q-Breathers and thermalization in acoustic chains with arbitrary nonlinearity index
M. V. Ivanchenko
Theory of Oscillations Department, Univeristy of Nizhniy Novgorod,
603950 Nizhniy Novgorod, Russia
Abstract
Nonlinearity shapes lattice dynamics affecting vibrational
spectrum, transport and thermalization phenomena. Beside breathers and
solitons one finds the third fundamental class of nonlinear modes -
q-breathers - periodic orbits in nonlinear lattices, exponentially
localized in the reciprocal mode space. To date, the studies of q-breathers
have been confined to the cubic and quartic nonlinearity in the interaction
potential. In this paper we study the case of arbitrary nonlinearity index
γ in an acoustic chain. We uncover qualitative difference in the
scaling of delocalization and stability thresholds of q-breathers with the
system size: there exists a critical index γ*=6, below which both
thresholds (in nonlinearity strength) tend to zero, and diverge when above.
We also demonstrate that this critical index value is decisive for the
presence or absense of thermalization. For a generic interaction potential
the mode space localized dynamics is determined only by the three lowest
order nonlinear terms in the power series expansion.