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SUMMARY:title: A new approach to address scrambling of quantum information
  using Graph and Ergodic theories. - Uzy Smilansky (Weizmann Institute of 
 Science)
DTSTART:20260211T140000Z
DTEND:20260211T150000Z
UID:TALK242062@talks.cam.ac.uk
DESCRIPTION:\\noindent Abstract: Together with Arkady Kurnosov and Sven Gn
 utzmann\\\\&nbsp\; \\noindent Given a quantum hamiltonian\, represented as
  a $N\\times N$ Hermitian matrix $H$\, we derive an expression for the lar
 gest $\\it Lyapunov \\ exponent$ of the $\\it classical\\ trajectories$ in
  the $\\it phase-space$ appropriate for the dynamics induced by $H$. To th
 is end we associate to $H$ a graph with $N$ vertices and derive a $\\it qu
 antum\\ map$ on functions defined on the directed edges of the graph. Usin
 g the $\\it semi-classical\\ approach\\ in\\ the \\ reverse\\ direction$ w
 e obtain the corresponding classical evolution (Liouvillian) operator. Usi
 ng ergodic theory methods (Sinai\, Ruelle\, Bowen\, Pollicot...) we obtain
  close expressions for the Lyapunov exponent\, as well as for its variance
 . Applications for random matrix models will be presented. \\end{document}
LOCATION:Seminar Room 2\, Newton Institute
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