The dynamics of a one-dimensional disordered morse attice: Cooling caused by adiabatic stretching

The dynamics of a disordered one-dimensional lattice of a finite length consisting of N particles interacting according to the Morse potential was studied. Disordering was caused by random interaction potential values between neighboring particles. The dynamics of adiabatic stretching of the Morse lattice was considered in detail. An equation relating temperature to the geometric mean normal vibration frequency, that is, $ T propto sqrt[N]{{omega ^1 omega ^2 ldots omega ^N }} The dynamics of a disordered one-dimensional lattice of a finite length consisting of N particles interacting according to the Morse potential was studied. Disordering was caused by random interaction potential values between neighboring particles. The dynamics of adiabatic stretching of the Morse lattice was considered in detail. An equation relating temperature to the geometric mean normal vibration frequency, that is, , was obtained in the quasi-harmonic limit. At low temperatures and certain deformation values, strong interaction between modes was observed which resulted in intense energy exchange between them. The reason for this was pair resonances of the nω ⁱ = ω ^j type. In addition, there were triple resonances ω ⁱ + ω ^j = ω ^k . Close agreement between analytic results and numerical simulation was obtained. At low specific energy € values, the dynamics of the Morse lattice closely resembled the dynamics of the Fermi-Pasta-Ulam lattice. Original Russian Text ? V.N. Likhachev, T.Yu. Astakhova, G.A. Vinogradov, 2009, published in Khimicheskaya Fizika, 2009, Vol. 28, No. 1, pp. 71–82.