Gauge-invariant quantum kinetic equations for interacting electrons are deduced using the Keldysh diagrammatic technique. The Dyson equations are transformed using a special type of the Wigner representation that produces gauge-invariant Green functions. As a result, they depend on the variables having a meaning of position and kinetic momentum. The Wigner representation used makes it necessary to modify the diagrammatic technique in such a way that it will be able to account for the momentum-energy exchange between the system and the electromagnetic field. The formalism obtained makes it possible to carry out many-particle calculations for non-linear systems in arbitrary electromagnetic fields. Some particular simple cases are considered. A special discussion is given regarding the meaning of the detailed balance in such a formulation.

A gauge-invariant Wigner quasi-distribution function for charged particles in classical electromagnetic fields is derived in a rigorous way. Its relation to the axial gauge is discussed, as well as the relation between the kinetic and canonical momenta in the Wigner representation. Gauge-invariant quantum analogs of Hamilton-Jacobi and Boltzmann kinetic equations are formulated for arbitrary classical electromagnetic fields in terms of the 'slashed' derivatives and momenta, introduced for this purpose. The kinetic meaning of these slashed quantities is discussed. We introduce gaugeinvariant conditional moments and use them to derive a kinetic momentum continuity equation. This equation provides us with a hydrodynamic representation for quantum transport processes and a definition of the 'collision force'. The hydrodynamic equation is applied for the rotation part of the electron motion. The theory is illustrated by its application in three examples. These are: Wigner quasi-distribution function and equations for an electron in a magnetic field and harmonic potential; Wigner quasi-distribution function for a charged particle in periodic systems using the kq representation; two Wigner quasi-distribution functions for heavy-mass polaron in an electric field.

A multiphonon mechanism of neutron scattering in glasses is considered. It is due to the interaction of the neutrons with strongly fluctuating double-well potentials characteristic of glasses which may be of importance at not too low temperatures (above the liquid helium temperature). The cross section of this process is calculated and its dependence on the temperature and the neutron energy transfer is found. It is shown that, contrary to the relaxation mechanism, the multiphonon mechanism produces a cross section without a maximum in its temperature dependence. This, as well as some other features, corresponds better to the experimental observations.

The absorption of electromagnetic waves and Raman scattering in glasses are calculated. The principal scattering mechanism considered is the interaction of the electromagnetic waves with atoms tunnelling in strongly fluctuating double-well potentials which are characteristic of glasses. The temperature and frequency dependences of the absorption coefficient and the cross section of the small frequency shift Raman scattering are obtained. The results are fitted to the experimental data.

We consider the role of the third dimension in the conductivity of a quasi-two-dimensional electron gas (Q2DEG). If the transverse correlation radius of the scattering potential is smaller than the width of the channel, i.e. the width of the transverse electron density distribution, then virtual scattering to higher levels of the confinement potential becomes important, which causes a broadening of the current flow profile. The resulting conductivity is larger than that obtained from a quasi-classical two-dimensional Boltzmann equation. A magnetic field, parallel to the driving electric field, effectively adds strength to the confining potential. As a result, the width of the current flow profile decreases and a positive longitudinal magnetoresistivity of the Q2DEG is expected.