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UID:1743667200@ist.ac.at
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DESCRIPTION:Speaker: Joscha Henheik\nhosted by Johann Danzl\nAbstract: This
  thesis deals with several different models for complex quantum mechanical
  systems and is structured in three main parts.    In Part I\, we study
  mean field random matrices as models for quantum Hamiltonians. Our focus 
 lies on proving concentration estimates for resolvents of random matrices\
 , so-called local laws\, mostly in the setting of multiple resolvents. The
 se estimates have profound consequences for eigenvector overlaps and therm
 alization problems. More concretely\, we obtain\, e.g.\, the optimal eigen
 state thermalization hypothesis (ETH) uniformly in the spectrum for Wigner
  matrices\, an optimal lower bound on non-Hermitian eigenvector overlaps\,
  and prethermalization for deformed Wigner matrices. In order to prove our
  novel multi-resolvent local laws\, we develop and devise two main methods
 \, the static Psi-method and the dynamical Zigzag strategy.    In Part 
 II\, we study Bardeen-Cooper-Schrieffer (BCS) theory\, the standard mean f
 ield microscopic theory of superconductivity. We focus on asymptotic formu
 las for the characteristic critical temperature and energy gap of a superc
 onductor and prove universality of their ratio in various physical regimes
 . Additionally\, we investigate multi-band superconductors and show that i
 nter-band coupling effects can only enhance the critical temperature.   
  In Part III\, we study quantum lattice systems. On the one hand\, we sho
 w a strong version of the local-perturbations-perturb-locally (LPPL) princ
 iple for the ground state weakly interacting quantum spin systems with a u
 niform on-site gap. On the other hand\, we introduce a notion of a local g
 ap and rigorously justify response theory and the Kubo formula under the w
 eakened assumption of a local gap.    Additionally\, we discuss two cla
 sses of problems which do not fit into the three main parts of the thesis.
  These are deformational rigidity of Liouville metrics on the torus and re
 lativistic toy models of particle creation via interior-boundary-condition
 s (IBCs). 
LOCATION:Office Bldg West / Ground floor / Heinzel Seminar Room (I21.EG.101
 ) and Zoom\, ISTA
ORGANIZER:
SUMMARY:Joscha Henheik: Thesis Defense: Modeling complex quantum systems - 
 Random matrices\, BCS theory\, and quantum lattice systems
URL:https://talks-calendar.ista.ac.at/events/5596
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