Solids vibrational energy propagation

The experimental and theoretical investigation of higher order vibrational motion and relaxation in solids should now advance quite rapidly as, in fact, there are no lack of suitable problems and the methods to tackle them. We note in this context, and in anticipation of the section on vibrational energy propagation, that the existance of polariton bound states has been inferred from the production of additional gaps in the phonon-polariton dispersion curves of ionic crystals having a molecular subgroup. ... 

In a second example the discrete time-reversible propagation scheme for mixed quantum-classical dynamics is applied to simulate the photoexcitation process of I2 immersed in a solid Ar matrix initiated by a femtosecond laser puls. This system serves as a prototypical model in experiment and theory for the understanding of photoinduced condensed phase chemical reactions and the accompanied phenomena like the cage effect and vibrational energy relaxation. It turns out that the energy transfer between the quantum manifolds as well as the transfer from the quantum system to the classical one (and back) can be very well described within the mixed mode frame outlined above. 

The rate of heat transfer in a thermal gradient is lower than might be expected for transport of vibrational energy heat transport by conductivity is much slower than sound propagation. The accepted physical model for heat transfer is a process of diffusing phonons (wave packets in the vibrating lattice) heat conduction in solids and in fluids is observed to be diffusive. 

Phonons are nomial modes of vibration of a low-temperatnre solid, where the atomic motions around the equilibrium lattice can be approximated by hannonic vibrations. The coupled atomic vibrations can be diagonalized into uncoupled nonnal modes (phonons) if a hannonic approximation is made. In the simplest analysis of the contribution of phonons to the average internal energy and heat capacity one makes two assumptions (i) the frequency of an elastic wave is independent of the strain amplitude and (ii) the velocities of all elastic waves are equal and independent of the frequency, direction of propagation and the direction of polarization. These two assumptions are used below for all the modes and leads to the famous Debye model. 

Thermal conduction through electrically insulating solids depends on the vibration of atoms in their lattice sites, which, as discussed in section 3.7, is the mechanism of thermal energy storage. These vibrations act as the conduit for heat transfer by the propagation of waves ( phonons ) superimposed on these vibrations (schematically depicted in Figure 8.1). An analogy... 

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