Open RQC colloquium. Lecture 34

Abstract

Many-body systems are represented by an infinite-dimensional networks in a Hilbert space. That is why the single-particle localization on such networks is an important playground for modeling Many-Body Localization in interacting quantum systems. I show how these two problems are related and demonstrate that certain simple statistics on such random networks mimic in great detail the experimental results in ultra-cold interacting atomic systems. Then I review new developments on Anderson localization on Bethe lattice and Random Regular Graphs, in particular the discovery of the non-ergodic extended phases in these systems and transitions between the localized, non-ergodic extended and ergodic (fully extended) phases. The new results are based on the one-step Replica Symmetry Breaking formalism borrowed from the theory of spin glasses and the newly developed numerical algorithm of Inflationary Population Dynamics. Both of these methods will be shortly discussed.

Biography

Vladimir Kravtsov is an Emeritus Scientist of International Centre for Theoretical Physics, Trieste, Italy. He was born in 1952 in Nizhnii Novgorod, Russia. He finished Moscow Institute of Physics and Technology in 1976. He received the Ph.D. degree from MIPT. He served a member of V.M. Agranovich Theory Group in Institute of Spectroscopy Russian Academy of Sciences from 1979 to 1995. Vladimir Kravtsov was a Humboldt Fellow in Wuerzburg University, Germany, in 1990-1991, and a Postdoc Fellow in University of Heidelberg, Germany, in 1991-1993. In 1993 he defended the Thesis and received the title of Dr.Rer.Nat.Habil. (Dr.Habilitation, the senior doctor degree in Germany) on behalf of the University of Heidelberg. In 1993 he also became a Visiting Staff Associate in International Centre for Theoretical Physics, Trieste, Italy, and a Staff Member of ICTP (Associate Professor) in 1998. In the period of 1995-2008 he was a Staff Member of Landau Institute for Theoretical Physics and remains an Associate Staff Member of Landau Institute until now. From 2002 to 2014, he was a Head of Condensed Matter and Statistical Physics Section (Professor Chair) in ICTP. Vladimir Kravtsov has over 100 publications. His research interests include superconductivity in strongly disordered systems, random matrix ensembles with multifractal eigenstates, anderson localization in the space and time domains, relaxation and transport in non-equilibrium quantum systems and others.

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