Search results for "sine-Gordon"
showing 10 items of 16 documents
Influence of a nonlinear coupling on the supratransmission effect in modified sine-Gordon and Klein–Gordon lattices
2017
International audience; In this paper, we analyze the conditions leading to the nonlinear supratransmission phenomenon in two different models: a modified fifth order Klein–Gordon system and a modified sine-Gordon system. The modified models considered here are those with mixed coupling, the pure linear coupling being associated with a nonlinear coupling. Especially, we numerically quantify the influence of the nonlinear coupling coefficient on the threshold amplitude which triggers the nonlinear supratransmission phenomenon. Our main result shows that, in both models, when the nonlinear coupling coefficient increases, the threshold amplitude triggering the nonlinear supratransmission pheno…
Analysis of soliton dynamics and noise induced effects on the superconductive lifetime in long Josephson junctions.
2013
The influence of various noise sources on the transient dynamics of long Josephson junctions (LJJ) is investigated in the presence of an oscillating bias current signal and a noise source with Gaussian or non-Gaussian (i.e. Cauchy-Lorentz or Lévy-Smirnov) probability distributions. These systems are computationally analyzed integrating the perturbed Sine-Gordon equation describing the phase evolution. We found evidence of noise induced effects on trends of the mean escape time (MET) from the superconductive metastable state, varying different system parameters, as the bias frequency, noise intensity and junction length. In particular, we find resonant activation (RA) and noise enhanced stab…
Transient dynamics in driven long Josephson junctions.
2013
The switching time from the superconductive metastable state of a long Josephson junction (LJJ)[1] is computationally analyzed in the framework of the perturbed sine-Gordon equation. The model includes an external bias current term and a stochastic noise source, i.e. a Lévy noise term. The effects of this noise on the mean escape time (MET) from the superconductive state are analyzed. The investigation is performed by considering a wide range of values of system parameters and different noise statistics: Gaussian, Cauchy-Lorentz and Lévy-Smirnov[2]. We found evidence of well known noise induced phenomena on the MET behavior, that is the noise enhanced stability (NES) and resonant activation…
Supratransmission-induced traveling breathers in long Josephson junctions
2022
The emergence of travelling sine-Gordon breathers due to the nonlinear supratransmission effect is theoretically studied in a long Josephson junction driven by suitable magnetic pulses, taking into account the presence of dissipation, a current bias, and a thermal noise source. The simulations clearly indicate that, depending on the pulse's shape and the values of the main system parameters, such a configuration can effectively yield breather excitations only. Furthermore, a nonmonotonic behavior of the breather-only generation probability is observed as a function of the noise intensity. Finally, the dynamics of the supratransmission-induced breathers is characterized by looking at quantit…
Breather dynamics in a stochastic sine-Gordon equation: evidence of noise-enhanced stability
2023
The dynamics of sine-Gordon breathers is studied in the presence of dissipative and stochastic perturbations. Taking a stationary breather with a random phase value as the initial state, the performed simulations demonstrate that a spatially-homogeneous noisy source can make the oscillatory excitation more stable, i.e., it enables the latter to last significantly longer than it would in a noise-free scenario. Both the frequency domain and the localization of energy are examined to document the effectiveness of the noise-enhanced stability phenomenon, which emerges as a nonmonotonic behavior of an average characteristic time for the breather as a function of the noise intensity. The influenc…
Impurity effects on soliton dynamics in planar ferromagnets
1993
Abstract We investigate numerically the dynamics of solitons in a ferromagnetic spin chain and we show that the sine-Gordon approximation provides only a poor description of the solitary excitations in the presence of impurities. Depending on their energy and the strength of the impurity, solitons can be reflected or transmitted. When they are reflected, they can suffer abrupt changes in velocity, which are associated to the switch from one soliton branch to another. In some cases the scattering by an impurity can excite an internal mode of the soliton, which is able to store some energy and modify the output of the scattering.
Classical thermodynamics of the Heisenberg chain in a field by generalized Bethe ansatz method
1990
Abstract Using the classical action-angle variables for the continuous model, we study the thermodynamics of the classical Heisenberg chain in an applied field by a generalized Bethe ansatz approach. The crucial point consists in the derivation of a phase-shifted density of states for the excitations of the model, obtained by imposing periodic boundary conditions. In the thermodynamic limit, the free energy can be expressed in terms of the solution of a non-linear integral equation, showing the universal dependece of the variable x=(JH) 1 2 /T .
Statistical Mechanics of the Sine-Gordon Equation
1986
We give two fundamental methods for evaluation of classical free energies of all the integrable models admitting soliton solutions; the sine-Gordon equation is one example. Periodic boundary conditions impose integral equations for allowed phonon and soliton momenta. From these, generalized Bethe-Ansatz and functional-integration methods using action-angle variables follow. Results for free energies coincide, and coincide with those that we find by transfer-integral methods. Extension to the quantum case, and quantum Bethe Ansatz, on the lines to be reported elsewhere for the sinh-Gordon equation, is indicated.
Analytical investigation of solitary waves in nonlinear Kerr medium
2004
Abstract We study analytically the solution of nonlinear equation which result from the propagation of electromagnetic waves within a nonlinear Kerr medium. The medium is characterized by a dielectric constant which varies periodically and depends on the local field intensity. As a first step, we detail the resolution of the nonlinear equations with a quadratic nonlinearity. After that, we apply the slowly varying envelope approximation to obtain a Sine–Gordon equation. In this kind of nonlinearity, a gap solitons occurs. Moreover we verify that the solutions of the nonlinear equation for all frequencies within the gap are solitons solutions. After that we study the conditions of apparition…
Nonlinear relaxation in quantum and mesoscopic systems
2013
The nonlinear relaxation of three mesoscopic and quantum systems are investigated. Specifically we study the nonlinear relaxation in: (i) a long Josephson junction (LJJ) driven by a non-Gaussian Lévy noise current; (ii) a metastable quantum open system driven by an external periodical driving; and (iii) the electron spin relaxation process in n-type GaAs crystals driven by a fluctuating electric field. In the first system the LJJ phase evolution is described by the perturbed sine-Gordon equation. Two well known noise induced effects are found: the noise enhanced stability and resonant activation phenomena. We investigate the mean escape time as a function of the bias current frequency, nois…