# Aktuelle Veranstaltungen

## Kolloquium

Thema:

### tba

Datum:

31.05.21

Uhrzeit:

16:15

Ort:

cyberspace

Vortragender:

Dima Kharzeev

Stony Brook University

Inhalt:

Ansprechpartner:

F. Karsch/TR211

## Kolloquium Mathematische Physik

Thema:

### 20210723 - Jon Keating - TBC

Datum:

23.07.21

Uhrzeit:

16:15

Ort:

ZOOM/Konferenzschaltung

Vortragender:

Jon Keating

Oxford University

Inhalt:

TBC

Ansprechpartner:

G. Akemann

## Seminar Hochenergiephysik

Thema:

### Is Our Universe the Remnant of Chiral Anomaly in Inflation?

Datum:

27.04.21

Uhrzeit:

14:15

Ort:

Online, via ZOOM

Vortragender:

CERN, Geneva

Inhalt:

Modern cosmology has been remarkably successful in describing the Universe from a second after the Big Bang until today. However, its physics before that time is still much less certain. It profoundly involves particle theory beyond the Standard Model to explain long-standing puzzles: the origin of the observed matter asymmetry, nature of dark matter, massive neutrinos, and cosmic inflation. In this talk, I will explain that a new framework based on embedding axion-inflation in left-right symmetric gauge extensions of the SM can possibly solve and relate these seemingly unrelated mysteries of modern cosmology. The baryon asymmetry and dark matter today are remnants of a pure quantum effect (chiral anomaly) in inflation which is the source of CP violation in inflation. As a smoking gun, this setup has robust observable signatures for the GW background to be probed by future CMB missions and laser interferometer detectors.

Ansprechpartner:

D. Bödeker

## Seminar Kondensierte Materie

Thema:

### 16:00 Quantum scars and Hilbert space fragmentation of color and ice

Datum:

06.05.21

Uhrzeit:

16:00

Ort:

ZOOM / Konferenzschaltung

Vortragender:

Hitesh J. Changlani

Florida State University and National High Magnetic Field Laboratory

Inhalt:

Non-equilibrium properties of quantum materials present many intriguing properties, among them athermal behavior, which violates the eigenstate thermalization hypothesis. Such behavior has primarily been observed in disordered systems. More recently, experimental, and theoretical evidence for athermal eigenstates, known as quantum scars", has emerged in non-integrable disorder-free models in one dimension with constrained dynamics [1]. I will focus on directions that my group is pursuing in the context of geometrically frustrated magnets. First, I show the existence of quantum scar eigenstates and investigate their dynamical properties in many simple two-body Hamiltonians with staggered interactions, involving ferromagnetic and antiferromagnetic motifs, in arbitrary dimensions. These magnetic models include simple modifications of widely studied ones (e.g., the XXZ model) on a variety of lattices [2]. I will demonstrate our ideas by focusing on the two-dimensional frustrated spin 1/2 kagome antiferromagnet, which was previously shown to harbor a special exactly solvable point with "three-coloring" ground states in its phase diagram [3,4,5]. Next, I discuss how Hilbert space fragmentation naturally arises in many frustrated magnets with low energy ice manifolds'' which gives rise to a broad range of relaxation times for different initial states [6]. We study the Balents-Fisher-Girvin Hamiltonian, and a phenomenological three-coloring model with loop excitations (previously explored in the context of quantum spin liquids), both with constrained Hilbert spaces. We characterize the formation of the fragmented Hilbert space of these Hamiltonians, their level statistics, and initial state dependence of relaxation dynamics to develop a coherent picture of glassiness in various limits of the XXZ model on the kagome lattice. [1] H. Bernien et al., Nature 551, 579–584 (2017); C. Turner et al., Nature Physics 14, 745-749 (2018) [2] K. Lee, R. Melendrez, A. Pal, H.J. Changlani, Phys. Rev. B 101, 241111(R) (2020) [3] H.J. Changlani, D. Kochkov, K. Kumar, B. K. Clark, E. Fradkin, Phys. Rev. Lett. 120, 117202 (2018) [4] H.J. Changlani, S. Pujari, C-M. Chung, B K. Clark, Phys. Rev. B 99, 104433 (2019) [5] S. Pal, P. Sharma, H. J. Changlani, and S. Pujari, Phys. Rev. B 103, 144414 (2021) [6] K. Lee, A. Pal, H.J. Changlani, arXiv:2011.01936 (2020)

Ansprechpartner:

FOR2692/Jürgen Schnack

## Seminar Mathematische Physik

Thema:

### The Character Expansion in effective Theories for chiral Symmetry Breaking

Datum:

03.12.20

Uhrzeit:

16:30

Ort:

ZOOM / Konferenzschaltung

Vortragender:

Noah Aygün

Universität Bielefeld

Inhalt:

Ansprechpartner:

Gernot Akemann

## Seminar Bielefeld-Melbourne Zufallsmatrizen

Thema:

### Recent advances in large sample correlation matrices and their applications

Datum:

05.05.21

Uhrzeit:

09:00

Ort:

ZOOM / Konferenzschaltung

Vortragender:

Johannes Heiny

Ruhr Universität Bochum

Inhalt:

Many fields of modern sciences are faced with high-dimensional data sets. In this talk, we investigate the spectral properties of large sample correlation matrices. First, we consider a $p$-dimensional population with iid coordinates in the domain of attraction of a stable distribution with index $\alpha\in (0,2)$. Since the variance is infinite, the sample covariance matrix based on a sample of size $n$ from the population is not well behaved and it is of interest to use instead the sample correlation matrix $R$. We find the limiting distributions of the eigenvalues of $R$ when both the dimension $p$ and the sample size n grow to infinity such that $p/n\to \gamma$. The moments of the limiting distributions $H_{\alpha,\gamma}$ are fully identified as the sum of two contributions: the first from the classical Marchenko-Pastur law and a second due to heavy tails. Moreover, the family $\{H_{\alpha,\gamma}\}$ has continuous extensions at the boundaries $\alpha=2$ and $\alpha=0$ leading to the Marchenko-Pastur law and a modified Poisson distribution, respectively. A simulation study on these limiting distributions is also provided for comparison with the Marchenko-Pastur law. In the second part of this talk, we assume that the coordinates of the $p$-dimensional population are dependent and $p/n \le 1$. Under a finite fourth moment condition on the entries we find that the log determinant of the sample correlation matrix $R$ satisfies a central limit theorem. In the iid case, it turns out the central limit theorem holds as long as the coordinates are in the domain of attraction of a stable distribution with index $\alpha>3$, from which we conjecture a promising and robust test statistic for heavy-tailed high-dimensional data. The findings are applied to independence testing and to the volume of random simplices. %%%%%%%%%%% Reference: Limiting distributions for eigenvalues of sample correlation matrices from heavy-tailed populations https://arxiv.org/abs/2003.03857 %%%%%%%%%%%

Ansprechpartner:

Anas Rahman

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