In this presentation, I will show where several recent projects in our group are situated on the vast [(integrable vs chaotic)x(classical vs quantum)] two-dimensional plane of dynamical systems of interest. I will start from our work demonstrating that the Eigenstate Thermalization effect of Deutsch-Srednicki qualifies as the origin of irreversibility in (otherwise linear) Quantum Mechanics [Nature, 452, 854 (2008)]. I will next present our suggestion for a conceptually and computationally simple thermodynamic ensemble that describes the outcome of the time evolution of a completely integrable quantum system [PRL 98, 050405 (2007)]. We will further look at the integrability breaking in a Bose-Hubbard model [PRL 102, 025302 (2009)], and in two systems of waveguide-confined bosons: three transversally cold [PRL 96, 163201 (2006)] and two transversally hot [PRL 106, 025303 (2011)] atoms respectively; further discussion on the universalities in the disappearance of the integrals of motion in quantum systems with no selection rules---Anderson model in particular---will follow. Next, we will look at the connection between the Quantum-Mechanical Supersymmetry (QM-SUSY) and both the solitons in the sine-Gordon model [arXiv:1012.2843] and solutions of the Bogoliubov-de-Gennes equations for a one-dimensional attractive BEC. Finally, I will discuss the breaking, under quantization, of the classical Pitaevkii-Rosch dynamical symmetry in a two-dimensional harmonically trapped Bose gas [PRL 105, 095302 (2010]. In collaboration with: Marcos Rigol, Vladimir Yurovsky, Amy Cassidy, Andrew Koller, Kurt Jacobs, Helene Perrin, Vincent Lorent, Abraham Ben-Reuven, Vanja Dunjko, Douglas Mason, Yassine Ait El Aoud, Cavan Stone, and Harry Kennard
Maxim Olshanii received his PhD in 1992 from the Institute of Spectroscopy in Troitzk, Russia. In 1994 he became a postdoc at Ecole Normale Superieure in Paris, where he worked on dark-state cooling of atoms. For his second post-doctoral term, 1995-1999, Maxim held a dual appointment at Harvard University and ITAMP, and studied confined collisions. In 1999 he joined the faculty of the University of Southern California as an Assistant Professor, becoming an Associate Professor there in 2004. Since 2007, Maxim Olshanii has been an Associate Professor at the University of Massachusetts Boston. The central topic of his current research is the transition from integrability to thermalization in cold atomic gases.