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 hard-core 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 hard-core 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 ill-defined.
In this talk we will explore a third approach which depends on a formulation of the dynamics in terms of multi-time 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 mean-field limit of interacting bosons
e consider the dynamics of N bosons, which initially form a
Bose-Einstein condensate and interact via a pair potential in the mean
field scaling regime. We derive a sequence of N-body functions which
approximate the true many-body 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 so-called 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/\rho-waveguide. 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 quantum-mechanical theory of motion for a fixed, finite number of electrons, photons, and their anti-particles, 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 quantum-mechanical wave function for a single photon, and use that to obtain a Lorenz-covariant system of multi-time wave equations for an interacting two-body system in one space dimension, comprised of one electron and one photon. I will demonstrate that the corresponding initial-boundary-value problem is well-posed, 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 Tahvildar-Zadeh |
Wed 10.07.19, 16:00 |
B005 |
Minisuperspace with dust: deriving dark energy and eliminating cosmological singularities
The minisuperspace model describing a Friedmann-Lemaitre-Robertson-Walker 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 |
Multi-time formulation of particle creation and annihilation of particles via interior-boundary conditions
Interior-boundary 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+1-dimensional model that interior-boundary conditions are compatible with multi-time 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 functional-analytic approach to define quantum dynamic, which I will sketch in a fairly non-technical way. This is joint work with Lukas Nickel ( source).
|
Matthias Lienert |