Oberseminar Mathematische Physik
im Sommer Semester 2019 von Prof. Dr. Detlef Dürr und
Prof. Peter Pickl
The seminar is usually on Wednesdays, 16:15h, in room B004 starting on the 23th of October.
Organizer: Markus NÃ¶th
News:
updates may be distributed on short notice by mail to all peoplle on an internal list. People interested in should contact
Prof. Dr. Detlef Dürr or
Prof. Peter Pickl.
Talks
Date 
Room 
Title 
Speaker 

Wed 23.10.19, 16:15 
B004 
shifted to the 30.10. 
shifted to the 30.10. 
Wed 30.10.19, 16:15 
B004 
Wilson Cloud Chamber Problem
In this talk I am going to quickly recapitulate what the Cloud Chamber Problem is, why it cannot be considered as a solved one even in the standard Quantum Mechanics and why we need Bohmian Mechanics treatment of it.
After that I am going to tell about some interesting results we have obtained recently, which provide the insight into why the quantum elementary particles flying through the cloud chamber leave classical bubble tracks.

Serj Aristarhov 
Wed 06.11.19, 16:15 
B004 
Why bother with Categorie Theorie? An explanation attempt using Algebraic Geometry.
The aim of the talk is to give some motivation for the abstract, function focused approach of Categorie Theorie. We will start by giving some interesting definitions of Categorie Theory and then move on to see some cases where these notions come in handy. After that we will take a small detour, introducing the most important notions of Algebraic Geometry, to understand how Categorie Theory helps finding the correct notion of separateness on schemes.

Kajetan SÃ¶hnen 
Wed 13.11.19, 16:15 
B004 
PostMeasurement Wave Functions & an Incorrect Approach to TimeofArrival Distributions
In the textbook Quantum Mechanics formalism, when a particle is found at a particular location, the wave function is projected to that location. But how is the wave function modified when a particle is looked for, but not found? An argument is presented showing that no FTLcommunication gives an almost unique result for the wave function after measurement. If time permits, I will use the result to show that a naive "textbook" approach to derive a timeofarrival distribution yields the incorrect result that the particle never arrives, so the approach is invalid. Modifying the approach using weak measurements does not help to save it.

Felix Feist 
Wed 20.11.19, 16:15 
B004 
An ion trap implementation of our arrival time experiment
The talk recapitulates the arrival time experiment proposed in [S. Das and D. D\"urr, Sci. Rep. 9, 2242 (2019)] and discuss a basic radio frequency ion trap implementation of the same. Historically, these traps have played a key role in precision measurements, e.g., g2 experiments. Currently, they are quite sought after for quantum computing applications. We recall the working principle of the Paul trap and explain the classical and quantum mechanical motion of a charged particle (in particular a spin1/2 particle) embedded in such a trap, thus setting the stage for Dr. Ferdinand SchmidtKaler's talk next week. If time permits, we will mention the weak magnetic fields induced by the r.f. currents and the changes they bring about on the Bohmian arrival time distributions.

Siddhant 
Wed 27.11.19, 16:15 
B004 
Modern Quantum Technologies with trapped ions
Quantum technologies allow for fully novel schemes of computing, simulation and sensing. For
quantum computing, we employ trapped ions in modern segmented ion traps as scalable and freely reconfigurable qubit register [1]. I will give an overview of the recent progress, where gate fidelities of 99.995% (single bit) and 99.6% (two bit) are reached. This includes a discussion of different architectures, the required trap technologies and fabrication methods, control electronics for quantum register reconfigurations, and recent improvements of qubit coherence and gate performance. Using a segmented microion trap for implementing a reconfigurable qubit register we have realized multiqubit entanglement [2]. Topological quantum error correction [3] is a current aim, as well as an execution of quantum gates in few ns [4].
Alternative platforms for quantum computers in solid state technology would largely benefit from determinsitic schemes to fabricate qubit registers with nmaccuracy. I describe our deterministic ion source, which allows for delivering Ca+ ions on demand and focus it into a spot of a few nm [5]. The source can be operated with any other doping ion, which is cotrapped and sympathetically cooled together with a single Ca+ ion, eventually extracted and implanted. We have started structuring solid state samples such as diamond with N2+ molecular ions to generate NV centers, rateearth Presodym ions [6] in YAG samples and will start implanting P+ ions into ultrapure Silicium, with the vision to fabricate devices for quantum information processing.
[1] Blatt, Wineland, Nat. 453, 1008 (2008), Kielpinski, Wineland, Nat. 417, 709 (2002), Schindler et al, NJP 15, 123012 (2013), Friis et al, Phys. Rev. X 8, 021012 (2018), Debenath et al, Nat. 536, 63 (2016)â€¨
[2] Kaufmann er al, Phys. Rev. Lett.Â 119, 150503 (2017)â€¨
[3] Bermudez, et al, Phys. Rev. X 7, 041061 (2017)â€¨
[4] Vogel et al, Phys. Rev. Lett. 123, 153603 (2019)â€¨
[4] Jacob etÂ al, Phys. Rev. Lett. 117, 043001 (2016) â€¨
[5] GrootBerning, et al, Phys. Rev. Lett.123, 106802 (2019)

Ferdinand SchmidtKaler 
Wed 04.12.19, 16:15 
B004 
Variational methods for an elliptic singular SPDE describing the magnetization ripple
The magnetization ripple is a microstructure formed by the magnetization in a thinfilm ferromagnet due to the random orientation of the grains in the polycrystalline material.
In an approximation of the micromagnetic model the ripple can be described by a strongly anisotropic elliptic PDE driven by white noise in two dimensions. However, the noise is too rough to make sense of the nonlinearities appearing in the equation.
I will explain how one can construct solutions to this singular SPDE based on a renormalization of the corresponding energy functional and prove optimal regularity estimates.
This is based on a joint work with Radu Ignat, Felix Otto, and Pavlos Tsatsoulis.

Tobias Ried 
Wed 11.12.19, 16:15 
B004 
Cancelled 

Wed 18.12.19, 16:15 
B004 
Analytically solvable Barrier 
Siddhant Das 
Wed 8.1.20, 16:15 
B004 
cancelled 

Wed 15.1.20, 16:15 
B004 
tba 

Wed 22.1.20, 16:15 
B004 
The Localization Problem in Relativistic Quantum Theory
In this talk I will consider some aspects of the so called localization problem in relativistic quantum theory. I will present a mathematical framework which implies a number of celebrated results such as Hegerfeldtâ€™s theorem, Malamentâ€™s theorem and generalizations thereof, the ReehSchlieder theorem and its implications as well as some very special properties of positive energy wave functions. The talk will focus on a derivation of a generalized version of Malamentâ€™s theorem, formulated operationally in terms of detector click statistics.

Christian Beck 
Wed 29.1.20, 16:15 
B004 
Direct removal of UV and IR divergences in a QED toy model
This talk will concern the problem of defining time dynamics in a Quantum Field Theory like QED using the Hamiltonian formalism. In my Master Thesis, I could establish the dynamics of a QFT toy model  but only with an Ultraviolet (UV)cutoff. This cutoff can be removed in a limit process. The remaining Hamiltonian may, however only be defined on a vector space orthogonal to $ L^2 $. This problem is usually resolved by a dressing transformation. A recently developed technique named IBC (InteriorBoundary Condition) allows for a direct removal of UVdivergences in certain models. The combination with a formal dressing now indeed yields a selfadjoint Hamiltonian on $ L^2 $ in a QEDmodel with stationary sources, which can not be achieved by IBCs without dressing.
The talk will also mention (IR) difficulties, i.e. problems appearing in QFTs for low momenta. Several frameworks for defining QFTs and different methods to tackle UV and IR problems (as the EpsteinGlaser construction, Adiabatic Cutoffs and Dollard Modifiers) are presented. A collection of a number of interesting open questions concerning dynamics in QFTs will also be presented. This collection is nowhere claimed to be complete and I explicitly encourage for controversial discussions about them.

Sascha Lill 