On modulational instability and energy localization in anharmonic lattices at finite energy density

The localization of vibrational energy, induced by the modulational instability of the Brillouin-zone-boundary mode in a chain of classical anharmonic oscillators with finite initial energy density, is studied within a continuum theory. We describe the initial localization stage as a gas of envelope solitons and explain their merging, eventually leading to a single localized object containing a macroscopic fraction of the total energy of the lattice. The initial-energy-density dependences of all characteristic time scales of the soliton formation and merging are described analytically. Spatial power spectra are computed and used for the quantitative explanation of the numerical results.Comment: 12 pages, 7 figure

On a simple model of the photonic or phononic crystal

A model is proposed for a one-dimensional dielectric or elastic superlattice (SL) that relatively simply describes the frequency spectrum of electromagnetic or acoustic waves. The band frequency spectrum is reduced to mini-bands contracting with increasing frequency. A procedure is suggested for obtaining local states near a defect in a SL, and the simplest of these states is described. Conditions for the initiation of Bloch oscillations of a wave packet in a SL are discussed

Formation of soliton complexes in dispersive systems

The concept of soliton complex in a nonlinear dispersive medium is formulated. It is shown that interacting identical topological solitons in the medium can form bound soliton complexes which move without radiation. This phenomenon is considered to be universal and applicable to various physical systems. The soliton complex and its “excited” states are described analytically and numerically as solutions of nonlinear dispersive equations with the fourth and higher order spatial or mixed derivatives. The dispersive sine-Gordon, double and triple sine-Gordon, and piecewise models are studied in detail. Mechanisms and conditions of the formation of soliton complexes, and peculiarities of their stationary dynamics are investigated. A phenomenological approach to the description of the complexes and the classification of all the possible complex states are proposed. Some examples of physical systems, where the phenomenon can be experimentally observed, are briefly discussed.Формулюється концепція солітонних комплексів в нелінійному дисперсійному середовищі. Показано, що взаємодіючі тотожні топологічні солітони у такому середовищі здатні утворювати солітонні комплекси, що рухаються без випромінювання. Вважається, що це явище є універсальним і зустрічається у різних фізичних системах. Солітонні комплекси і їхні збуджені стани описуються аналітично і чисельно як розв’язки нелінійних дисперсійних рівнянь з четвертою і вищими просторовимі і змішаними похідними. Ретельно вивчаються дисперсійні системи синус-Гордон, подвійний і потрійний синус-Гордон, а також кусково-лінійна модель. Досліджуються механізми і умови формування солітонних комплексів і особливості їхньої стаціонарної динаміки. Запропоновано феноменологічний підхід до описання комплексів і класифікацію усіх можливих їхніх станів. Стисло розглянуті кілька прикладів фізичних систем, в яких це явище може експериментально спостерігатись

Quantum carpet interferometry for trapped atomic Bose-Einstein condensates

We propose an ``interferometric'' scheme for Bose-Einstein condensates using near-field diffraction. The scheme is based on the phenomenon of intermode traces or quantum carpets; we show how it may be used in the detection of weak forces.Comment: 4 figures. Submitted to Phys. Rev.

Some mechanisms of "spontaneous" polarization of superfluid He-4

Previously, a quantum "tidal" mechanism of polarization of the atoms of He-II was proposed, according to which, as a result of interatomic interaction, each atom of He-II acquires small fluctuating dipole and multipole moments, oriented chaotically on the average. In this work, we show that, in the presence of a temperature or density gradient in He-II, the originally chaotically oriented tidal dipole moments of the atoms become partially ordered, which results in volume polarization of He-II. It is found that the gravitational field of the Earth induces electric induction U =10(-7)V in He-II (for vessel dimensions of the order of 10 cm). We study also the connection of polarization and acceleration, and discuss a possible nature of the electric signal dU = kdT/2e observed by A.S. Rybalko in experiments with second sound.Comment: 13 pages; the calculation is extended and refined; v4: reconstructio

Evolution of discrete local levels into an impurity band in solidified inert gas solution

The density of states g(w) of disordered solutions of solidified inert gases have been calculated using the Jacobian matrix method. The transformation of a discrete vibrational level into an impurity zone at a growing concentration of light impurity atoms has been investigated. It is shown that a 1–10% change in the impurity concentration leads to smearing the local discrete level into an impurity band. As this occurs, additional resonance levels appear which carry important information about the impurity–impurity and impurity– basic lattice force interactions in such solutions

Low Temperature Static and Dynamic Behavior of the Two-Dimensional Easy-Axis Heisenberg Model

We apply the self-consistent harmonic approximation (SCHA) to study static and dynamic properties of the two-dimensional classical Heisenberg model with easy-axis anisotropy. The static properties obtained are magnetization and spin wave energy as functions of temperature, and the critical temperature as a function of the easy-axis anisotropy. We also calculate the dynamic correlation functions using the SCHA renormalized spin wave energy. Our analytical results, for both static properties and dynamic correlation functions, are compared to numerical simulation data combining cluster-Monte Carlo algorithms and Spin Dynamics. The comparison allows us to conclude that far below the transition temperature, where the SCHA is valid, spin waves are responsible for all relevant features observed in the numerical simulation data; topological excitations do not seem to contribute appreciably. For temperatures closer to the transition temperature, there are differences between the dynamic correlation functions from SCHA theory and Spin Dynamics; these may be due to the presence of domain walls and solitons.Comment: 12 pages, 14 figure

Elementary excitations in one-dimensional spin-orbital models: neutral and charged solitons and their bound states

We study, both numerically and variationally, the interplay between different types of elementary excitations in the model of a spin chain with anisotropic spin-orbit coupling, in the vicinity of the "dimer line" with an exactly known dimerized ground state. Our variational treatment is found to be in a qualitative agreement with the exact diagonalization results. Soliton pairs are shown to be the lowest excitations only in a very narrow region of the phase diagram near the dimer line, and the phase transitions are always governed by magnon-type excitations which can be viewed as soliton-antisoliton bound states. It is shown that when the anisotropy exceeds certain critical value, a new phase boundary appears. In the doped model on the dimer line, the exact elementary charge excitation is shown to be a hole bound to a soliton. Bound states of those "charged solitons" are studied; exact solutions for N-hole bound states are presented.Comment: 11 pages revtex, 6 figure

Directed motion of domain walls in biaxial ferromagnets under the influence of periodic external magnetic fields

Directed motion of domain walls (DWs) in a classical biaxial ferromagnet placed under the influence of periodic unbiased external magnetic fields is investigated. Using the symmetry approach developed in this article the necessary conditions for the directed DW motion are found. This motion turns out to be possible if the magnetic field is applied along the most easy axis. The symmetry approach prohibits the directed DW motion if the magnetic field is applied along any of the hard axes. With the help of the soliton perturbation theory and numerical simulations, the average DW velocity as a function of different system parameters such as damping constant, amplitude, and frequency of the external field, is computed.Comment: Added references, corrected typos, extended introductio

Glide and Superclimb of Dislocations in Solid 4^4He

Glide and climb of quantum dislocations under finite external stress, variation of chemical potential and bias (geometrical slanting) in Peierls potential are studied by Monte Carlo simulations of the effective string model. We treat on unified ground quantum effects at finite temperatures $T$. Climb at low $T$ is assisted by superflow along dislocation core -- {\it superclimb}. Above some critical stress avalanche-type creation of kinks is found. It is characterized by hysteretic behavior at low $T$. At finite biases gliding dislocation remains rough even at lowest $T$ -- the behavior opposite to non-slanted dislocations. In contrast to glide, superclimb is characterized by quantum smooth state at low temperatures even for finite bias. In some intermediate $T$-range giant values of the compressibility as well as non-Luttinger type behavior of the core superfluid are observed.Comment: Updated version submitted to JLTP as QFS2010 proceedings; 11 pages, 6 figure