Thema:

Spectral properties of the trap model on sparse networks

Datum:

21.01.19

Uhrzeit:

16:15

Ort:

H6

Vortragender:

Prof. Dr. Peter Sollich

Universität Göttingen

Inhalt:

One of the simplest models for the slow relaxation and aging of glasses is the trap model by Bouchaud and others, which represents a system as a point in configuration-space hopping between local energy minima. The time evolution depends on the transition rates and the network of allowed jumps between the minima. We consider the case of sparse configuration-space connectivity given by a random graph, and study the spectral properties of the resulting master operator. We develop a general approach using the cavity method that gives access to the density of states in large systems, as well as localisation properties of the eigenvectors, which are important for the dynamics. We illustrate how, for a system with sparse connectivity and finite temperature, the density of states and the average inverse participation ratio have attributes that arise from a non-trivial combination of the corresponding mean field (fully connected) and random walk (infinite temperature) limits. In particular, we find a range of eigenvalues for which the density of states is of mean-field form but localisation properties are not, and speculate that the corresponding eigenvectors may be concentrated on extensively many clusters of network sites.

Ansprechpartner:

G. Akemann

Thema:

Introduction to the non commutative topology of topological insulators

Datum:

25.01.19

Uhrzeit:

16:15

Ort:

T2-213

Vortragender:

Johannes Kellendonk

Universite Claude Bernard - Lyon I

Inhalt:

Topological insulators are insulating materials which are in a topological non-trivial phase. Perhaps the most exciting consequence of this is the existence of boundary resonances (for instance boundary currents) which are robust against disorder. Mathematically this is related to a bulk boundary correspondance linking topological invariants of the bulk of the material to topological invariants associated to the boundary. Our approach uses K-theory and cyclic cohomology of operator algebras.

Ansprechpartner:

M. Baake

Thema:

Abundant sets of internal spaces for string theory

Datum:

31.01.19

Uhrzeit:

14:15

Ort:

D6-135

Vortragender:

Harald Skarke

TU Wien und Univ. Bielefeld

Inhalt:

The ten-dimensional spacetime of string theory is usually interpreted as a cartesian product of a four-dimensional manifold corresponding to the universe we observe and a six-dimensional compact space which is taken to be a Calabi-Yau (CY) threefold (a space of three complex, i.e. six real dimensions). A different construction known as F-theory combines the data of the internal space and of some background fields into those of a CY fourfold. The most fertile construction method for CY manifolds comes from a branch of algebraic geometry known as toric geometry, where families of CY n-folds are associated to (n+1)-dimensional polytopes that have a certain property called reflexivity. I will explain the concepts introduced above. Then I will outline how we managed to classify all 476,800,776 reflexive 4-polytopes almost 20 years ago, which corresponds to the world's largest list of CY threefolds. Finally I will report on recent work on the classification of a particular class of reflexive 5-polytopes (there are 322,383,760,930), which resulted in the largest existing database for CY fourfolds.

Ansprechpartner:

D. Schwarz

Thema:

Eine kurze Einführung in CUDA

Datum:

17.01.19

Uhrzeit:

14:15

Ort:

D5-153

Vortragender:

Matthias Götte

Universität Bielefeld

Inhalt:

Ansprechpartner:

Thomas Dahm

Thema:

Convergence in High Probability of the Quantum Diffusion in a Random Band Matrix Model

Datum:

17.01.19

Uhrzeit:

16:00

Ort:

D5-153

Vortragender:

Vlad Margarint

University of Oxford

Inhalt:

We consider Hermitian random band matrices in $d > 1$ dimensions. The matrix elements are independent, uniformly distributed random variable if the distance between points is less than the band width, and zero otherwise. In this talk I will present an update of the previous results of the converge of quantum diffusion in a random band matrix model from convergence of the expectation to convergence in high probability. The proof relies on graphical representations of the various quantities involved in the analysis. This work was done under the supervision of Prof. Antti Knowles.

Ansprechpartner:

Gernot Akemann

Thema:

The level spacing distribution at the hard edge

Datum:

28.11.18

Uhrzeit:

16:15

Ort:

V3-201

Vortragender:

Valentin Gorski

Bielefeld University

Inhalt:

The level spacing distribution in the bulk of a spectrum is approximately given by the Wigner surmise. Yet, at the hard and the soft edge one can expect strong deviations from these laws. Using the orthogonal polynomial method we derive the spacing distribution of the smallest two singular values of the chiral Gaussian unitary ensemble (chGUE) at finite matrix dimension with additional characteristical polynomials in the weight. The number of these polynomials represents the number of flavors (types of quarks) in the physical system. This ensemble approximates the Euclidean Dirac operator in Quantum Chromodynamics (QCD). In my talk, I will report on the behavior of the level spacing distribution in this particular setting.

Ansprechpartner:

Gernot Akemann