I give a rather elementary introduction to the recent manuscript by Hollands and Sanders: arXiv:1702.04924 and related approaches to entanglement in QFT, with glimpses into the advanced mathematics that enters the analysis.
Topological insulators are bulk-insulating physical materials which carry boundary resonances.
The resonances are robust against perturbations that do not change the topological phase of the material.
A rigorous mathematical description of topological phases which remains valid for aperiodic structures can be
given using C*-algebras and their K-theory.
In that context, numerical topological invariants characterising the topological phase can be obtained via pairing
with cyclic cocycles. In the presence of time reversal symmetry, the numerical invariants may be torsion valued.
A key goal of quantum chaos is to establish a relationship between widely observed universal spectral fluctuations of clean quantum systems and random matrix theory (RMT). For single particle systems with fully chaotic classical counterparts, the problem has been partly solved by Berry (1985) within the so-called diagonal approximation of semiclassical periodic-orbit sums. Derivation of the full RMT spectral form factor K(t) from semiclassics has been completed only much later in a tour de force by Mueller et al (2004). In recent years, the questions of long-time dynamics at high energies, for which the full many-body energy spectrum becomes relevant, are coming at the forefront even for simple many-body quantum systems, such as locally interacting spin chains. Such systems display two universal types of behaviour which are termed as `many-body localized phase' and `ergodic phase'. In the ergodic phase, the spectral fluctuations are excellently described by RMT, even for very simple interactions and in the absence of any external source of disorder. In my talk I will provide the first theoretical explanation for these observations. I will compute K(t) explicitly in the leading two orders in t and show its agreement with RMT for non-integrable, time-reversal invariant many-body systems without classical counterparts, a generic example of which are Ising spin 1/2 models in a periodically kicking transverse field.
14h00 Opening
14h10 Nicolo Drago (Pavia): Thermal state with quadratic interaction
14h50 Matteo Capoferri (London): Hadamard states for quantum Abelian duality
Coffee break
16h00 Vasily Sazonov (Paris): Constructive matrix theory for higher order interaction (work with T. Krajewski and V. Rivasseau)
16h40 Alexander Stottmeister (Rom): Hamiltonian lattice-gauge theory and Duflo-Weyl quantization
Coffee break
17h50 Jochen Zahn (Leipzig): Global anomalies on Lorentzian space-times
19h30 Dinner
Saturday Feb 03
9h00 Beatriz Elizaga de Navascués (Erlangen): Fock quantization of the Dirac field in cosmology with unitary dynamics
9h40 Francesco Bussola (Pavia): Ground state for a massive scalar field in BTZ spacetime with Robin boundary conditions
Coffee break
10h50 Vincenzo Morinelli (Rom): An algebraic condition for the Bisognano-Wichmann property
11h30 Luca Giorgetti (Rom): Minimal index and dimension for 2-C*-categories
Lunch break
14h00 Rodrigo Vargas Le-Bert (Camerino): Non-perturbative renormalization via projective non-gaussian white noise analysis
14h40 Daniel Siemssen (Wuppertal): Feynman propagators in a functional analytic setting