Discrete moving breather collisions in a Klein-Gordon chain of oscillators

We study the collisions of moving breathers with the same frequency, traveling with opposite directions within a Klein-Gordon chain of oscillators. Two types of collisions have been analyzed: symmetric and non-symmetric, head-on collisions. For low enough frequency the outcome is strongly dependent of the dynamical states of the two colliding breathers just before the collision. For symmetric collisions, several results can be observed: breather generation, with the formation of a trapped breather and two new moving breathers; breather reflection; generation of two new moving breathers; and breather fusion bringing about a trapped breather. For non-symmetric collisions some possible results are: breather generation, with the formation of three new moving breathers; breather fusion, originating a new moving breather; breather trapping with breather reflection; generation of two new moving breathers; and two new moving breathers traveling as a bound state. Breather annihilation has never been observed.     

Discrete nonlinear Schrödinger breathers in a phonon bath

We study the dynamics of the discrete nonlinear Schr?dinger lattice initialized such that a very long transitory period of time in which standard Boltzmann statistics is insufficient is reached. Our study of the nonlinear system locked in this non-Gibbsian state focuses on the dynamics of discrete breathers (also called intrinsic localized modes). It is found that part of the energy spontaneously condenses into several discrete breathers. Although these discrete breathers are extremely long lived, their total number is found to decrease as the evolution progresses. Even though the total number of discrete breathers decreases we report the surprising observation that the energy content in the discrete breather population increases. We interpret these observations in the perspective of discrete breather creation and annihilation and find that the death of a discrete breather cause effective energy transfer to a spatially nearby discrete breather. It is found that the concepts of a multi-frequency discrete breather and of internal modes is crucial for this process. Finally, we find that the existence of a discrete breather tends to soften the lattice in its immediate neighborhood, resulting in high amplitude thermal fluctuation close to an existing discrete breather. This in turn nucleates discrete breather creation close to a already existing discrete breather. Received 21 January 1999 and Received in final form 20 September 1999     

Breather‐to‐soliton transitions and nonlinear wave interactions for the nonlinear Schrödinger equation with the sextic operators in optical fibers

We find that the sextic nonlinear Schrödinger (NLS) equation admits breather‐to‐soliton transitions. With the Darboux transformation, analytic breather solutions with imaginary eigenvalues up to the second order are explicitly presented. The condition for breather‐to‐soliton transitions is explicitly presented and several examples of transitions are shown. Interestingly, we show that the sextic NLS equation admits not only the breather‐to‐bright‐soliton transitions but also the breather‐to‐dark‐soliton transitions. We also show the interactions between two solitons on the constant backgrounds, as well as between breather and soliton.     

Discrete breathers in nonlinear lattices: experimental detection in a josephson array

We present the experimental detection of discrete breathers in an underdamped Josephson-junction array. Breathers exist under a range of dc current biases and temperatures, and are detected by measuring dc voltages. We find that the maximum allowable bias current for the breather is proportional to the array depinning current, while the minimum current seems to be related to a junction retrapping mechanism. We have observed that this latter instability leads to the formation of multisite breather states in the array. We have also studied the domain of existence of the breather at different values of the array parameters by varying the temperature.     

Decay of Z boson into photon and unparticle

We study the decay of the standard model Z boson into unparticle plus a single photon through a one-loop process. As in the anomaly type decay, only the axial-vector part of the Z coupling matching with the vector unparticle and/or the vector part of the Z coupling matching with the axial-vector unparticle can give a nonzero contribution to the decay. We show that the photon spectrum terminates at the end point in accord with Yang's theorem. Existing data on single photon production at LEP I is used to constrain the unparticle sector.     

Dynamics of oscillator chains from high frequency initial conditions: comparison of phi4 and FPU-beta models

The dynamics of oscillator chains are studied, starting from high frequency initial conditions (h.f.i.c.). In particular, the formation and evolution of chaotic breathers (CB's) of the Klein-Gordon chain with quartic nonlinearity in the Hamiltonian (the phi(4) model) are compared to the results of the previously studied Fermi-Pasta-Ulam (FPU-beta) chain. We find an important difference for h.f.i.c. is that the quartic nonlinearity, which drives the high frequency phenomena, being a self-force on each individual oscillator in the phi(4) model is significantly weaker than the quartic term in the FPU-beta model, which acts between neighboring oscillators that are nearly out-of-phase. The addition of a self-force breaks the translational invariance and adds a parameter. We compare theoretical results, using the envelope approximation to reduce the discrete coupled equations to a partial differential equation for each chain, indicating that various scalings can be used to predict the relative energies at which the basic phenomena of parametric instability, breather formation and coalescence, and ultimately breather decay to energy equipartition, will occur. Detailed numerical results, comparing the two chains, are presented to verify the scalings.     

Compact and almost compact breathers: a bridge between an anharmonic lattice and its continuum limit

We demonstrate that certain strictly anharmonic one-dimensional FPU lattices with a suitable quartic site potential appended support almost-compact discrete breathers over a macroscopic localized domain that is essentially fixed independently of the sparseness of the lattice. Beyond that domain the discrete breather tails decay at a double-exponential rate in the lattice-cell index, becoming truly compact in the continuum limit. Furthermore, the discrete breather is stable for amplitudes below a sharp threshold that depends on the sparseness of the lattice. For the two-dimensional version of the problem, the continuum limit of a planar hexagonal lattice with a purely quartic interaction potential begets an isotropic multidimensional nonlinear wave equation. When a quartic site potential of the appropriate sign is appended, the continuum equation has a compactly supported radial breather solution.     

The modified nonlinear Schrödinger equation: facts and artefacts

We argue that the integrable modified nonlinear Schr?dinger equation with the nonlinearity dispersion term is the true starting point to analytically describe subpicosecond pulse dynamics in monomode fibers. Contrary to the known assertions, solitons of this equation are free of self-steepening and the breather formation is possible. Received 29 September 2001 / Received in final form 25 January 2002 Published online 2 October 2002 RID="a" ID="a"doktorov@dragon.bas-net.by     

Mutual-focusing of two co-propagating beams and formation of trapped spatial breather pair in saturable nonlinear media

In this paper, using parabolic equation approach, coupled propagation of two coaxially co-propagating and mutually incoherent bright cylindrical beams in saturable nonlinear medium has been investigated. Considering the coupling coefficient equal to unity (κ=1), a detailed account of formation of spatial soliton pair (i.e. both beams are stationary trapped) and spatial breather pair (i.e. width of each beam oscillates with the propagation distance) has been provided and existence of spatially trapped breather pair (i.e. average width of each breather of the pair does not change with the propagation distance) has been shown. Conditions of formation of trapped spatial breather pair and their existence line has also been revealed for arbitrary beam width ratio of the beams. It is revealed that spatial soliton pairs are just a special case of trapped breather pair. The regions (conditions) of mutual-focusing and mutual-defocusing of spatial soliton pair/breather pair have also been identified. Lastly, the law of trapped breather pair formation is proposed.     

Comparison between Si/SiO<Subscript>2</Subscript> and InP/Al<Subscript>2</Subscript>O<Subscript>3</Subscript> based MOSFETs

The discrete breathers in graphane in thermodynamic equilibrium in the temperature range 50–600 K are studied by molecular dynamics simulation. A discrete breather is a hydrogen atom vibrating along the normal to a sheet of graphane at a high amplitude. As was found earlier, the lifetime of a discrete breather at zero temperature corresponds to several tens of thousands of vibrations. The effect of temperature on the decay time of discrete breathers and the probability of their detachment from a sheet of graphane are studied in this work. It is shown that closely spaced breathers can exchange energy with each other at zero temperature. The data obtained suggest that thermally activated discrete breathers can be involved in the dehydrogenation of graphane, which is important for hydrogen energetics.     

Moving breather collisions in Klein-Gordon chains of oscillators

We investigate the collisions of moving breathers, with the same frequency, in three different Klein-Gordon chains of oscillators. The on-site potentials are: the asymmetric and soft Morse potential, the symmetric and soft sine-Gordon potential and the symmetric and hard φ⁴ potential. The simulation of a collision begins generating two identical moving breathers traveling with opposite velocities, they are obtained after perturbing two identical stationary breathers which centers are separated by a fixed number of particles. If this number is odd we obtain an on-site collision, but if this number is even we obtain an inter-site collision. Apart from this distinction, we have considered symmetric collisions, if the colliding moving breathers are vibrating in phase, and anti-symmetric collisions, if the colliding moving breathers are vibrating in anti-phase. The simulations show that the collision properties of the three chains are different. The main observed phenomena are: breather generation with trapping, with the appearance of two new moving breathers with opposite velocities, and a stationary breather trapped at the collision region; breather generation without trapping, with the appearance of new moving breathers with opposite velocities; breather trapping at the collision region, without the appearance of new moving breathers; and breather reflection. For each Klein-Gordon chain, the collision outcomes depend on the lattice parameters, the frequency of the perturbed stationary breathers, the internal structure of the moving breathers and the number of particles that initially separates the stationary breathers when they are perturbed.     

Almost compact breathers in anharmonic lattices near the continuum limit

Certain strictly anharmonic one-dimensional lattices support discrete breathers over a macroscopic localized domain that in the continuum limit becomes exactly compact. The discrete breather tails decay at a double-exponential rate, so such systems can store energy locally, especially since discrete breathers appear to be stable for amplitudes below a sharp stability threshold. The effective width of other solutions broadens over time, but, under appropriate conditions, only after a positive waiting time. The continuum limit of a planar hexagonal lattice also supports a compact breather.     

Emission from,WKB quantization,and stochastic decay of sine-Gordon solitons in external fields

Various dynamical problems for solitons (kinks and breathers) of the sine-Gordon equation perturbed by small terms describing constant or time-dependent (both periodic and random) external fields in several physical problems, e.g. long Josephson junctions and weak ferromagnets, are formulated, and results, with only few details of calculations, are presented. Among these problems are energy emission from a kink or small-amplitude breather oscillating in a constant or time-periodic external field, perturbation-induced corrections to the WKB spectrum of a quantized small-amplitude breather, and stochastic decay of a weakly bound breather into a kink-antikink pair under the action of an external field.     

DNA dynamics - Experiment proposals

We argue that a breather wave, describing DNA dynamics, behaves like a real soliton. We rely on a Peyrard-Bishop-Dauxois (PBD) model. In addition, we propose a couple of experiments to confirm or reject this statement. These experiments should study solitonic interactions using micromanipulation technique. Also, we suggest how to measure a solitonic width and its amplitude.     

Formation mechanism of asymmetric breather and rogue waves in pair-transition-coupled nonlinear Schr?dinger equations

Based on the developed Darboux transformation, we investigate the exact asymmetric solutions of breather and rogue waves in pair-transition-coupled nonlinear Schr?dinger equations. As an example, some types of exact breather solutions are given analytically by adjusting the parameters. Moreover, the interesting fundamental problem is to clarify the formation mechanism of asymmetry breather solutions and how the particle number and energy exchange between the background and soliton ultimately form the breather solutions. Our results also show that the formation mechanism from breather to rogue wave arises from the transformation from the periodic total exchange into the temporal local property.     

ESR investigation on the breather mode and the spinon-breather dynamical crossover in Cu benzoate

A "breather excitation" is observed directly by electron spin resonance in the quantum spin chain Cu benzoate, in which an unexpected field-induced gap has recently been found. The nonlinear field dependence of the resonance field agrees well with the formula based on a quantum sine-Gordon model. The power-law temperature dependence of the linewidth is observed in the gapless spinon regime while the width decreases exponentially for the gapped breather regime. In the intermediate range, a distinct anomaly is found, which is the manifestation of "the spinon-breather dynamical crossover."     

Breather trapping and breather transmission in a DNA model with an interface

We study the dynamics of moving discrete breathers in an interfaced piecewise DNA molecule. This is a DNA chain in which all the base pairs are identical and there exists an interface such that the base pairs dipole moments at each side are oriented in opposite directions. The Hamiltonian of the Peyrard-Bishop model is augmented with a term that includes the dipole-dipole coupling between base pairs. Numerical simulations show the existence of two dynamical regimes. If the translational kinetic energy of a moving breather launched towards the interface is below a critical value, it is trapped in a region around the interface collecting vibrational energy. For an energy larger than the critical value, the breather is transmitted and continues travelling along the double strand with lower velocity. Reflection phenomena never occur. The same study has been carried out when a single dipole is oriented in opposite direction to the other ones. When moving breathers collide with the single inverted dipole, the same effects appear. These results emphasize the importance of this simple type of local inhomogeneity as it creates a mechanism for the trapping of energy. Finally, the simulations show that, under favorable conditions, several launched moving breathers can be trapped successively at the interface region producing an accumulation of vibrational energy. Moreover, an additional colliding moving breather can produce a saturation of energy and a moving breather with all the accumulated energy is transmitted to the chain.     

Extremal entropy for a constrained probability density

The state of extremal entropy for a one-dimensional probability density is considered. This density is constrained by fixed values of the first and second moment. The grandcanonical distribution yields the extremum of the entropy within a certain range of values of the moments. A different type of density corresponds to an extremum of entropy when the moments are outside this range. The shape of this density is approximated with the Ritz variation method. The results are applied to the formation of breathers in the discrete nonlinear Schrödinger equation.     

Decay and decoupling of heavy right-handed Majorana neutrinos in the L–R model

Heavy right-handed neutrinos are of current interest. The interactions and decay of such neutrinos determine their decoupling epoch during the evolution of the universe. This in turn affects various observable features like the energy density, nucleosynthesis, CMBR spectrum, galaxy formation and baryogenesis. Here, we consider reduction of right-handed electron-type Majorana neutrinos, in the left–right symmetric model, by the channel and the channel originating from an anomaly, involving the gauge group, as well as decay of such neutrinos. We study the reduction of these neutrinos for different ranges of left–right model parameters, and find that, if the neutrino mass exceeds the right-handed gauge boson mass, then the neutrinos never decouple for realistic values of the parameters, but, rather, decay in equilibrium. Because there is no out-of-equilibrium decay, no mass bounds can be set for the neutrinos. Received: 1 November 2000 / Published online: 23 February 2001