Cheianov Group (Quantum Many Body Physics in Condensed Matter and Ultracold Atomic Systems)
The research in my group addresses a range of topics related to quantum many-body physics.
Mobile Quantum Impurities
In 1785 Jan Ingenhousz reported the observation of a remarkable phenomenon of chaotic motion of small dust particles immersed in a fluid. The comprehensive theory of such motion was developed more than two centuries later in works by Einstein, who demonstrated the universal nature of the phenomenon and who derived the mathematical laws governing it.
Einstein's theory is purely classical in nature and it doesn't apply if the mobile particles are of quantum size or if the fluid that accommodates them is a quantum fluid. Recent advances in experimental techniques, in particular in the area of ultracold atomic
matter, enabled observation of the motion of individual atoms in quantum fluids exhibiting different quantum orders. This research
investigates the laws governing such mobile quantum particles.
Adiabatic protocols in Driven many-body systems
Quantum adiabatic protocols are routines in which the Hamiltonian of a quantum system undergoes gradual deformation from a given initial to a given final value. Adiabaticity means that the routine is performed slowly enough to ensure complete control, in some well defined sense, over the system’s quantum state. Adiabatic protocols offer a natural framework for coherent quantum state manipulation, therefore the last several years have been marked by increasing interest in their practical implementation.
The existence of an adiabatically slow regime for every quantum protocol is guaranteed by the adiabatic theorem established by Born and Fock as early as 1928. However, the practically important question of what specific conditions are needed to ensure adiabaticity
of a given protocol remains largely unresolved. This research addresses outstanding methodological issues arising from this problem.
Non-Ergodic Quantum Systems
The whole edifice of statistical mechanics rests on the assumption of ergodicity, that is the propensity of a generic closed many-body system to have pure stationary states which are locally indistinguishable from mixed states obeying the Gibbs distribution.
There are three notable exceptions from ergodicity. Spin glasses, disordered systems in a many-body localised state, and Bethe-Ansatz integrable systems.
In the first two classes, non-ergodicity is stable against small perturbations. In the third, it is unstable. All three are encountered in various contexts in solid state physics, ultracold atomic systems, and quantum optics. This research focuses on the exploration of the non-ergodic behavior as resulting from these different mechanisms.
Chiral Anomaly in Condensed Matter Systems and Beyond
Quantum anomaly is a phenomenon by which a quantity conserved at the level of classical equations of motion acquires time dependence in quantum theory. An archetypal example of quantum anomaly is the axial anomaly in quantum electrodynamics discovered by Adler, Bell and Jackiw in 1969.
Since its discovery, the anomaly has been found to play an important role not only in particle physics, but also in condensed matter systems with topological quantum orders. A closer relationship between the anomaly and the hydrodynamic effects such as the chiral magnetic effect and the gyrotropic magnetic effect has also been found.
This research addresses the macroscopic role of anomalies, and the conditions for their emergence in various contexts ranging from condensed matter systems to the evolution of the early Universe.