Dissipative Interaction and Anomalous Surface Absorption of Bulk Phonons at a Two-Dimensional Defect in a Solid

We predict an extreme sensitivity to the dissipative losses of the resonant interaction of bulk phonons with a 2D defect in a solid. We show that the total resonant reflection of the transverse phonon at the 2D defect, described earlier without an account for dissipation, occurs only in the limit of extremely weak dissipation and is changed into almost total transmission by relatively weak bulk absorption. Anomalous surface absorption of the transverse phonon, when one half of the incident acoustic energy is absorbed at the 2D defect, is predicted for the case of "intermediate" bulk dissipation.Comment: 11 preprint pages, no figure

Deeply Penetrating Elastic and Coupled Surface Waves in Crystals

Deeply penetrating elastic and coupled surface waves (DPSW) in crystals are treated. It is shown that the parameters of the DPSW are very sensitive to near-surface disturbances of the acoustic and electromagnetic paraipeters of the crystal, which is essential for the technical applications of DPSW.Zadanie pt. Digitalizacja i udostępnienie w Cyfrowym Repozytorium Uniwersytetu Łódzkiego kolekcji czasopism naukowych wydawanych przez Uniwersytet Łódzki nr 885/P-DUN/2014 zostało dofinansowane ze środków MNiSW w ramach działalności upowszechniającej naukę

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

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

Nano-wires with surface disorder: Giant localization lengths and dynamical tunneling in the presence of directed chaos

We investigate electron quantum transport through nano-wires with one-sided surface roughness in the presence of a perpendicular magnetic field. Exponentially diverging localization lengths are found in the quantum-to-classical crossover regime, controlled by tunneling between regular and chaotic regions of the underlying mixed classical phase space. We show that each regular mode possesses a well-defined mode-specific localization length. We present analytic estimates of these mode localization lengths which agree well with the numerical data. The coupling between regular and chaotic regions can be determined by varying the length of the wire leading to intricate structures in the transmission probabilities. We explain these structures quantitatively by dynamical tunneling in the presence of directed chaos.Comment: 15 pages, 12 figure

Excitation of travelling multibreathers in anharmonic chains

We study the dynamics of the "externally" forced and damped Fermi-Pasta-Ulam (FPU) 1D lattice. The forcing has the spatial symmetry of the Fourier mode with wavenumber p and oscillates sinusoidally in time with the frequency omega. When omega is in the phonon band, the p-mode becomes modulationally unstable above a critical forcing, which we determine analytically in terms of the parameters of the system. For omega above the phonon band, the instability of the p-mode leads to the formation of a travelling multibreather, that, in the low-amplitude limit could be described in terms of soliton solutions of a suitable driven-damped nonlinear Schroedinger (NLS) equation. Similar mechanisms of instability could show up in easy-axis magnetic structures, that are governed by such NLS equations.Comment: To appear in Physica D (2002

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