Wandering breathers and self-trapping in weakly coupled nonlinear chains: classical counterpart of macroscopic tunneling quantum dynamics

We present analytical and numerical studies of phase-coherent dynamics of intrinsically localized excitations (breathers) in a system of two weakly coupled nonlinear oscillator chains. We show that there are two qualitatively different dynamical regimes of the coupled breathers, either immovable or slowly-moving: the periodic transverse translation (wandering) of low-amplitude breather between the chains, and the one-chain-localization of high-amplitude breather. These two modes of coupled nonlinear excitations, which involve large number of anharmonic oscillators, can be mapped onto two solutions of a single pendulum equation, detached by a separatrix mode. We also study two-chain breathers, which can be considered as bound states of discrete breathers with different symmetry and center locations in the coupled chains, and bifurcation of the anti-phase two-chain breather into the one-chain one. Delocalizing transition of 1D breather in 2D system of a large number of parallel coupled nonlinear chains is described, in which the breather, initially excited in a given chain, abruptly spreads its vibration energy in the whole 2D system upon decreasing breather frequency or amplitude below the threshold one. The threshold breather frequency is above the cut off phonon frequency in 2D system, and the threshold breather amplitude scales as square root of the inter-chain coupling constant. Delocalizing transition of discrete vibrational breather in 2D and 3D systems of coupled nonlinear chains has an analogy with delocalizing transition for Bose-Einstein condensates in 2D and 3D optical lattices.Comment: 33 pages, 16 figure

Numerical Simulation of an Electroweak Oscillon

Numerical simulations of the bosonic sector of the $SU(2)\times U(1)$ electroweak Standard Model in 3+1 dimensions have demonstrated the existence of an oscillon -- an extremely long-lived, localized, oscillatory solution to the equations of motion -- when the Higgs mass is equal to twice the $W^\pm$ boson mass. It contains total energy roughly 30 TeV localized in a region of radius 0.05 fm. A detailed description of these numerical results is presented.Comment: 12 pages, 8 figures, uses RevTeX4; v2: expanded results section, fixed typo

Multiphonon anharmonic decay of a quantum mode

A nonperturbative theory of multiphonon anharmonic transitions between energy levels of a local mode is presented. It is shown that the rate of transitions rearranges near the critical level number $n_{cr}$: at smaller $n$ the process slows down, while at larger $n$ it accelerates in time, causing a jump-like loss of energy followed by the generation of phonon bursts. Depending on parameters, phonons are emitted in pairs, triplets etc.Comment: submitted to Europhys.Let

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

Supersonic Discrete Kink-Solitons and Sinusoidal Patterns with "Magic" wavenumber in Anharmonic Lattices

The sharp pulse method is applied to Fermi-Pasta-Ulam (FPU) and Lennard-Jones (LJ) anharmonic lattices. Numerical simulations reveal the presence of high energy strongly localized ``discrete'' kink-solitons (DK), which move with supersonic velocities that are proportional to kink amplitudes. For small amplitudes, the DK's of the FPU lattice reduce to the well-known ``continuous'' kink-soliton solutions of the modified Korteweg-de Vries equation. For high amplitudes, we obtain a consistent description of these DK's in terms of approximate solutions of the lattice equations that are obtained by restricting to a bounded support in space exact solutions with sinusoidal pattern characterized by the ``magic'' wavenumber $k=2\pi/3$. Relative displacement patterns, velocity versus amplitude, dispersion relation and exponential tails found in numerical simulations are shown to agree very well with analytical predictions, for both FPU and LJ lattices.Comment: Europhysics Letters (in print

Conductance of a tunnel point-contact of noble metals in the presence of a single defect

In paper [1] (Avotina et al. Phys. Rev. B,74, 085411 (2006)) the effect of Fermi surface anisotropy to the conductance of a tunnel point contact, in the vicinity of which a single point-like defect is situated, has been investigated theoretically. The oscillatory dependence of the conductance on the distance between the contact and the defect has been found for a general Fermi surface geometry. In this paper we apply the method developed in [1] to the calculation of the conductance of noble metal contacts. An original algorithm, which enables the computation of the conductance for any parametrically given Fermi surface, is proposed. On this basis a pattern of the conductance oscillations, which can be observed by the method of scanning tunneling microscopy, is obtained for different orientations of the surface for the noble metals.Comment: 8 pages, 5 figure

Signature of Fermi surface anisotropy in point contact conductance in the presence of defects

In a previous paper (Avotina et al.,Phys. Rev. B Vol.71, 115430 (2005)) we have shown that in principle it is possible to image the defect positions below a metal surface by means of a scanning tunnelling microscope. The principle relies on the interference of electron waves scattered on the defects, which give rise to small but measurable conductance fluctuations. Whereas in that work the band structure was assumed to be free-electron like, here we investigate the effects of Fermi surface anisotropy. We demonstrate that the amplitude and period of the conductance oscillations are determined by the local geometry of the Fermi surface. The signal results from those points for which the electron velocity is directed along the vector connecting the point contact to the defect. For a general Fermi surface geometry the position of the maximum amplitude of the conductance oscillations is not found for the tip directly above the defect. We have determined optimal conditions for determination of defect positions in metals with closed and open Fermi surfaces.Comment: 23 pages, 8 figure

On the theory of magnetization in multiferroics: competition between ferro- and antiferromagnetic domains

Many technological applications of multiferroics are based on their ability to reconstruct the domain structure (DS) under the action of small external fields. In the present paper we analyze the different scenarios of the DS behavior in a multiferroic that shows simultaneously ferro- and antiferromagnetic ordering on the different systems of magnetic ions. We consider the way to control a composition of the DS and macroscopic properties of the sample by an appropriate field treatment. We found out that sensitivity of the DS to the external magnetic field and the magnetic susceptibility in a low-field region are determined mainly by the destressing effects (that have magnetoelastic origin). In a particular case of Sr$_{2}$Cu$_{3}$O$_{4}$Cl$_{2}$ crystal we anticipate the peculiarities of the elastic and magnetoelastic properties at $T\approx 100$ K.Comment: 16 pages, 10 figure

Emergence of Oscillons in an Expanding Background

We consider a (1+1) dimensional scalar field theory that supports oscillons, which are localized, oscillatory, stable solutions to nonlinear equations of motion. We study this theory in an expanding background and show that oscillons now lose energy, but at a rate that is exponentially small when the expansion rate is slow. We also show numerically that a universe that starts with (almost) thermal initial conditions will cool to a final state where a significant fraction of the energy of the universe -- on the order of 50% -- is stored in oscillons. If this phenomenon persists in realistic models, oscillons may have cosmological consequences.Comment: 13 pages, 4 .eps figures, uses RevTeX4; v2: clarified details of expansion, added reference