PDE and mathematical physics

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3 March 2022
16:00-17:00

Prof. Dr. Stephan De Bievre
University of Lille

Event Details

Title	Optical nonclassicality, decoherence and entanglement
Speaker, Affiliation	Prof. Dr. Stephan De Bievre, University of Lille
Date, Time	3 March 2022, 16:00-17:00
Location	HG G 19.1
Abstract	A state (density matrix) of a bosonic quantum field, such as an n-mode optical field, is said to be optically classical if it is a mixture of coherent states. Whereas this definition is straightforward, a simple characterization of the optically classical density matrices is not available. A variety of witnesses have been introduced to characterize optical (non)classicality. Optically classical states have, for example, a positive Wigner function, but the opposite is not true. In this talk I will review some of the recent and not so recent literature on this question and present a new such witness, the Quadrature Coherence Scale (QCS). Using the QCS and other nonclassicality witnesses, the link between optical nonclassicality, entanglement and decoherence will be elucidated.

Optical nonclassicality, decoherence and entanglementread_more

10 March 2022
16:00-17:00

Prof. Dr. Klaus Widmayer
Universität Zürich

Event Details

Title	Global axisymmetric Euler flows with rotation
Speaker, Affiliation	Prof. Dr. Klaus Widmayer, Universität Zürich
Date, Time	10 March 2022, 16:00-17:00
Location	HG G 19.1
Abstract	We discuss the construction of a class of global, dynamical solutions to the 3d Euler equations near the stationary state given by uniform "rigid body" rotation. These solutions are axisymmetric, of Sobolev regularity and have non-vanishing swirl. At the heart of this result is a dispersive effect due to rotation, which is captured in our "method of partial symmetries". This approach is adapted to maximally exploit the symmetries of this anisotropic problem, both for the linear and nonlinear analysis, and allows to globally propagate sharp decay estimates. This is joint work with Y. Guo and B. Pausader (Brown University).

Global axisymmetric Euler flows with rotationread_more

31 March 2022
16:00-17:00

Prof. Dr. David Damanik
Rice University

Event Details

Title	The topological structure of the spectrum of almost periodic Schr\"odinger operators
Speaker, Affiliation	Prof. Dr. David Damanik, Rice University
Date, Time	31 March 2022, 16:00-17:00
Location	HG G 19.1
Abstract	In this talk we discuss the topological structure of the spectrum of almost periodic Schr\"odinger operators, both in one dimension and in higher dimensions. The problem is quite well understood in the one-dimensional case and the talk will briefly describe some of the known results. The question is significantly less well understood in higher dimensions. The Bethe-Sommerfeld conjecture for periodic potentials serves as a guiding principle for the different mechanisms and phenomena that should be expected to play a role. Passing from periodic to non-periodic almost periodic potentials, we discuss both positive and negative results in the spirit of the Bethe-Sommerfeld conjecture.

The topological structure of the spectrum of almost periodic Schr\"odinger operatorsread_more

2 June 2022
16:00-17:00

Prof. Dr. Evelyne Miot
University of Grenoble

Event Details

Title	Dynamics of point vortices for the lake equations
Speaker, Affiliation	Prof. Dr. Evelyne Miot, University of Grenoble
Date, Time	2 June 2022, 16:00-17:00
Location	HG G 19.1
Abstract	We study the asymptotic dynamics of point vortices for the lake equations with positive depth, when the vorticity is initially sharply concentrated around N points. More precisely, we show that the vorticity remains concentrated in some sense around N points for all times, and that the trajectories follow the level lines of the depth function. This is joint work with Lars Eric Hientzsch (Universität Bielefeld) and Christophe Lacave (Université Grenoble Alpes).

Dynamics of point vortices for the lake equationsread_more

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