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SUMMARY:Javier Magan (University of Pennsylvania)
DTSTART:20221005T193000Z
DTEND:20221005T203000Z
DTSTAMP:20260423T005709Z
UID:HET/37
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/HET/37/">A t
 ale of two hungarians: tridiagonalizing random matrices</a>\nby Javier Mag
 an (University of Pennsylvania) as part of Purdue HET\n\n\nAbstract\nThe H
 ungarian physicist Eugene Wigner introduced random matrix models in physic
 s to describe the energy spectra of atomic nuclei. As such\, the main goal
  of Random Matrix Theory (RMT) has been to derive the eigenvalue statistic
 s of matrices drawn from a given distribution. The Wigner approach gives p
 owerful insights into the properties of complex\, chaotic systems in therm
 al equilibrium.  Another Hungarian\, Cornelius Lanczos\, suggested a metho
 d of reducing the dynamics of any quantum system to a one-dimensional chai
 n by tridiagonalizing the Hamiltonian relative to a given initial state. I
 n the resulting matrix\, the diagonal and off-diagonal Lanczos coefficient
 s control transition amplitudes between elements of a distinguished basis 
 of states. This method suggests a computable notion of complexity which we
  describe in detail. We then connect the Wigner/Lanczos approaches by anal
 yzing RMT in time-dependent scenarios.  This is first accomplished by nume
 rically studying time-evolved thermofield double states in chaotic systems
 \, where our complexity measure shows parallel regimes as the Spectral For
 m Factor in RMT. Secondly\, to approach these problems analytically\, we i
 nitiate a novel approach to Random Matrix Theory based on matrix tridiagon
 zalition\, deriving the statistics of the tridiagonal matrix.\n
LOCATION:https://researchseminars.org/talk/HET/37/
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