Research Activity (in Theoretical and
Mathematical
Physics)
- Analogue
QED
with ultra-cold atoms in optical lattices [PD at Univ. Duisburg-Essen]
- Analog models of quantum fields living in curved spaces with
defective graphene --> WWW
- Analog models of quantum fields living in curved spaces with
optical lattices containing structural defects --> WWW
- Quantum simulator of supercritical fields of QED and of the
spontaneous pair creation (in 1+1
dimension)
- Ultra-cold fermions/bosons in bichromatic (doubly-periodic)
optical potentials
- Band splitting and relativistic dispersion relation in
Bose-Hubbard models
- Nonlinear
stability
and late-time asymptotics for nonlinear wave equations [PD at AEI, Golm-Potsdam] --> description
[2008], report
[2009]
- Nonlinear stability of Schwarzschild / Kerr black holes
- Stability and decay for
nonlinear wave equations
- Perturbation theory and
stability for nonlinear systems
- Propagation of nonlinear
gravitational waves
- Relaxation to (intermediate)
attractors
- Orbital/modular stability
- QED in external
fields [PhD at Univ.
Frankturt/Main]
- evolution and scattering in Fock space
- time-dependent Hamiltonians,
pair production,
adiabatic processes
- spontaneous creation of electron-positron
pairs in overcritical potentials:
- definition (by the adiabatic limit)
- proof of the existence
- vacuum instability and decay
- analysis of eigenvalues diving in the
(negative) continuum
(--> resonances)
- numerical simulations (coupled channels formalism)
- Critical
phenomena in gravitational collapse [collab.
with Univ. Southampton]
- self-similarity of solutions, eigenvalue
problem,
log-periodicity
- naked singularity formation and analytic
continuation of
solutions behind the future light-cone
- Theory of
resonances and quasinormal modes
- Estimation methods:
- shooting-to-a-fitting-point in ODE
- complex scaling (analytic continuations,
Stokes
phenomenon)
- complex path integrals (anti-Stokes
lines)
- continued fractions
- resummation of divergent series
(asymptotics):
Borel, Pade
- superasymptotics, hyperasymptotics
- Theory of Sturm-Liouville problems,
(non)self-adjoint operators
- Quasinormal mode expansion of the
evolution
as an exact solution of the Cauchy problem
- Nonlinear
evolution (wave) equations [M.Th.
at Univ.
Cracow]
- singularity formation (universality)
- intermediate attractors and critical
phenomena
(between blowup
and dispersion)
- relaxation to attractors (as relaxation in
open
systems):
- time-asymmetric boundary conditions
- quasinormal modes (universality)
Scientific Interests
- Quantum Field Theory (QFT) on curved space-times / in
non-inertial frames:
- Gauge theories: geometric interpretation in terms of
connections
and the meaning of gauge freedom in physics
- Riemann-Cartan geometry with curvature and torsion
- Decoherence and measurement in quantum theory:
- the process of measurement
- interaction of a quantum system with "environment",
evolution to
pointer states
- Neural networks - brain modeling:
- self-organizing and self-learning systems
- synchronization and waves
- consciousness and attention as top-down/bottom-up processes