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SUMMARY:System dependent random matrix ensembles: an unavoidable tool for 
 many body theories [MPIM]
DTSTART:20250811T123000Z
DTEND:20250811T133000Z
DTSTAMP:20260721T131300Z
UID:indico-event-592@math-events.uni-bonn.de
DESCRIPTION:Speakers: Pragya Shukla (IIT Kharagpur/MPIM)\n\nNumber theory 
 lunch seminar\nThe ignorance of the detail in a complex system e.g one wit
 h manybody interactions introduces a degree of randomness in its matrixrep
 resentation (even in absence of disorder) and it can be modeled by arandom
  matrix (with some or all random entries). While the statisticalbehavior o
 f many body systems in ergodic regime can be well-modeledby the stationary
  random matrix ensembles\, the non-ergodic regimerequires consideration of
  system-dependent random matrix ensembles:those which take into account th
 e physical constraints on the systeme.g. local interactions\, dimensionali
 ty\, symmetry\, local conservationlaws. For example\, the combined e ect o
 f nearest neighbor interactionsand dimensionality can lead to a sparse ran
 dom matrix representationof the Hamiltonian in a basis of interest\, with 
 sparsity and nature ofrandomness dependent on system-specific details.\nTh
 e statistical analysis of various many body systems requires\,therefore\, 
 a thorough probing of a wide range of random matrixensembles which is not 
 an easy task. It is highly desirable\, if possible\,to identify a common m
 athematical structure among the ensemblesand analyze it to gain informatio
 n about the physical properties. Oursuccessful search in this direction le
 ads to Brownian ensembles as thehidden skeleton for a wide range of system
 s. A complete investigationof Brownian ensembles can then help us in the s
 pectral analysis of awide range of many body systems. \n\nhttps://math-ev
 ents.uni-bonn.de/event/592/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/592/
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