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Exact Results in Quantum TheoryŚcisłe rezultaty teorii kwantów2025/2026prof. dr hab. Jan Dereziński prof. dr hab. Krzysztof Meissner prof. dr hab. Krzysztof Pachucki dr Wojciech Kamiński dr inż. Tymon Kilich <-- Pasteura 5, room 1.40, Fridays 14:15 - < 16:00 --> |
The seminar series "Exact Results in Quantum Theory" (colloquially called "Exakty" in Polish) was started in the early 21st century by Jan Dereziński and Krzysztof Meissner, as a platform for the exchange of ideas between various branches of mathematical and theoretical physics. The name has not been chosen at random: the word "exact" does not necessarily mean "rigorous", however it implies our appreciation of exact computations and mathematically sophisticated structures in physics.
In the academic year 2024/25 Krzysztof Pachucki joins the organizing committee of the seminar. Using his expertise and guidance, we organize talks and discussions about methods of relativistic quantum mechanics and quantum electrodynamics used in multi-particle systems. We plan to confront various scientific communities interested in this topic, including theoretical chemists, mathematical physicists, and physicists dealing with quantum field theory. Our aim is to understand the status of computational methods based on the multi-particle Dirac equation, which, without proper physical foundations, are commonly used to describe atoms and molecules, with the ultimate goal to construct quantum electrodynamic theory of correlated atomic systems.
Besides Dereziński, Meissner and Pachucki the organizing committee includes Wojciech Kamiński. His interests and expertise include quantum field theory on curved spacetimes and general relativity.
We invite everyone interested in theoretical and mathematical physics to attend the seminar. Some of the talks will be given online – we warmly welcome participants from outside Warsaw to attend.
Ścisłe Rezultaty Teorii Kwantów
Historia seminariów "Ścisłe Rezultaty Teorii Kwantów" (zwana potocznie "Exakty") została rozpoczęta w początkach XXI wieku przez Jana Derezińskiego i Krzysztofa Meissnera, jako platforma dla wymiany idei między różnymi gałęziami fizyki teoretycznej i matematycznej. Warto podkreślić, że angielska nazwa seminarium zawiera słowo "Exact", a nie "Rigorous", co wskazuje na to, że bardziej niż formalną ścisłość cenimy tu dokładne obliczenia i wyrafinowane struktury matematyczne w fizyce.
W roku akademickim 2024/25 do komitetu organizacyjnego seminarium dołącza Krzysztof Pachucki. Korzystając z jego ekspertyzy i zaangażowania organizujemy wykłady i dyskusje o metodach relatywistycznej mechaniki kwantowej oraz elektrodynamiki kwantowej wykorzystywane w układach wielu ciał. Planujemy skonfrontować różne środowiska naukowe zainteresowane tym tematem, takie jak chemików teoretycznych, fizyków matematycznych i fizyków zajmujących się kwantową teorią pola. Chcielibyśmy zrozumieć status metod obliczeniowych opartych na wielociałowym równaniu Diraca, które, mimo braku zadowalających podstaw fizycznych, jest powszechnie używane do opisu atomów i cząsteczek. Dalekosiężnym naszym celem jest konstrukcja teorii skorelowanych układów atomowych opartej na elektrodynamice kwantowej.
Poza Derezińskim, Meissnerem i Pachuckim komitet organizacyjny obejmuje Wojciecha Kamińskiego. Do jego zainteresowań i ekspertyzy należy kwantowa teoria pola na zakrzywionych czasoprzestrzeniach i ogólna teoria względności.
Zapraszamy wszystkich zainteresowanych teoretyczną i matematyczną fizyką do udziału w seminarium. Niektóre wykłady będą się odbywać zdalnie – gorąco zachęcamy do uczestnictwa w nich słuchaczy spoza Warszawy.
Abstract:
The Schrödinger equation describes the time evolution of quantum states as elements of a suitable Hilbert space. For this reason, the continuous equation on L2(ℜd) has been extensively studied, especially with regard to the behaviour of the eigenvalues and eigenfunctions of the associated Schrödinger operator as the physical parameters vary.
By contrast, much less is known about the discrete analogue, despite its fundamental role in numerical analysis and in lattice models from mathematical physics.
In this talk, I will discuss the asymptotic behaviour of the eigenvalues of the operator HN = −N²⁄2Δ + λNVN acting on ℓ2(ℤd). Here, the parameter N governs the continuum limit, while λN is related to a semiclassical regime in which ℏ → 0. In particular, I will identify a regime for the semiclassical parameter in which the eigenvalues of the discrete Schrödinger operator converge to those of an associated continuous harmonic oscillator in the N → +∞ limit. I will also show that, in certain parameter regimes, the behaviour of HN differs significantly from its continuous counterpart. As a byproduct, I will also present a new technique for deriving upper and lower bounds for all energy levels of a class of Schrödinger operators that arises naturally in the analysis.
The talk is based on joint work (arXiv:2602.23156) with Christian van de Ven and Matthias Keller.
Zoom link: https://uw-edu-pl.zoom.us/j/2780321940
| Date | Speaker | Title | Slides |
|---|---|---|---|
| 10.10.2025 | Marcin Napiórkowski (KMMF FUW) | The Gibbs state of the mean-field Bose gas | |
| 17.10.2025 | Błazej Ruba | Lattice Stabilizer States | |
| 24.10.2025 | Jan Dereziński | One-dimensional Schröodinger operators solvable in confluent functions | |
| 31.10.2025 | (no seminar) | (Rector's Day) | |
| 07.11.2025 | Andrey Surzhykov (PTB, Braunschweig) | King's plot analysis and search for new physics | |
| 21.11.2025 | Trond Saue (Universite Toulouse III-Paul Sabatier, France) | Vacuum polarization in a finite basis | |
| 28.11.2025 | Maria Przybylska (IF UZ, Zielona Góra) | Analytical determination of spectra for selected quantum optics systems | |
| 05.12.2025 | Peter J Mohr (NIST, Gaithersburg, USA) | Magnetic moments in the Poynting theorem, Maxwell equations, Dirac equation, and QED | |
| 12.12.2025 | Michał Siłkowski (UAM) | Nonadiabatic Perturbation Theory | |
| 19.12.2025 | Mikhail Molodyk (Stanford University) | The massive Feynman propagator on radiative spacetimes | |
| 09.01.2026 | Markus Fröb (University of Erlangen) | Tomita-Takesaki modular theory and relative entropy | |
| 16.01.2026 | Mathieu Lewin (Universite Paris-Dauphine) | Counterexample to the convexity of the energy of quantum electrons in atoms and molecules | |
| 23.01.2026 | Luis Cort (KCIK, UG) | Keldysh Nonequilibrium Green's Functions for Open Quantum Systems | |
| 30.01.2026 | (winter break) | — | |
| 06.02.2026 | (winter break) | — | |
| 13.02.2026 | (winter break) | — | |
| 20.02.2026 | (winter break) | — | |
| 27.02.2026 | (winter break) | — | |
| 06.03.2026 | Evgeny Epelbaum (Ruhr-Universitaet Bochum) | Nuclear interactions from chiral lagrangians using gradient flow | |
| 13.03.2026 | Jean-Philippe Karr | QED calculations in molecular hydrogen ions | |
| 20.03.2026 | Maciej Kolanowski | (Near-)extremal black holes: classical, semiclassical and quantum effects | |
| 27.03.2026 | Alex Strohmaier (University of Hannover) | Scattering by metric perturbation and the analytic theory of the stress energy tensor | |
| 10.04.2026 | Marianna Safronova | Atomic theory in the 21st century: breakthrough advances, neural networks, and remaining challenges | |
| 17.04.2026 | Jan Dereziński | Damping of phonons in Bose gas at low temperatures | |
| 24.04.2026 | Lorenzo Pettinari (Universita di Trento) | Coupling of the continuum and semiclassical limits for Schrödinger equations on a lattice | |
| 08.05.2026 | (no seminar - Juwenalia) | — | |
| 15.05.2026 | Rudrajit Bannerjee (Okinawa Inst. Sci. Tech) | | |
| 22.05.2026 | Janusz Rosiek | | |
| 29.05.2026 | Mateusz Piorkowski (KTH, Stockholm) | | |
| 12.06.2026 | | ||
| 19.06.2026 | | ||
| 26.06.2026 | |