[2011] "Pop Science", New Scientist, 29 October 2011, p.26 .

[2011] A universality in the regular-to-chaos transition in rough quantum billiards. We demonstarte that in rough quantum billiards, the memory of the initial conditions is governed by a single universal energy-dependent parameter---one of the inverse participation ratios---that governs all functions of the to-be-destroyed integrals of motion as observables and all eigenstates of the to-be-perturbed integrable system as the initial states [ Nature Communications 3, 641 (2011)] and [ Phys. Rev. Lett. 106, 025303 (2011) ].

The equipartition of energy between the x- and y-hoppings in a 2D Anderson lattice, subject to a (vanishingly weak) Aharonov-Bohm flux A, is universally governed by the inverse participation ratio η. The relative strength ε of the integrability-breaking perturbation (disorder that is) scans the whole range of the q-chaos regimes, from the Poisson through the Wigner-Dyson.

[2011] We reveal the mathematical mechanism behind the reflectionless property of the Lax operators for the sine-Gordon and Nonlinear Schrodinger equations. As in the Korteweg-de Vries case, absence of reflection at all energies is a consequence of a supersymmetric (SUSY-QM) link to a problem with no scatterers. Our results can also be used to explain the "no-population-inversion-at-any-detuning" property of the sech-laser pulse acting on a two-level atom [ Phys. Rev. E 84, 066601 (2011) ].

Two representative applications of our theory: (i) Lax operator for a two-soliton solution of the sine-Gordon equation; (ii) a two-level atom under a sech-laser pulse.

[2010] A quantum anomaly in ultracold quantum gases. A system of two-dimensional cold bosons possesses, at the mean-field level, a hidden symmetry, discovered by Rosch and Pitaevskii in 1997. We show [ Phys. Rev. Lett. 105, 095302 (2010) ] that under quantization, this symmetry becomes broken, thus manifesting the first known example of a quantum anomaly in physics of ultra-cold gases.

Two-dimensional bosons in an HO trap. At the mean-field level, there exists an algebra of three observables that closed under Poisson brackets. However, this algebra opens under quantization, thus constituting a quantum anomaly.

[2009] Mean-field dynamics of quantum gases from the point of view of classical chaos. We show that in a system of one-dimensional lattice bosons, the regular-to-chaos transition does survive in thermodynamic limit [ Phys. Rev. Lett. 102, 025302 (2009].

Lyapunov exponent as a function of the intensive parameters governing the system of 1D lattice bosons

[2008] The Eigenstate Thermalization effect, suggested by Deutsch and Srednicki in the eary 90s, is conjectured to be the governing mechanizm behing relaxation in isolated quantum systems.  We confirm this conjecture through ab initio numerical tests [ Nature, 452, 854 (2008)].

Quantum vs. classical thermalization

[2006-2007] Quasi-thermalization in integrable systems. A simple thermodynamical ensemble that describes the outcome of relaxation in an isolated integrable quantum system is suggested [ Phys. Rev. Lett. 98, 050405 (2007)].  The integrability-induced suppression of chemical reactions has been studied as well [ Phys. Rev. Lett. 96, 163201 (2006)].

Relaxation of spatial and momentum distributions in a 1D gas of hard-core bosons

[1989-present] A complete publication list can be found here.