Reaction rate theory in solids is modified taking into account intrinsic localized modes or discrete breathers (DBs) that can appear in crystals with sufficient anharmonicity, resulting in violation of Arrhenius’ law. Large-amplitude oscillations of atoms about their equilibrium positions in the lattice cause local potentials of alternating sign, which are described in terms of time-periodic modulations of the potential barriers for chemical reactions taking place in the vicinity of DBs. The reaction rate averaged over large macroscopic volumes and times including many DBs is increased by a factor that depends on the DB statistics. The breather statistics in thermal equilibrium and in thermal spikes in solids under irradiation with swift particles is considered, and the corresponding reaction rate amplification factors are derived.

We investigate the charge transport in synthetic DNA polymers built up from single type of base pairs. In the context of a polaronlike model, for which an electronic tight-binding system and bond vibrations of the double helix are coupled, we present estimates for the electron-vibration coupling strengths utilizing a quantum-chemical procedure. Subsequent studies concerning the mobility of polaron solutions, representing the state of a localized charge in unison with its associated helix deformation, show that the system for poly(dG)–poly(dC) and poly(dA)–poly(dT) DNA polymers, respectively possess quantitatively distinct transport properties. While the former supports unidirectionally moving electron breathers attributed to highly efficient long-range conductivity, the breather mobility in the latter case is comparatively restrained, inhibiting charge transport. Our results are in agreement with recent experimental results demonstrating that poly(dG)–poly(dC) DNA molecules acts as a semiconducting nanowire and exhibit better conductance than poly(dA)–poly(dT) ones.

In this paper we develop a dynamical model of the propagating nonlinear localized excitations, supersonic kinks, in the cation layer in a silicate mica crystal. We start from purely electrostatic Coulomb interaction and add the Ziegler-Biersack-Littmark short-range repulsive potential and the periodic potential produced by other atoms of the lattice. The proposed approach allows the construction of supersonic kinks which can propagate in the lattice within a large range of energies and velocities. Due to the presence of the short-range repulsive component in the potential, the interparticle distances in the lattice kinks with high energy are limited by physically reasonable values. The introduction of the periodic lattice potential results in the important feature that the kinks propagate with the single velocity and single energy, which are independent on the excitation conditions. The unique average velocity of the supersonic kinks on the periodic substrate potential we relate with the kink amplitude of the relative particle displacements, which is determined by the interatomic distance corresponding to the minimum of the total, interparticle plus substrate, lattice potential. The found kinks are ultradiscrete and can be described with the “magic wave number” $q=2\pi /3a$, which was previously revealed in the nonlinear sinusoidal waves and supersonic kinks in the Fermi-Pasta-Ulam lattice. The extreme discreteness of the observed supersonic kinks, with basically two particles moving at the same time, allows the detailed interpretation of their double-kink structure, which is not possible for the multikinks without an account for the lattice discreteness. Analytical calculations of the displacement patterns and energies of the supersonic kinks are confirmed by numerical simulations. The computed energy of the found supersonic kinks in the considered realistic lattice potential is in a good agreement with the experimental evidence for the transport of localized energetic excitations in silicate mica crystals between the points of ${}^{40}\mathrm{K}$ recoil and subsequent sputtering.

Moving breathers is a means of transmitting information in DNA. We study the existence and properties of moving breathers in a DNA model with short range interaction, due to the stacking of the base pairs, and long range interaction, due to the finite dipole moment of the bond within each base pair. In our study, we have found that mobile breathers exist for a wide range of the parameter values, and the mobility of these breathers is hindered by the long range interaction. This fact is manifested by: (a) an increase of the effective mass of the breather with the dipole–dipole coupling parameter; (b) a poor quality of the movement when the dipole–dipole interaction increases; and (c) the existence of a threshold value of the dipole–dipole coupling above which the breather is not movable. An analytical formula for the boundaries of the regions where breathers are movable is calculated. Concretely, for each value of the breather frequency, it can be obtained the maximum value of the dipole–dipole coupling parameter and the maximum and minimum values of the stacking coupling parameter where breathers are movable. Numerical simulations show that, although the necessary conditions for the mobility are fulfilled, breathers are not always movable. Finally, the value of the dipole–dipole coupling constant is obtained through quantum chemical calculations. They show that the value of the coupling constant is small enough to allow a good mobility of breathers.European Commission under the RTN project LOCNET, HPRN-CT-1999-0016

We analyse the influence of an impurity in the evolution of moving discrete breathers in a Klein–Gordon chain with non-weak nonlinearity. Three different types of behaviour can be observed when moving breathers interact with the impurity: they pass through the impurity continuing their direction of movement; they are reflected by the impurity; they are trapped by the impurity, giving rise to chaotic breathers, as their Fourier power spectra show. Resonance with a breather centred at the impurity site is conjectured to be a necessary condition for the appearance of the trapping phenomenon. This paper establishes a difference between the resonance condition of the non-weak nonlinearity approach and the resonance condition with the linear impurity mode in the case of weak nonlinearity.