Multistable Pulse-like Solutions in a Parametrically Driven Ginzburg-Landau Equation

It is well known that pulse-like solutions of the cubic complex Ginzburg-Landau equation are unstable but can be stabilised by the addition of quintic terms. In this paper we explore an alternative mechanism where the role of the stabilising agent is played by the parametric driver. Our analysis is based on the numerical continuation of solutions in one of the parameters of the Ginzburg-Landau equation (the diffusion coefficient $c$), starting from the nonlinear Schr\"odinger limit (for which $c=0$). The continuation generates, recursively, a sequence of coexisting stable solutions with increasing number of humps. The sequence "converges" to a long pulse which can be interpreted as a bound state of two fronts with opposite polarities.Comment: 13 pages, 6 figures; to appear in PR

Quantum squeezing of optical dissipative structures

We show that any optical dissipative structure supported by degenerate optical parametric oscillators contains a special transverse mode that is free from quantum fluctuations when measured in a balanced homodyne detection experiment. The phenomenon is not critical as it is independent of the system parameters and, in particular, of the existence of bifurcations. This result is a consequence of the spatial symmetry breaking introduced by the dissipative structure. Effects that could degrade the squeezing level are considered.Comment: 4 pages and a half, 1 fugure. Version to appear in Europhysics Letter

Two and three-dimensional oscillons in nonlinear Faraday resonance

We study 2D and 3D localised oscillating patterns in a simple model system exhibiting nonlinear Faraday resonance. The corresponding amplitude equation is shown to have exact soliton solutions which are found to be always unstable in 3D. On the contrary, the 2D solitons are shown to be stable in a certain parameter range; hence the damping and parametric driving are capable of suppressing the nonlinear blowup and dispersive decay of solitons in two dimensions. The negative feedback loop occurs via the enslaving of the soliton's phase, coupled to the driver, to its amplitude and width.Comment: 4 pages; 1 figur

Analysis technique for exceptional points in open quantum systems and QPT analogy for the appearance of irreversibility

We propose an analysis technique for the exceptional points (EPs) occurring in the discrete spectrum of open quantum systems (OQS), using a semi-infinite chain coupled to an endpoint impurity as a prototype. We outline our method to locate the EPs in OQS, further obtaining an eigenvalue expansion in the vicinity of the EPs that gives rise to characteristic exponents. We also report the precise number of EPs occurring in an OQS with a continuum described by a quadratic dispersion curve. In particular, the number of EPs occurring in a bare discrete Hamiltonian of dimension $n_\textrm{D}$ is given by $n_\textrm{D} (n_\textrm{D} - 1)$; if this discrete Hamiltonian is then coupled to continuum (or continua) to form an OQS, the interaction with the continuum generally produces an enlarged discrete solution space that includes a greater number of EPs, specifically $2^{n_\textrm{C}} (n_\textrm{C} + n_\textrm{D}) [2^{n_\textrm{C}} (n_\textrm{C} + n_\textrm{D}) - 1]$, in which $n_\textrm{C}$ is the number of (non-degenerate) continua to which the discrete sector is attached. Finally, we offer a heuristic quantum phase transition analogy for the emergence of the resonance (giving rise to irreversibility via exponential decay) in which the decay width plays the role of the order parameter; the associated critical exponent is then determined by the above eigenvalue expansion.Comment: 16 pages, 7 figure

Genetic analysis of 'Moscato branco' and other muscat grapes held by the grape germplasm bank in Brazil.

Resumo 3128

Impurity-induced stabilization of solitons in arrays of parametrically driven nonlinear oscillators

Chains of parametrically driven, damped pendula are known to support soliton-like clusters of in-phase motion which become unstable and seed spatiotemporal chaos for sufficiently large driving amplitudes. We show that the pinning of the soliton on a "long" impurity (a longer pendulum) expands dramatically its stability region whereas "short" defects simply repel solitons producing effective partition of the chain. We also show that defects may spontaneously nucleate solitons.Comment: 4 pages in RevTeX; 7 figures in ps forma

Polarisation Patterns and Vectorial Defects in Type II Optical Parametric Oscillators

Previous studies of lasers and nonlinear resonators have revealed that the polarisation degree of freedom allows for the formation of polarisation patterns and novel localized structures, such as vectorial defects. Type II optical parametric oscillators are characterised by the fact that the down-converted beams are emitted in orthogonal polarisations. In this paper we show the results of the study of pattern and defect formation and dynamics in a Type II degenerate optical parametric oscillator for which the pump field is not resonated in the cavity. We find that traveling waves are the predominant solutions and that the defects are vectorial dislocations which appear at the boundaries of the regions where traveling waves of different phase or wave-vector orientation are formed. A dislocation is defined by two topological charges, one associated with the phase and another with the wave-vector orientation. We also show how to stabilize a single defect in a realistic experimental situation. The effects of phase mismatch of nonlinear interaction are finally considered.Comment: 38 pages, including 15 figures, LATeX. Related material, including movies, can be obtained from http://www.imedea.uib.es/Nonlinear/research_topics/OPO

Heuristic Models of Two-Fermion Relativistic Systems with Field-Type Interaction

We use the chain of simple heuristic expedients to obtain perturbative and exactly solvable relativistic spectra for a family of two-fermionic bound systems with Coulomb-like interaction. In the case of electromagnetic interaction the spectrum coincides up to the second order in a coupling constant with that following from the quantum electrodynamics. Discrepancy occurs only for S-states which is the well-known difficulty in the bound-state problem. The confinement interaction is considered too. PACS number(s): 03.65.Pm, 03.65.Ge, 12.39.PnComment: 16 pages, LaTeX 2.0

Stabilization of Spatial Solitons by Gain Diffusion

It is shown, that diffusion of saturated gain (e.g. diffusion of population inversion in lasers) causes, and/or enhances a modulational instability of generated light field. In case of a subcritical system (e.g. a laser with saturable absorber) the enhancement of the modulational instability stabilizes spatial solitons. These predictions are made for general nonlinear optical systems, and are illustrated by numerical simulation of lasers with saturable absorber.Comment: 10 pages, 4 figures, submitted to Phys.Rev.