AG Mathematische Physik (Wintersemester 2020/21)
- Dozent*in: Prof. Dr. Dirk Hundertmark
- Veranstaltungen: Seminar (0127100)
- Semesterwochenstunden: 2
AG Seminar, Mathematische Physik.
Wöchentliches Arbeitsgruppenseminar mit Sprechern aus der AG Hundertmark.
15. Februar 14:00-15:30 Sprecher: Marco Olivieri
Thema: SCHRÖDINGER OPERATORS AS SEMICLASSICAL EFFECTIVE MODELS FOR QFT: GROUND STATE PROPERTIES
The study of the interaction between matter and radiation by means of Quantum Field Theories (QFT) represents a challenge due to the lack of a general, rigorous mathematical frame and the difficulty of the calculations involved. A successful strategy to overcome these obstacles is the derivation of effective models, which retain the important physical features of the microscopic ones, but are simpler to analyze. When a field is really intense, it behaves like a macroscopic object and semiclassical analysis can be used to mathematically approximate its canonical observables by their classical counterparts. In the present talk we show how in this regime the ground state and ground state energy of the QFT models converge in suitable topologies to the ground state and ground state energy of effective Schrodinger models.
22. Februar 14:00-15:30 Sprecherin: Lucrezia Cossetti
Thema: Absence of eigenvalues of Schrödinger, Dirac and Pauli Hamiltonians via the method of multipliers
Originally arisen to understand characterizing properties connected with dispersive phenomena, in the last decades the method of multipliers has been recognized as a useful tool in Spectral Theory, in particular in connection with proof of absence of point spectrum for both self-adjoint and non self-adjoint operators.
In this seminar we will see the developments of the method reviewing some recent results concerning self-adjoint and non self-adjoint Schrödinger operators in different settings, specifically both when the configuration space is the whole Euclidean space \R^d and when we restrict to domains with boundaries. We will show how this technique allows to detect physically natural repulsive and smallness conditions on the potentials which guarantee total absence of eigenvalues. Some very recent results concerning Pauli and Dirac operators will be presented as well.
The talk is based on joint works with L. Fanelli and D. Krejcirik.
For guests: If you want to attend the upcoming talk,
please contact Marvin Schulz (see below for E-mail contact).
Invitations Links for Zoom will be sent shortly before the talk.
It is planed to add a permament link for Zoom with a customized password.
25. Januar, 14:00-15:30 Sprecher: Dirk Hundertmark
Thema: Quantum Systems at the Brink: Helium
01. Februar 14:00-15:30 Sprecher: Ioannis Anapolitanos
Thema: Convergence towards the Hartree dynamics in Topology of moments of the position
08. Februar 14:00-15:30 Sprecher: Ioannis Anapolitanos
Thema: Convergence towards the Hartree dynamics in Topology of moments of the position Part II
|Seminar:||Montag 14:00-15:30||Corona-Bedingt Online|
|Seminarleitung||Prof. Dr. Dirk Hundertmark|
|Zimmer 2.028 Kollegiengebäude Mathematik (20.30)|
|Email: firstname.lastname@example.org||Seminarleitung||M.Sc. Marvin Raimund Schulz|
|Sprechstunde: Nach Vereinbarung|
|Zimmer 2.026 Kollegiengebäude Mathematik (20.30)|