## Non-equilibrium classical and quantum statistical mechanics

- Transport phenomena in low dimensional systems: integrable & non-integrable, classical & quantum
- Open quantum systems
- Phase transitions in open systems far from equilibrium
- Canonical quantization in Fock space of operators (
*Third quantization*)

## Quantum information theory

- Quantum entanglement and critical phenomena
- Simulability of quantum states and operators
- Entanglement of random states
- Quantum algorithms

## Classical and quantum chaos

- Hamiltonian dynamical systems: from integrability to chaos
- Ergodicity and dynamical mixing
- Loschmidt echoes and fidelity decay
- Classical and quantum billiards
- Semiclassics, Wigner functions

## Mathematical methods in quantum and classical statistical physics

- Operator algebras and functional analysis
- Algebraic Bethe ansatz
- Quantum groups and their representations
- Random matrix theory

SeeĀ List of Publications