** Lecture 1**.

**1. **Consider a collision-less gas in one dimension. At time
*t=0* it

has a zero density at positive x and a constant density
*n *at

negative *x.* Distribution function of the atoms
is Maxwellian with the

temperature *T *. This gas expands into vacuum. Find its
distribution

function, density *n(x,t)*, current * j
(x,t)*
and energy density

**2. **A satellite has a shape of a disc and moves in the rare,

collision-less gas. Find density distribution
of this gas

in the trace of the satellite.
Velocity of the satelite is larger,

than the thermal velocity of the atams.

**3.** Electrons are interacting with phonons. Write
the collision

integral for the electron phonon collisions in the Boltzmann
equation

for electrons and for phonon-electron collisions in the equation
for

phonons. How the conditions of the detailed balance look like
for both

integrals? Which integrals of the motion these detailed balances
preserve?

**Lecture 2**.

**1.** Find the equation, which describes the Maxwell
relaxation of an

extra charge in a conducting film in the presence of a perpendicular

magnetic field.

**2 **. Find the frequency dependence of electric conductivity

**3. ** Consider an electron gas with the energy dependent
collision rate .

Calculate the current ** j **in the
presence of temperature gradient and electric field

**4.** Consider a gas with binary collisions and find its viscosity
and

thermoconductivity.

**5.** Consider a uniform neutral mixture of negative and positive

particles (electrons and holes), colliding with irregularities
of the

background and with each other. Finds the conductivity, its
dependence

on magnetic field and the Hall resistance.

**6.** Consider thermo-conductivity of electron gas.Compare it with

electric conductivity and find their ratio. (Wiedemann-Franz
Law and the

Lorentz factor) .

** Lecture 4.**

**1. ** Find static dielectric function from Eq
(4.10). Find electrostatic potential

of an external charge, located at the origin.

** 2. ** Consider a neutral plasma with electron
temperature *Te* much

lager, than that *Ti
*of
the ions ( T*e >> Ti
*). Find dielectric

function at *v(Te)
>> vph >>
v(Ti) * and show
that there

is a low lying branch of collective excitations (ionic sound).
Find its

damping.

**3. ** Consider a Maxwellian plasma and a beam of fast
electrons in

it. Show that under these conditions plasma waves have a negative

damping at certain wave vectors (the beam instability).

4. Consider a cloud of electrons and ions in a medium. Electrons

diffuse in it with the diffusion coefficient *De*
and ions - with

*Di . *Find electrostatic
potential and effective diffusion coefficient

of whole cloud.

**5.** Consider sound attenuation in metals.

** Lecture 5 - 6**

**1. ** Using Fokker-Planck equation, find mobility of a heavy
particle in

a gas of light particles.

** 2.** Plasma oscillations with the wave vector **q**
result in

oscillations of the distribution function *f( v t)
~ exp [ -i q v t ] *those survive the Landau

damping (see Lectur 4). Assuming that electron-electron collisions are characterized

by the small momentum transfer, find relaxation rate of this oscillations.

**Lecture 7.**

1. Calculate conductance of a thin film of thickness d
>> l ( l is

the mean free path of electrons in the material) with

a diffusive scattering of electron on inner boundary of the
film (*Klaus Fuchs problem *).

2. Consider absorption of infra-red light on a metal
surface at so

high frequency that the quasi-static condition
is not valid.

3. Use Pippard's efficiency concept for a qualitative
analysis of

resonant high frequency field absorption by a metal in magnetic
field

parallel to its surface ( *V.Heine
)*

**4. ** Neutrons are diffusing in a nuclear reactor
close to its

plane well. Escaped neutrons are never comming back. Consider
kinetic

problem and derive effective boundary condition for the diffusion

equation. ( *Milne problem* )

** Lecture 8**.

** 1. ** Consider phonon thermo-conductivity
in a dielectric with

elastic mean free path l being invercely proportional
to fourth power of the frequency.

Derive effective equation for spreading a hot spot.

** 2. ** Analyse fluctuation of distribution function
in the process of space uniform

down-conversion cascade.

**Lectures 9-10.**

**Lectures 11-12**

**1. ** Factor Lande of electrons in a metal depends on its
position **p ** on the Fermi surface
g( **p** ) .

Find how the line shape

of electron spin resonance (ESR) depends upon disorder in a
metal, that

causes a momentum relaxation.

**Problems for whole course**

**1. **Using consept of effectiveness, consider electron spin
resonance on

conduction electrons under conditions of the anomalous

skin-effect. ( *Dyson; Azbel, Gerasimenko and
I.Lifshits* )

2. Consider sound attenuation in metals in magnetic field
**B** when

the sound wave vector **q** is perpendicular
to the field direction

( **B q** = 0 ). Show that the attenuation
coefficient exhibits

the so called ``Pippard geometric resonance'', i.e. resonance

enhancemment of attenuation at sound wave lengthes commensurable
with

the Larmor radius of electrons.

**3. ** Find high frequency sound attenuation
in the Bose-liquid, keeping

in mind that its dispersion relation in the frame, moving with
velocity

** v** is given by the Galilean law w( **q**) = s|
**q**|
- **v**s **q **. ( *Andreev -
Khalatnikov*})

3. Consider oscillations in collision-less Fermi-liquid.
Find

conditions, when longitudinal sound, transverse sound and spin-waves

exist.( *Landau*)