
Nanotechnology for fast DNA
sequencing
One
of the great scientific and technological problems
of today is understanding the structure and function
of DNA and closely related development of
inexpensive methods for DNA sequencing. The latter
promises to revolutionize both our understanding of
DNA as well as significantly advance personalized
medicine. Two aspects of the problem that are
currently being investigated are noncovalent
interactions and nonequilibrium electronic
transport properties at nanometer scale.
Noncovalent interactions are known to play an
important role in biochemistry, notably the
Hydrogenbonding that pairs nucleotides in the
double helix of DNA, as well as stacking
interactions of DNA strands or surfaceadsorbed
nucleotides, which we study using the numerical
simulation based on the density function theory
(DFT). Our main research activity in this area is
theoretical understanding of the promising approach
to the fast DNA sequencing via measurement of the
transverse electronic current while a singlestrand
of DNA is passing through a nanopore equipped with
nanoelectrodes, where the task is to decode the
nucleotide sequence based on the measured current.
Since the main electronic transport mechanism is
tunneling, it is advantageous to apply large biases
to increase the current, and the correct theoretical
modeling of such experimental setups requires use of
nonequilibrium transport, which we study using DFT
in combination with the Kelydish Green's function
formalism.
Photovoltaics
An
important area of applied physics today is
development of novel as well as improvement of
current solarcell technologies, characterized by
the efficiency of material in converting the light
into electrical current. The most efficient in this
respect are (poly)crystalline and amorphous Silicon
based photovoltaics. Among the most promising
alternatives are those based on TiO2, and our
research is oriented towards studying electronic
structure of physically as well as chemically
modified different phases of TiO2, using numerical
DFT simulations to better understand results of
experimental measurements. The second direction of
our research is concerned with the dominant
mechanism of the photon conversion into electrical
current via creation and transport of excitons
formed after the photon capture in optoelectric
materials. Efficacy of photovoltaics is determined
to a large extent by the lifetime and dynamics of
excitons, and our current research activities are
also oriented towards a better understanding of the
exciton dynamics with the perspective of material
design with higher exciton to electron transfer
rates upon the photon capture, using numerical
modeling of Markov processes describing the exciton
dynamics.
Quantummechanical disordered and chaotic systems
Since
the discovery of the Anderson localization, one of
the main problems of the theory of disordered
systems was theoretical understanding of the
transition from the insulating localized phase of
strongly disordered conductors to the metallic
delocalized phase of weakly disordered conductors,
its nature, universal properties and transport
mechanisms. In this respect the first area of
research is the development of the scaling theory of
the Anderson metalinsulator transition, using
numerical simulations and applying the
renormalizationgroup formalism. An important class
of the disordered systems are 2d Anderson models
with chiral symmetry, most notably the randomflux
and the randombond Anderson models. They appear in
certain effective theoretical descriptions of
highTc superconductivity as well as quantumHall
effect. Their main property is the appearance of
nonlocalized states at the band center, in
contradistinction to the 2d Anderson model where all
electronic states are at most exponentially
localized, and properties of these exceptional
states remain in focus of the second area of the
ongoing research. Third area is statistical
properties of disordered conductors, which are by
large governed by the randommatrix theory and the
related notion of quantum chaos. Notably, the far
tail of distribution of electronic eigenstate
intensities of mesoscopic metallic grains are
determined by the rare realizations of the disorder,
which proper understanding remains a difficult
problem in the theory of disordered and
quantumchaotic system.
Quasicrystals
This
year's Nobel prize for Chemistry was awarded for the
experimental discovery of quasicrystals, strange
materials whose Xray diffractometry shows from the
physics viewpoint crystalographically impossible
symmetries. Those are rapidly cooled alloys
exhibiting unusual diffraction patterns: fivefold
in the case of AlMn and AlFe, twelvefold in the
case of NiCr grains, as well as eightfold in the
case of VNiSi and VNiCr thin films. The puzzle
was explained by (mathematically longknown)
quasicrystaline arrangements of atoms, where each
set of atoms of the material repeats indefinitely
throughout the crystal, sometimes with rotational
symmetry and always without the presence of
translational symmetry. Such arrangements of atoms
can be obtained mathematically by tiling of plane or
space with a finite number of specially chosen
tiles, from recursive rewrite systems, or by
projecting translationally symmetric lattices in
higher dimensional spaces onto 3d hyperplanes.
Quasicrystals are weakly conducting, exhibiting
remarkable spectral and transport properties such as
singularcontinuous spectrum and anomalous
diffusion. In these respects, as well as in the
sense that they are only partly symmetric,
quasicrystals are intermediates between periodic
crystals and amorphous solids.
Highperformance scientific programming
Growth
in applicability of numerical methods in modern
science is by large driven by the rapid increase in
computational capabilities of hardware due to
multicore processors, connecting of computational
units via fast networks as well as rapidly
increasing capabilities of graphical processing
units. An efficient use of such a variety of
hardware resources still remains difficult from the
viewpoint of software, underlying the necessity for
development of a nextgeneration programming
languages that will allow an efficient highlevel
abstraction of hardware while allowing fast
development of efficient parallel and correct
programs for use in computational physics, chemistry
and biology. In this context our research is
directed towards development of highlevel
arrayoriented parallel language of the APL family
with features of modern purely functional
programming languages, by utilizing programming
techniques of Haskell programming language and
category theory. 