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 B005 starting on the 8th of May.
Organizer: Markus Nöth
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 08.05.19, 16:15 
B005 
The Boltzmann Equation
After Boltzmanns and Maxwells finding, that the physics of gases can be explained by the microscopic motion of atoms, there has been a dispute, whether the idea of an microscopic explanation of our universe in fact makes sense.
One argument against the idea of atomism was irreversibility: While microscopic motions are usually following reversible laws, the macroscopic world does know a direction of time.
Boltzmann gave an argument against this criticism by showing that for a dilute gas of particles subject to hardcore repulsion one can in fact get an irreversible macroscopic equation: the Boltzmann equation.
The rigorous prove of the validity of this equation has been an important topic in mathematical physics for many years. So far only results which hold for short times have been established.

Prof. Peter Pickl 
Wed 15.05.19, 16:15 
B005 
The Boltzmann Equation 2
After Boltzmanns and Maxwells finding, that the physics of gases can be explained by the microscopic motion of atoms, there has been a dispute, whether the idea of an microscopic explanation of our universe in fact makes sense.
One argument against the idea of atomism was irreversibility: While microscopic motions are usually following reversible laws, the macroscopic world does know a direction of time.
Boltzmann gave an argument against this criticism by showing that for a dilute gas of particles subject to hardcore repulsion one can in fact get an irreversible macroscopic equation: the Boltzmann equation.
The rigorous prove of the validity of this equation has been an important topic in mathematical physics for many years. So far only results which hold for short times have been established.

Prof. Peter Pickl 
Wed 22.05.19, 16:15 
B005 
Dirac Particles Interacting Directly
There are two traditional ways to introduce interaction into a quantum mechanical theory of particles.
1. Couple the motion of the particles by means of a potential.
2. Introduce a dynamical field that couples to all particles and hence the particles to one another.
Both of these methods face difficulties in the relativistic regime. The first approach runs into inconsistencies or violates relativistic invariance, in the second approach infinities appear rendering the dynamics illdefined.
In this talk we will explore a third approach which depends on a formulation of the dynamics in terms of multitime wavefunctions, direct interaction along lightcones.

Markus Nöth 
Wed 29.05.19, 16:15 
 
entällt 

Wed 05.06.19, 16:15 
B005 

Entfällt 
Wed 12.06.19, 16:15 
B005 
Higher order corrections to the meanfield limit of interacting bosons
e consider the dynamics of N bosons, which initially form a
BoseEinstein condensate and interact via a pair potential in the mean
field scaling regime. We derive a sequence of Nbody functions which
approximate the true manybody dynamics in norm to arbitrary precision
in powers of 1/N. The approximating functions are constructed as Duhamel
expansions of finite order in terms of the first quantized analogue of a
Bogoliubov time evolution.
Joint work with Natasa Pavlović, Peter Pickl and Avy Soffer, based on
arXiv:1905.06164

Lea Boßmann 
Wed 26.06.19, 16:15 
B005 
In the past one and a half year a decent nonrelativistic picture of our arrival time experiment [S. Das & D. Dürr, Sci. Rep. 9: 2242 (2019)] has emerged (see e.g., [S. Das, M. Nöthe and D. Dürr, Phys. Rev. A 99, 052124 (2019)])). In this talk I will quickly summarise the current state of affairs and motivate the need for a relativistic investigation. I will discuss analytic separability of the Dirac equation in cylindrical coordinates and the socalled M.I.T. bag boundary condition used for confining a particle in a box (originally proposed for modelling quark confinement in hadrons). Analytical solutions will be presented for a particle moving within a 1/\rhowaveguide. Lastly, if time permits, a new implementation of our experiment will be discussed, which exploits the interaction of a neutron's anomalous magnetic moment with an electric field (cf. Aharonov Casher effect).

Entfällt 
Wed 03.07.19, 16:15 
B005 
Classical and Quantum Laws of Motion for Singularities of Spacetime
In this talk I report on recent developments towards a relativistic quantummechanical theory of motion for a fixed, finite number of electrons, photons, and their antiparticles, as well as its possible generalizations to other particles and interactions. I will briefly explain the necessary conditions under which worldlines of charged particles can be identified with timelike singularities of spacetime and/or classical fields permeating the spacetime, and show examples of classical as well as quantum theories of motion for them when these conditions are satisfied. I will then show how one can define a quantummechanical wave function for a single photon, and use that to obtain a Lorenzcovariant system of multitime wave equations for an interacting twobody system in one space dimension, comprised of one electron and one photon. I will demonstrate that the corresponding initialboundaryvalue problem is wellposed, and that both electron and photon trajectories exist globally for typical initial particle positions. I will conclude by presenting preliminary results of numerical experiments that illustrate Compton scattering in this context, as well as a possible new phenomenon: photon capture and release by the electron. This talk is a summary of joint work with Michael Kiessling, Matthias Lienert, Annegret Burtscher, and others.

Shadi TahvildarZadeh 
Wed 10.07.19, 16:00 
B005 
Minisuperspace with dust: deriving dark energy and eliminating cosmological singularities
The minisuperspace model describing a FriedmannLemaitreRobertsonWalker space time with dust as matter is a very simple toy model of quantum gravity. We show two things:
(1) that dark energy can be derived as a quantum effect.
(2) that by choosing a suitable operator ordering, the big bang/big crunch singularity can be avoided.
For the latter, we consider a novel proposal for what it means to avoid a singularity in the context of quantum mechanics.

Ward Struyve 
Wed 17.07.19, 16:00 
B005 
Multitime formulation of particle creation and annihilation of particles via interiorboundary conditions
Interiorboundary conditions are a new approach (due to Teufel and Tumulka) towards a rigorous formulation of creation and annihilation of particles in quantum field theories. In this talk, I will introduce the concept and show that the approach can be extended to a relativistic setting. More precisely, I will show at the example of a simple 1+1dimensional model that interiorboundary conditions are compatible with multitime wave functions (a concept due to Dirac where the wave function depens on N spacetime points for N particles). To prove the existence and uniqueness of solutions in this setting requires to go beyond the usual functionalanalytic approach to define quantum dynamic, which I will sketch in a fairly nontechnical way. This is joint work with Lukas Nickel ( source).

Matthias Lienert 