Research problematics covers :
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Disorder can drastically influence superconducting state of the initially
clean system.
We address this point by analyzing
the two component alloys with the site diagonal disorder.
To treat this model we apply the
coherent potential approximation (CPA) which allows us
for a reliable description of both:
normal and superconducting phases. Supplementary we
also use the recursion method to
solve the Bogolubov - de Gennes equations. Recently
we have estimated the charge and
order parameter fluctuactions as induced by strong
correlations.
ad 3)
Theoretical aspects of the quantum Hall effect are studied in two dimensional
systems using various methods.
The recent study of the percolation problem within
the quantum mechanical treatment
gives the information about the critical exponents.
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We investigate superconducting and normal phase properties of the correlated
system
composed of itinerant elecrons
and localized hard-core bosons (which can be envisioned
as, for instance, polarons). Hybridization
between these two species can, under certain
conditions, induce superconductivity.
Superconducting behaviour of electrons' subsystem
is due to superfluidity of bosons.
This model is an evident example of the non Fermi liquid
exhibiting characteristic anomalies
above transition into superconducting phase. One of
the effects is a pseudogap formation
in the normal state density of states. Mechanism
responsible for a formation of
this pseudogap is at present under our consideration.