Doppler Institute conducts research in several directions, each being
headed by a senior member, specifically
- Quantum graphs and waveguides
(Exner)
Quantum systems of nontrivial shapes and submicron sizes are important,
in particular, as building blocks of of next-generation electronic
devices. Their models are intensively investigated; the aim is to
understand how the spectral and scattering properties depend on the
geometric and topological structure, presence of external fields and
interaction between the electrons. The current goals are analysis of
wave function behavior at the branching points, of properties related
to quantum tunneling, and emergence of structures in large graphs.
- Symmetries and integrable
systems (Burdík)
The main goal is to develop methods for investigation of new symmetries
such as quantum groups, quadratic algebras, etc., extending results
well known for classical Lie algebras. Applications concern in the
first place matrix integrable models, quantum theories with higher
spins, the BRST quantization, and other current problems where these
symmetries can be effectively used.
- Quantum information and
communication, quantum optics (Jex)
Devoted to study of quantum optical systems which could be used for
transmission and processing of quantum information, in the first place
problems of universal processes, quantum comparison and its
applications in quantum cryptography and measurement, furthermore,
problems of optical networks, relations to statistical physics and
random-walk theory. The work in quantum optics will aim at
ultracold atom and molecular effects and the use of interference for
quantum communication, including development of state-of-art numerical
methods.
- Aperiodic structures (Pelantová)
They are interesting both from
purely mathematical point of view as well as from the viewpoint of
applications in quantum mechanics, theoretical informatics and
elsewhere. The main goal in the onedimensional case is to extend the
class of quasiperiodic sequences for which the palindromic structure is
known, in the multidimensional one attention will be paid to aperiodic
Delone sets with finite local complexity and quasicrystal models with
selfsimilarity. This activity expanded into a systematic study of
theoretical informatics; more about
activities of this group can be found here.
- Parametric properties of
quantum systems (Šťovíček)
The topics include stability of time dependent quantum systems and
spectral analysis of the corresponding Floquet operators, semiclassical
approximations and asymptotic analysis, furthermore, a study of
Aharonov-Bohm systems with a larger number of fluxes, both in the
nonrelativistic and relativistic case.
- Analytical and algebraical
methods in quantum theory (Znojil)
A systematic study of exactly solvable problems, especially in
many-body quantum mechanics, and their applications in perturbation
expansions. To use general properties of dynamical equations more
efficiently we would aim at a broader scope of physical theory, making
connections between the mathematical and physical approaches to quantum
theory characterized by relativistic kinematics.
- Applications of quantum chaos
methods (Šeba)
Investigations of complicated correlations in time series is related to
properties of random matrix ensembles familiar from quantum chaos
studies; this observation is applicable to investigation of data
ensembles in medicine and elsewhere. The first goal is to analyze
cardioballistic and postural data from force plates with implications
for studies of cardiovascular and neural system, neuromuscular system
reaction to neural controlling signals, as well as interpretation of
time series coming from EEG measurement, all in collaboration with a
medicine professor who takes part in the project.
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Last update: December 7, 2009