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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
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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
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Diffusive Photoelectric Effect in
Hydrogen Atom:
- classical chaos border
- dynamical photonic localization
- Kepler map
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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
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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
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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
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Quantum Chaos and Quantum Computers:
- quantum chaos border for quantum computing
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Directed transport and ratchets:
- equilibrium systems under monochromatic driving, semi-disk Galton board
with chaos, ac-force and dissipation
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Synchronization:
- classical and quantum, in qubits and rings of Saturn
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Networks and Google matrix:
- Ulam networks, university networks
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