P. Gartner

Macroscopic behaviour of a charged Boltzmann gas

We consider a classical charged gas (with self-consistent Coulomb interaction) described by a solvable linearized Boltzmann equation with thermalization on uniformly distributed scatterers. It is shown that if one scales the time t, the reciprocal space coordinate k and the Debye length l as λ2t, (1/λ)k, λl, respectively, in the λ → ∞ limit the charge density is equal to the solution of the corresponding diffusion-conduction (macroscopic) equation.

On the connection between the macroscopical and microscopical evolution in an exactly soluble hopping model

The hopping rate equation for neutral particles, on an arbitrary periodical lattice, can be solved exactly. It is shown that if one scales the time t and the distances x(t→λ2t, x→λx) then, in the λ→∞ limit, the particle density tends to the solution of the diffusion equation faster than λ−3. The diffusion coefficient is the same as obtained from both Kubo and Miller-Abrahams theory via the Einstein relation.

On the Nyquist noise

A quantum-statistical derivation of the general frequency dependent Nyquist theorem is given, that has also a simple circuit-theoretical interpretation. Attention is brought on its application to some very low conductivity materials, where already at 100 Hz the equilibrium noise should be attenuated with a factor of 10−7, with respect to its zero frequency value.

The macroscopic electrodynamic behaviour of a soluble hopping model

The scaling procedure we proposed in previous papers to obtain the macroscopic behaviour from the microscopic (kinetic) description is applied here to a soluble hopping model, on a periodic lattice, which exhibits both conductive and dielectric properties. The Kubo and the Clausius-Mossotti approaches are discussed in the light of our exact results.

Meissner effect in gauge-invariant, self-consistent pairing theories

Within the frame of a self-consistent pairing theory, with potential interelectron interaction, a gauge-invariant discussion of the Meissner effect is given. It is shown that the terms that are usually ignored, proportional to the variation of the order parameter due to the magnetic field, are indeed vanishing in the Coulomb gauge, provided that the pairing phase is locally stable. An instructive example is given, where due to the degeneracy of the phase, although a pairing gap exists, there is no Meissner effect at all.

On the hopping conductivity in the presence of a magnetic field

It is shown that, for hopping systems, even in the presence of a magnetic field, the Kubo approach for zero frequency gives the same DC conductivity tensor as the generalised stationary Miller-Abrahams approach. In general, the result relies on certain assumptions of macroscopic homogeneity about the system, which for periodic lattices turn out to hold exactly.