Dynamics of disordered 1D Morse lattice. Cooling under adiabatic elongation and Chirikov's resonances

In the present Letter we thoroughly investigated the dynamics of the one-dimensional disordered Morse lattice of finite length. The disorder is conditioned by the random values of the interaction potential wells. This Letter is an extension and essential refinement of the earlier results [V.N. Likhachev, T.Yu. Astakhova, G.A. Vinogradov, Phys. Lett. A 354 (2006) 264], where the thermodynamics of 1D Toda and Morse lattices was formulated. Here the dynamics of the disordered Morse lattice was considered under the adiabatic elongation. A relation between the temperature and the mean-geometric value of vibrational frequencies was derived in quasi-harmonic approximation at adiabatic conditions, i.e. T∝ω1ω2⋯ωNN. At some values of elongation we observed strong interaction between few vibrational modes resulting in intensive energy exchange. The reason is Chirikov's resonances: nωi=mωj. Moreover, we firstly observed the triple resonances ωi+ωj=ωk. At small values of specific energy the dynamics of Morse and Fermi-Pasta-Ulam lattices is similar. Good agreement between analytic results and MD numerical simulation is observed.