Topic: 
Antrittsvorlesung: Calculating the properties of extremely hot end dense matter 
Date: 
25.06.18 
Time: 
16:15 
Place: 
H6 
Guest: 

Universität Bielefeld 

Abstract: 
Exploring the properties and phase structure of strong interaction matter from first principles is an extremely active and numerically intense field of research. The last 15 years have seen tremendous progress in the quality of lattice regularized Quantum Chromodynamics (QCD) calculations. It is now possible to perform QCD calculations with physical quark masses and reliable continuum extrapolations for bulk thermodynamic quantities at nonzero temperatures. A small baryon number density can be introduced by a Taylor expansion approach. In this accessible region the QCD phase diagram can now be explored in detail, with some applications to heavy ion physics and cosmology. What remains to be an important and unsolved issue are calculations at large baryon number densities. I will review recent lattice QCD results on bulk thermodynamics at nonzero temperature and small baryon number densities, which includes the equation of state as well as recent results on the density dependence of the QCD transition temperature. I will further discuss how thermal fluctuations of baryon number, electric charge and strangeness can be used to connect QCD calculations with heavy ion experiments conducted at the Relativistic Heavy Ion Collider (RHIC) in Brookhaven. Finally, I will sketch some strategies for QCD calculations that might help to go beyond a Taylor expansion and overcome the infamous sign problem that is faced in numerical QCD calculations. 
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Topic: 
Upper and lower Lipschitz bounds for the perturbation of edges of the essential spectrum 
Date: 
01.06.18 
Time: 
16:15 
Place: 
V3204 
Guest: 

TU Dortmund 

Abstract: 
Let $A$ be a selfadjoint operator, $B$ a bounded symmetric operator and $A+t B$ a perturbation. I will present upper and lower Lipschitz bounds on the function of $t$ which locally describes the movement of edges of the essential spectrum. Analogous bounds apply also for eigenvalues within gaps of the essential spectrum. The bounds hold for an optimal range of values of the coupling constant $t$. This is result is applied to Schroedinger operators on unbounded domains which are perturbed by a nonnegative potential which is mostly equal to zero. Unique continuation estimates nevertheless ensure quantitative bounds on the lifting of spectral edges due to this semidefinite potential. This allows to perform spectral engineering in certain situations. The talks is based on the preprint https://arxiv.org/abs/1804.07816 
Contact person: 
Topic: 
tba 
Date: 
10.07.18 
Time: 
14:15 
Place: 
D6135 
Guest: 
Jens Mund 
UFJF, Juiz de Fora, Brazil 

Abstract: 

Contact person: 
Topic: 
Impact of Eigenstate Thermalization on the Route to Equilibrium 
Date: 
14.06.18 
Time: 
14:15 
Place: 
D5153 
Guest: 

Universität Osnabrück 

Abstract: 
The eigenstate thermalization hypothesis (ETH) and the theory of linear response (LRT) are celebrated cornerstones of our understanding of the physics of manybody quantum systems out of equilibrium. While the ETH provides a generic mechanism of thermalization for states arbitrarily far from equilibrium, LRT extends the successful concepts of statistical mechanics to situations close to equilibrium. In our work, we connect these cornerstones to shed light on the route to equilibrium for a class of properly prepared states. We unveil that, if the odiagonal part of the ETH applies, then the relaxation process can become independent of whether or not a state is close to equilibrium. Moreover, in this case, the dynamics is generated by a single correlation function, i.e., the relaxation function in the context of LRT. Our analytical arguments are illustrated by numerical results for idealized models of randommatrix type and more realistic models of interacting spins on a lattice. Remarkably, our arguments also apply to integrable quantum systems where the diagonal part of the ETH may break down. 
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Topic: 
Eigenvectorrelated correlation functions and their connection with generalized chiral random matrix ensembles with a source 
Date: 
11.01.18 
Time: 
16:00 
Place: 
D5153 
Guest: 
Jacek Grela 
LPTMS Université ParisSud 

Abstract: 
We will introduce eigenvectorrelated correlation functions, discuss briefly their significance in dynamical Ginibre ensemble [1,2] and present asymptotic results in the large matrix size limit. Motivated by recent work [3] on joint eigenvectoreigenvalue correlation function valid for finite matrix size N in the complex and real Ginibre Ensembles, we study integrable structure of a certain generalized chiral Gaussian Unitary Ensemble with a source [4]. This model can be also interpreted as a deformation of the complex Ginibre Ensemble with an external source with additional determinant term. We present compact formulas for the characteristic polynomial, inverse characteristic polynomial and the kernel. In the case of a special source, we calculate asymptotics in the joint "bulkedge" regime of all aforementioned objects and show their Besseltype behaviour. References: [1] ''Dysonian dynamics of the Ginibre ensemble'', Z. Burda, J. Grela, M. A. Nowak, W. Tarnowski, P. Warcho?, Phys. Rev. Lett. 113, 104102 (2014) [2] ''Unveiling the significance of eigenvectors in diffusing nonhermitian matrices by identifying the underlying Burgers dynamics'', Z. Burda, J. Grela, M. A. Nowak, W. Tarnowski, P. Warcho?, Nucl. Phys. B 897, 421 (2015) [3] ''On statistics of biorthogonal eigenvectors in real and complex Ginibre ensembles: combining partial Schur decomposition with supersymmetry'', Y. V. Fyodorov, arXiv:1710.04699 [4] ''On characteristic polynomials for a generalized chiral random matrix ensemble with a source", Y. V. Fyodorov, J. Grela, E. Strahov, arXiv:1711.07061 
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Topic: 
The Random Normal Matrix Model: Insertion of a Point Charge 
Date: 
27.06.18 
Time: 
16:15 
Place: 
V3201 
Guest: 

Lund University 

Abstract: 
We study conditional twodimensional loggases in the determinantal case, given that there is a point charge in the interior of the support of the equilibrium measure (the ''droplet''). On a microscopic level, we obtain near the inserted charge a family of universal pointfields, depending on the strength of the charge and so on, which are characterized by special entire functions  MittagLeffler functions. The charge also affects the microscopic behaviour near the boundary of the droplet, where it gives rise to a kind of balayage operation. One motivation for studying this kind of conditional pointprocesses is that they are closely related to the characteristic polynomial of a random normal matrix  an object of interest for field theories and multiplicative chaos. The talk is based on joint work with Kang and Seo. 
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