3-4

Ballistic phonon propagation is the idea that phonons move with constant speed until they hit an obstacle.

Phonons can be visualized as particles or as waves in the lattice.

The Grüneisen relation tells how much the frequency of the phonons shift when the volume gets bigger. It is used in the thermal expansion coefficient

In a crystal with harmonic potential, the Grüneisen parameter would be zero.

If the Grüneisen parameter would take negative values, the material would shrink when it is heated. This is possible, but typical values would be 1-2

Yes, because the Phonon energy is not zero even at T=0K. It scales with (n+1/2)

Each phonon contributes equally to the heat transport, G= J/\Delta T = N*G_0.

One dimensional heat transport requires the thread to be thinner than half of the phonon wavelength.

By applying an oscillating current to a thread, the sample below can be heated in a cos curve. By measuring the temperature dependent voltage, an oscillation three times as fast as the original one (3 omega). The amplitude of this oscillation is linked to the thermal conductivity.

An approximation method for integrals. It is used to calculate e.g. the electronic part of heat capacity as well as Pauli Spin-Susceptibility.

The main idea is that we solve integrals over the electronic density of states and the fermi distribution by approximating that only the states around the fermi edge are important, and that they deviate by only a small amount from T=0.

Because the Pauli Principle suppresses it

An equation that simulates the propagation of particles (here: charge carriers) under a concentration gradient and scattering processes.

The energy of spin up and down electrons differs when applying a B-field. Since the fermi energy always wants to be the same for the whole system, some of the electrons in the higher part will perform a spin flip.

Etching

Because there the phonons and the dulong petit limit have much bigger contributions