Title: Reaction rate theory with account of discrete breathers

Author: VI Dubinko
With PA Selyshchev and JFR Archilla

Abstract:
The problem of escape from metastable states is of importance to many fields of physics, chemistry, engineering and biology. It is well-known that in thermal equilibrium the fluctuation-activated reaction rate is expressed by Arrhenius' law. It has been shown that in crystals with sufficient anharmonicity a special kind of time-periodic and spatially localized vibrations can appear named intrinsic localized modes (ILMs) or discrete breathers (DBs) [1-5]. MacKay and Aubry [2] suggested that this could result in apparent violation of Arrhenius law, that is, the phenomenon of chemical reactions taking place at much lower temperatures than expected. Further development of this hypothesis by Archilla et al [3] has taken into account the DB statistics [4] for the evaluation of the reaction rate due to the DBs having energies above the activation energy. In this report we show that reaction rates depend on DBs of all energies due to effect of the time-periodic modulation of the activation energy. Large amplitude oscillations of atoms about their equilibrium positions in the lattice cause local potentials of alternating sign, which may be described in terms of time-periodic modulations of the potential barriers for chemical reactions taking place in the vicinity of DBs. The modulation effect rapidly increases with increasing reaction barrier up to the maximum DB energy, above which it becomes the only mechanism of the reaction rate amplification

[1] A.J. Sievers and S. Takeno, Intrinsic Localized Modes in Anharmonic Crystals, Phys. Rev. Lett. 61, 970 (1988).
[2] R. S. MacKay; S. Aubry, Proof of existence of breathers for time-reversible or Hamiltonian networks of weakly coupled oscillators, Nonlinearity 7, 1623 (1994).
[3] J. F. R. Archilla, J. Cuevas, M. D. Alba, M. Naranjo, J. M. Trillo, Discrete breathers for understanding reconstructive mineral processes at low temperatures, J. Phys. Chem. B110 24112 (2006). 
[4] Piazza, F.; Lepri, S.; Livi, R. Cooling nonlinear lattices toward energy localization, Chaos 13, 637 (2003). 
[5] S. Flach, A.V. Gorbach, Discrete breathers Advances in theory and applications, Phys. Rep. 467, 1 (2008)

First Porto Meeting on Theory and Experiment in Nonlinear Physics, Porto, Portugal, July 7-9, 2010. Talk by VI Dubinko.