Volume 114, Number 4, May 2016
|Number of page(s)||6|
|Published online||13 June 2016|
Variational approach to renormalized phonon in momentum-nonconserving nonlinear lattices
1 State Key Laboratory of Surface Physics and Department of Physics, Fudan University - Shanghai 200433, China
2 Department of Mechanical Engineering, University of Colorado - Boulder, CO 80309, USA
3 Collaborative Innovation Center of Advanced Microstructures, Fudan University - Shanghai 200433, China
Received: 16 March 2016
Accepted: 24 May 2016
In this letter, we extend a previously proposed variational approach to systematically investigate general momentum-nonconserving nonlinear lattices. Two intrinsic identities characterizing optimal reference systems are firstly revealed, which enables us to derive explicit expressions for optimal variational parameters. The resulting optimal harmonic reference systems provide information for the band gap as well as the dispersion of renormalized phonons in momentum-nonconserving nonlinear lattices. As a demonstration, we consider the one-dimensional lattice. We show that the phonon band gap endows a simple power-law temperature dependence in the weak stochasticity regime where predicted dispersion is reliable by comparing with numerical results. In addition, an exact relation between ensemble averages of the lattice in the whole temperature range is found, regardless of the existence of the strong stochasticity threshold.
PACS: 05.45.-a – Nonlinear dynamics and chaos / 63.20.-e – Phonons in crystal lattices / 45.10.Db – Variational and optimization methods
© EPLA, 2016
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