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In this paper, interstitial migration generated by scattering with a mobile breather is investigated numerically in a Frenkel-Kontorova one-dimensional lattice. Consistent with experimental results it is shown that interstitial diffusion is more likely and faster than vacancy diffusion. Our simulations support the hypothesis that a long-range energy transport mechanism involving moving nonlinear vibrational excitations may significantly enhance the mobility of point defects in a crystal lattice.
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Discrete time quantum walks are unitary maps defined on the Hilbert space of coupled two-level systems. We study the dynamics of excitations in a nonlinear discrete time quantum walk, whose fine-tuned linear counterpart has a flat band structure. The linear counterpart is, therefore, lacking transport, with exact solutions being compactly localized. A solitary entity of the nonlinear walk moving at velocity $v$ would therefore not suffer from resonances with small amplitude plane waves with identical phase velocity, due to the absence of the latter. That solitary excitation would also have to be localized stronger than exponential, due to the absence of a linear dispersion. We report on the existence of a set of stationary and moving breathers with almost compact superexponential spatial tails. At the limit of the largest velocity $v=1$ the moving breather turns into a completely compact bullet.
Mutual interaction of localized nonlinear waves, e.g. solitons and modulation instability patterns, is a fascinating and intensively-studied topic of nonlinear science. In this research report, we report on the observation of a novel type of breather interaction in telecommunication optical fibers, in which two identical breathers propagate with opposite group velocities. Under certain conditions, neither amplification nor annihilation occur at the collision point and most interestingly, its amplitude is almost equal to another maximum of either oscillating breather. This ghost-like breather interaction dynamics can be fully described by the N-breather solution of the nonlinear Schrodinger equation.
We study the properties of discrete breathers, also known as intrinsic localized modes, in the one-dimensional Frenkel-Kontorova lattice of oscillators subject to damping and external force. The system is studied in the whole range of values of the coupling parameter, from C=0 (uncoupled limit) up to values close to the continuum limit (forced and damped sine-Gordon model). As this parameter is varied, the existence of different bifurcations is investigated numerically. Using Floquet spectral analysis, we give a complete characterization of the most relevant bifurcations, and we find (spatial) symmetry-breaking bifurcations which are linked to breather mobility, just as it was found in Hamiltonian systems by other authors. In this way moving breathers are shown to exist even at remarkably high levels of discreteness. We study mobile breathers and characterize them in terms of the phonon radiation they emit, which explains successfully the way in which they interact. For instance, it is possible to form ``bound states of moving breathers, through the interaction of their phonon tails. Over all, both stationary and moving breathers are found to be generic localized states over large values of $C$, and they are shown to be robust against low temperature fluctuations.
Recent papers that have studied variants of the Peyrard-Bishop model for DNA, have taken into account the long range interaction due to the dipole moments of the hydrogen bonds between base pairs. In these models the helicity of the double strand is not considered. In this particular paper we have performed an analysis of the influence of the helicity on the properties of static and moving breathers in a Klein--Gordon chain with dipole-dipole interaction. It has been found that the helicity enlarges the range of existence and stability of static breathers, although this effect is small for a typical helical structure of DNA. However the effect of the orientation of the dipole moments is considerably higher with transcendental consequences for the existence of mobile breathers.
A nonlinear chain with six-order polynomial on-site potential is used to analyze the evolution of the total to kinetic energy ratio during development of modulational instability of extended nonlinear vibrational modes. For the on-site potential of hard-type (soft-type) anharmonicity, the instability of $q=pi$ mode ($q=0$ mode) results in the appearance of long-living discrete breathers (DBs) that gradually radiate their energy and eventually the system approaches thermal equilibrium with spatially uniform and temporally constant temperature. In the hard-type (soft-type) anharmonicity case, the total to kinetic energy ratio is minimal (maximal) in the regime of maximal energy localization by DBs. It is concluded that DBs affect specific heat of the nonlinear chain and for the case of hard-type (soft-type) anharmonicity they reduce (increase) the specific heat.
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