Strongly correlated electron systems
(mainly prof. Karol I Wysokinski and dr Tadeusz Domanski)

Research problematics covers :

  1. superconductivity in the strongly correlated electron systems
  2. effect of disorder on superconductivity
  3. quantum Hall effect
  4. conductance of gases
  5. the boson-fermion model
ad 1)
       We study superconductivity of the strongly correlated electron systems described
by the extended Hubbard model. Within such systems there appear the local pairs which
eventually acquire the long range phase coherence with a certain symmetry of the order
parameter. Our interests concern the effect of the on-site interaction U on stabilization
of superconducting phases. This problem is closely related to the fundamental question
concerning a nature of the ground state of the model and the possible phase transitions
for a system to undergo.

ad 2)
       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.

ad 4)
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ad 5)
      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.