---
res:
  bibo_abstract:
  - "This thesis deals with several different models for complex quantum mechanical
    systems and is structured in three main parts. \r\n\t\r\nIn 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. These estimates have profound consequences
    for eigenvector overlaps and thermalization problems. More concretely, we obtain,
    e.g., the optimal eigenstate 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.\tIn 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. \r\n\t\r\nIn Part II,
    we study Bardeen-Cooper-Schrieffer (BCS) theory, the standard mean field microscopic
    theory of superconductivity. We focus on asymptotic formulas for the characteristic
    critical temperature and energy gap of a superconductor and prove universality
    of their ratio in various physical regimes. Additionally, we investigate multi-band
    superconductors and show that inter-band coupling effects can only enhance the
    critical temperature. \r\n\t\r\nIn Part III, we study quantum lattice systems.
    On the one hand, we show a strong version of the local-perturbations-perturb-locally
    (LPPL) principle for the ground state of weakly interacting quantum spin systems
    with a uniform on-site gap. On the other hand, we introduce a notion of a local
    gap and rigorously justify response theory and the Kubo formula under the weakened
    assumption of a local gap. \r\n\t\r\nAdditionally, we discuss two classes 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 relativistic toy models of particle
    creation via interior-boundary-conditions (IBCs).  @eng"
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Sven Joscha
      foaf_name: Henheik, Sven Joscha
      foaf_surname: Henheik
      foaf_workInfoHomepage: http://www.librecat.org/personId=31d731d7-d235-11ea-ad11-b50331c8d7fb
    orcid: 0000-0003-1106-327X
  bibo_doi: 10.15479/AT-ISTA-19540
  dct_date: 2025^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/2663-337X
  - http://id.crossref.org/issn/978-3-99078-057-2
  dct_language: eng
  dct_publisher: Institute of Science and Technology Austria@
  dct_title: 'Modeling complex quantum systems : Random matrices, BCS theory, and
    quantum lattice systems@'
...