Temperature and frequency dependent mean free paths of renormalized phonons in nonlinear lattices

Abstract

Unraveling general properties of renormalized phonons are of fundamental relevance to the heat transport in the regime of strong nonlinearity. In this work, we directly study the temperature and frequency dependent mean free path (MFP) of renormalized phonons with the newly developed numerical tuning fork method. The typical 1D nonlinear lattices such as Fermi-Pasta-Ulam β lattice and f 4 lattice are investigated in detail. Interestingly, it is found that the MFPs are inversely proportional to the frequencies of renormalized phonons rather than the square of phonon frequencies predicted by existing phonon scattering theory.

Projective truncation approximation study of one-dimensional $ϕ^4$ lattice model

“…Below, we present the numerical results obtained by solving the self-consistent equation Eq. (39) for the above two bases. Due to the scaling properties Eqs.…”

“…In the high temperature limit, due to large amplitude of oscillations, the x 4 i -term in H dominates the energy and nonlocal correlation between particles can be ignored [39]. One expects that the system be well described by an independent anharmonic oscillator with Hamiltonian H s = p 2 /2 + (γ/4)x 4 .…”

“…We apply PTA to the study of one-dimensional φ 4 lattice model [32,33], both to demonstrate the applicability of the method and to disclose the underlying physics of this model. This model has been the focus of a series studies in the context of low-dimensional heat transport [32][33][34][35][36][37][38][39] and chaotic dynamics [40,41]. The existence of quartic potential in this model opens a gap in the phonon spectrum at finite temperature and leads to normal heat transport behavior.…”

Phononic heat transport in molecular junctions: quantum effects and vibrational mismatch

“…Other techniques are based e.g. on the Born-Oppenheimer principle 38 , mixed quantum classical propositions 39,40 , and the renormalization of normal modes 41,42 . Numerically exact simulations in the language of wavefunctions 43 or path integral representations [44][45][46][47] are limited to minimal models such as the nonequilibrium spin-boson model.…”