title: Renormalized phonons in nonlinear lattices: A variational approach.
abstract: We propose a variational approach to study renormalized phonons in momentum-conserving nonlinear lattices with either symmetric or asymmetric potentials. To investigate the influence of pressure for phonon properties, we derive an inequality which provides both the lower and upper bound of the Gibbs free energy as the associated variational principle. This inequality is a direct extension to the Gibbs-Bogoliubov inequality. Taking the symmetry effect into account, the reference system for the variational approach is chosen to be harmonic with an asymmetric quadratic potential which contains variational parameters. We demonstrate the power of this approach by applying it to one-dimensional nonlinear lattices with a symmetric or asymmetric Fermi-Pasta-Ulam-type potential. For a system with a symmetric potential and zero pressure, we recover existing results. For other systems which are beyond the scope of existing theories, including those having symmetric potential and pressure and those having the asymmetric potential with or without pressure, we also obtain accurate sound velocity.
authors.affiliation: State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China.
authors.forename: Junjie
authors.initials: J
authors.lastname: Liu
authors.affiliation: Department of Physics and Centre for Computational Science and Engineering, National University of Singapore, 117546 Singapore.
authors.forename: Sha
authors.initials: S
authors.lastname: Liu
authors.affiliation: Center for Phononics and Thermal Energy Science, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China.
authors.forename: Nianbei
authors.initials: N
authors.lastname: Li
authors.affiliation: Department of Physics and Centre for Computational Science and Engineering, National University of Singapore, 117546 Singapore.|Center for Phononics and Thermal Energy Science, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China.|NUS Graduate School for Integrative Sciences and Engineering, 117456 Singapore.|Graphene Research Centre, Faculty of Science, National University of Singapore, 117542 Singapore.
authors.forename: Baowen
authors.initials: B
authors.lastname: Li
authors.affiliation: State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China.|Collaborative Innovation Center of Advanced Microstructures, Fudan University, Shanghai 200433, China.
authors.forename: Changqin
authors.initials: C
authors.lastname: Wu