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Main Scientific Interests

Classical Chaos:
Chirikov standard map
Poincare recurrences and slow power law correlations decay
modulational diffusion
chaos for color dynamics of classical homogeneous Yang-Mills fields
breakdown of universality in renormalization dynamics for critical invariant torus with two frequencies
Quantum Chaos:
kicked rotator and dynamical localization
2d and 3d Anderson localization in a 1d system with 2 and 3 frequencies
kicked Harper model
quantum ping-pong model
Diffusive Photoelectric Effect in Hydrogen Atom:
classical chaos border
dynamical photonic localization
Kepler map
Other Directions of Research:
qunatum optics and chaos in Janes-Cummings model
quantum Frenkel - Kontorova model
dynamical localization for Josephson junctions and cold atoms
Rydberg stabilization for atoms in a strong field
nonlinear wave propagation in a random media and delocalization of quantum chaos by weak nonlinearity
chaotic autoionization of molecular Rydberg states
Recent Directions of Research:
universal diffusion near the golden chaos border
low energy chaos in the Fermi-Pasta-Ulam problem
adiabatic destruction of Anderson localization
chaotic Landau level mixing in classical and quantum wells
chaotic enhancement of microwave excitation for chaotic Rydberg atoms
quantum chaos in rough billiards
quantum chaos in open systems
Interaction, Disorder and Anderson localization:
two interacting particles effect
two interacting particles in the Harper model
emergence of quantum chaos and thermalization in finite interacting Fermi systems
3d Anderson transition for two electrons in 2d
quantum ergodicity for electrons in 2d disordered systems
Kravchenko et al. experiment
quantum chaos in spin glass shards
Quantum Chaos and Quantum Computers:
quantum chaos border for quantum computing
Directed transport and ratchets:
equilibrium systems under monochromatic driving, semi-disk Galton board with chaos, ac-force and dissipation
classical and quantum, in qubits and rings of Saturn
Networks and Google matrix:
Ulam networks, university networks