be statically scoped using the standard pi-calculus mechanism to allow for scope migrations. Psi-calculi can be more general than other proposed extensions of the pi-calculus such as the applied pi-calculus, the spi-calculus, the fusion calculus, or the concurrent constraint pi-calculus. Symbolic semantics are necessary for an efficient implementation of the calculus in automated tools exploring state spaces, and the full abstraction property means the semantics of a process does not change from the original.

cs.LO↗

arXiv2009

Transmission thresholds in time-periodically driven nonlinear disordered systems

We study energy propagation in locally time-periodically driven disordered nonlinear chains. For frequencies inside the band of linear Anderson modes, three different regimes are observed with increasing driver amplitude: 1) Below threshold, localized quasiperiodic oscillations and no spreading; 2) Three different regimes in time close to threshold, with almost regular oscillations initially, weak chaos and slow spreading for intermediate times, and finally strong diffusion; 3) Immediate spreading for strong driving. The thresholds are due to simple bifurcations, obtained analytically for a single oscillator, and numerically as turning-points of the nonlinear response manifold for a full chain. Generically, the threshold is nonzero also for infinite chains.

nlin.PS↗

arXiv2008

Stability, mobility and power currents in a two-dimensional model for waveguide arrays with nonlinear coupling

A two-dimensional nonlinear Schrodinger lattice with nonlinear coupling, modelling a square array of weakly coupled linear optical waveguides embedded in a nonlinear Kerr material, is studied. We find that despite a vanishing energy difference (Peierls-Nabarro barrier) of fundamental stationary modes the mobility of localized excitations is very poor. This is attributed to a large separation in parameter space of the bifurcation points of the involved stationary modes. At these points the stability of the fundamental modes is changed and an asymmetric intermediate solution appears that connects the points. The control of the power flow across the array when excited with plane waves is also addressed and shown to exhibit great flexibility that may lead to applications for power-coupling devices. In certain parameter regimes, the direction of a stable propagating plane-wave current is shown to be continuously tunable by amplitude variation (with fixed phase gradient). More exotic effects of the nonlinear coupling terms like compact discrete breathers and vortices, and stationary complex modes with non-trivial phase relations are also briefly discussed. Regimes of dynamical linear stability are found for all these types of solutions.

nlin.PS↗

arXiv2006

Discrete soliton mobility in two-dimensional waveguide arrays with saturable nonlinearity

We address the issue of mobility of localized modes in two-dimensional nonlinear Schrödinger lattices with saturable nonlinearity. This describes e.g. discrete spatial solitons in a tight-binding approximation of two-dimensional optical waveguide arrays made from photorefractive crystals. We discuss numerically obtained exact stationary solutions and their stability, focussing on three different solution families with peaks at one, two, and four neighboring sites, respectively. When varying the power, there is a repeated exchange of stability between these three solutions, with symmetry-broken families of connecting intermediate stationary solutions appearing at the bifurcation points. When the nonlinearity parameter is not too large, we observe good mobility, and a well defined Peierls-Nabarro barrier measuring the minimum energy necessary for rendering a stable stationary solution mobile.

nlin.PS↗

arXiv2004

Statistical mechanics of general discrete nonlinear Schr{ö}dinger models: Localization transition and its relevance for Klein-Gordon lattices

We extend earlier work [Phys.Rev.Lett. 84, 3740 (2000)] on the statistical mechanics of the cubic one-dimensional discrete nonlinear Schrodinger (DNLS) equation to a more general class of models, including higher dimensionalities and nonlinearities of arbitrary degree. These extensions are physically motivated by the desire to describe situations with an excitation threshold for creation of localized excitations, as well as by recent work suggesting non-cubic DNLS models to describe Bose-Einstein condensates in deep optical lattices, taking into account the effective condensate dimensionality. Considering ensembles of initial conditions with given values of the two conserved quantities, norm and Hamiltonian, we calculate analytically the boundary of the 'normal' Gibbsian regime corresponding to infinite temperature, and perform numerical simulations to illuminate the nature of the localization dynamics outside this regime for various cases. Furthermore, we show quantitatively how this DNLS localization transition manifests itself for small-amplitude oscillations in generic Klein-Gordon lattices of weakly coupled anharmonic oscillators (in which energy is the only conserved quantity), and determine conditions for existence of persistent energy localization over large time scales.

cond-mat.stat-mech↗

arXiv2004

Quasiperiodic localized oscillating solutions in the discrete nonlinear Schrödinger equation with alternating on-site potential

We present what we believe to be the first known example of an exact quasiperiodic localized stable solution with spatially symmetric large-amplitude oscillations in a non-integrable Hamiltonian lattice model. The model is a one-dimensional discrete nonlinear Schrödinger equation with alternating on-site energies, modelling e.g. an array of optical waveguides with alternating widths. The solution bifurcates from a stationary discrete gap soliton, and in a regime of large oscillations its intensity oscillates periodically between having one peak at the central site, and two symmetric peaks at the neighboring sites with a dip in the middle. Such solutions, termed 'pulsons', are found to exist in continuous families ranging arbitrarily close both to the anticontinuous and continuous limits. Furthermore, it is shown that they may be linearly stable also in a regime of large oscillations.

nlin.PS↗

arXiv2004

Hamiltonian Hopf bifurcations in the discrete nonlinear Schrödinger trimer: oscillatory instabilities, quasiperiodic solutions and a 'new' type of self-trapping transition

Oscillatory instabilities in Hamiltonian anharmonic lattices are known to appear through Hamiltonian Hopf bifurcations of certain time-periodic solutions of multibreather type. Here, we analyze the basic mechanisms for this scenario by considering the simplest possible model system of this kind where they appear: the three-site discrete nonlinear Schrödinger model with periodic boundary conditions. The stationary solution having equal amplitude and opposite phases on two sites and zero amplitude on the third is known to be unstable for an interval of intermediate amplitudes. We numerically analyze the nature of the two bifurcations leading to this instability and find them to be of two different types. Close to the lower-amplitude threshold stable two-frequency quasiperiodic solutions exist surrounding the unstable stationary solution, and the dynamics remains trapped around the latter so that in particular the amplitude of the originally unexcited site remains small. By contrast, close to the higher-amplitude threshold all two-frequency quasiperiodic solutions are detached from the unstable stationary solution, and the resulting dynamics is of 'population-inversion' type involving also the originally unexcited site.

nlin.PS↗