Kinetic Theory Of Phonons Research Articles

Thermal transport in spin ice

In order to analyse low temperature heat transport in the spin ice compound Dy2Ti2O7, we derive thermodynamic field equations that are based on the kinetic theory of phonons and their interaction with localised magnetic excitations. It is shown that the solution of the derived field equations for given boundary and initial values of heat-pulse experiments well describes all measured temperature profiles recorded in the temperature range from 0.3 to 15 K and in magnetic fields up to 1.5 T. The evaluated temperature and field dependencies of both the specific heat contributions and their corresponding relaxation times indicate that the magnetic excitations above the ground-state manifold of the spin ice compound Dy2Ti2O7 take the form of magnetic monopoles.

Gradient expansions in kinetic theory of phonons

For simple models of the phonon transport in rigid insulators, it is demonstrated that the extended diffusional mode transforms into a second-sound mode after its coupling to a nonhydrodynamic mode at some critical value of the wave vector. This criticality shows up as a branching point of the extension of the diffusional mode within the Chapman-Enskog method, found explicitly for these models. The solution is used to test validity of several nonpolynomial approximate methods to capture this criticality.

Mean free path effects in superfluid4He

The mean free path effects in superfluid He II was studied with a vibrating wire method in the temperature range from Tλ down to 20 mK under the saturated vapour pressure. The transition from the hydrodynamic regime to the ballistic regime was clearly observed at around 0.7 K with a 47 µm diameter wire. In the hydrodynamic regime the usual Stokes' approximation was found to be insufficient to interpret the results. In the ballistic regime the results can be explained quantitatively with the kinetic theory of phonons. However, below about 0.15 K there appear non-linear effects such as the distortion of the resonance line shape and a hysteresis behavior, which become stronger with decreasing temperature.

Quelques problèmes actuels de la Physique des cristaux

A short description is given of actual problems of the dynamics of crystals. It is shown that thermal motions of atoms can be described by normal modes of vibrations, or by waves or then by the quanta, called phonons, carried by these waves. In terms of this gas of phonons, the dynamics of crystals becomes the kinetic theory of phonons. If the forces between the atoms are harmonic, the phonons behave like an ideal gas. If we introduce anharmonic forces, the gas of phonons is like a real gas, collisions between the particles playing an important part. The anharmonic forces produce waves which do not satisfy the principle of superposition; they can be Bragg-reflected one on another with a strong Doppler effect. It is possible to define a mean free path of the phonons and then such phenomena as heat conductivity and internal friction are easily interpreted either in terms of waves or phonons.