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Kolloquium

Thema:

Topological States of Matter: The Physics Nobel Prize 2016

Datum:

26.06.17

Uhrzeit:

16:15

Ort:

H6

Vortragender:

Prof. Dr. Thomas Dahm

Universität Bielefeld

Inhalt:

The 2016 Nobel Prize in Physics was awarded to David J. Thouless, F. Duncan M. Haldane, and J. Michael Kosterlitz. These theoretical physicists studied exotic kinds of phase transitions. Historically, it was assumed that phase transitions of matter are usually accompanied by the breaking of some kind of symmetry. The work of Thouless, Haldane, and Kosterlitz showed, however, that completely different kinds of phase transitions can appear in nature, which are not based on symmetry breaking but instead on topological concepts. Their work had a large impact and nowadays many such topological materials have been identified and are being discovered. In this talk I will describe the conventional view of phase transitions, contrast it with the findings of Thouless, Haldane, and Kosterlitz, and discuss some of the new materials that have been discovered recently.

Ansprechpartner:

T. Dahm

Kolloquium Mathematische Physik

Thema:

Random field of gradients - Critical Phenomena and Scaling limits

Datum:

02.06.17

Uhrzeit:

16:15

Ort:

V2-210/216

Vortragender:

Stefan Adams

University of Warwick

Inhalt:

Random fields of gradients are families of highly correlated random variables arising in the studies of e.g. random surfaces & interfaces and discrete Gaussian Free Fields (GFFs), random geometry, field theory, and elasticity theory. Recently their study has attained a lot of attention. There are several reasons for that. On one hand, these are approximations of critical systems and natural models for a macroscopic description of elastic systems as well as, in a different setting, for fluctuating phase interfaces. In addition, over continuum, the level lines of the GFF are connected to Schramm's SLE (an active field of modern mathematics for understanding critical phenomena) and the fields are natural space-time analog of Brownian motions and as such a simple random object of widespread application and great intrinsic beauty. Gradient fields are likely to be an universal class of models combining probability, analysis and physics in the study of critical phenomena, and these mass-less fields are also a starting point for many constructions in field theory. A more recent connection are mathematical models for the Cauchy-Born rule of materials, i.e., a microscopic approach to nonlinear elasticity. The latter class of models requires that interaction energies are non-convex functions of the gradients. Open problems over the last decades include unicity of Gibbs measures and strict convexity of the free energy as well as scaling limits to the Gaussian Free Field and the decay behaviour of two-point correlation functions. After giving a broad introduction to this recently active field of research we present in the talk Gaussian decay of correlations and the scaling to the Gaussian Free Field for a class of mass-less fields with non-convex interaction using a recent renormalisation group approach.

Ansprechpartner:

M. Baake

Seminar Hochenergiephysik

Thema:

tba

Datum:

18.07.17

Uhrzeit:

14:15

Ort:

D6-135

Vortragender:

Daniele Bertacca

Argelander Institut für Astronomie, Bonn

Inhalt:

Ansprechpartner:

D. Schwarz

Seminar Kondensierte Materie

Thema:

Connecting Spin Hamiltonians from DFT Calculations to Experiment

Datum:

06.04.17

Uhrzeit:

14:15

Ort:

D5-153

Vortragender:

Shadan Ghassemi

TU Berlin

Inhalt:

Ansprechpartner:

Jürgen Schnack

Seminar Mathematische Physik

Thema:

Non-orthogonality of eigenvectors from the Haagerup-Larsen theorem

Datum:

01.06.17

Uhrzeit:

17:00

Ort:

D5-153

Vortragender:

Wojciech Tarnowski

Jagiellonian University Krakow

Inhalt:

Biunitarily invariant ensembles have been thoroughly studied in recent years from the point of view of statistics of eigenvalues. An enhanced symmetry of the probability distribution function allows us to expect that all spectral properties will be determined by the singular values only. Indeed, for large matrices, a mapping between one-point densities is known as the Haagerup-Larsen theorem. Recently, this mapping has been extended to all k-point functions (Kieburg-Kösters). During my talk, I will present a recent extension of the Haagerup-Larsen theorem, which gives a simple mapping between the radial spectral cumulative distribution function and a certain one-point eigenvector correlation function, built out of (non-orthogonal) left- and right eigenvectors. I will discuss also its relation with the stability of the spectrum.

Ansprechpartner:

Gernot Akemann

Seminar AG Zufallsmatrizen

Thema:

Matrix product ensembles of Hermite-type

Datum:

21.06.17

Uhrzeit:

16:00

Ort:

V3-201

Vortragender:

Dang-Zheng Liu

Institute of Science and Technology Austria & University of Science and Technology of China

Inhalt:

We investigate spectral properties of a Hermitised random matrix product which, contrary to previous product ensembles, allows for eigenvalues on the full real line. We find an explicit expression of the joint probability density function as a bi-orthogonal ensemble. As an interesting example, we focus on the product of GUE and LUE matrices and provide explicit expressions both for the bi-orthogonal functions and the correlation kernel. Then a new double-side kernel is found at the origin, which is slightly different from the Bessel kernel. This talk is based on joint work with P. J. Forrester and J. R. Ipsen.

Ansprechpartner:

Gernot Akemann



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  • | Letzte Änderung: 23.11.2011
  •  Olaf Kaczmarek
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