Plenary Lecture

Continuous Time Quantum Walks and Quantum Recurrences in the Hilbert Space

Professor Alexander Iomin
Solid State Institute, Department of Physics
Technion-Israel Institute of Technology
Haifa, 32000, Israel

Abstract: An analytical consideration of quantum walks in the Hilbert space is suggested for chaotic systems. It is shown that in the semiclassical limit, statistics of the quantum recurrences relates to statistics of the Poincare recurrences of the classical counterpart. In particular, when the integrable part of the phase space emerges due to bifurcation, and the exponential distribution of the Poincare recurrences of chaotic trajectories is changed into the power law, the statistics of the quantum walks in the Hilbert space follows exactly its classical counterpart.

Brief Biography of the Speaker: Dr. Alexander Iomin graduated from Krasnoyarsk State University(USSR) in 1978 and started to work at the theoretical department of the Kirensky Institute of Physics of the USSR academy of Sciences. In 1988 he successfully defended his dissertation (Ph.D) in the field of quantum chaos. Since 1991 he works at the Technion - Israel Institute of Technology at the Department of Physics as a researcher and since 1998 as a Senior Researcher at the Solid State Institute of the Technion. The main scientific interests are: Quantum Chaos, Classical and Quantum Chaos in Mesoscopic Systems, Fractional Diffusion and Quantum Dynamics, Fractional Transport in Biological Systems, and Fractional Electrostatics of Composite Materials.

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