microseminar
informal seminar of Doppler Institute
on quantum theory and related topics and methods,
usually on Thursdays, usually at 10.45 a.m., usually 20 minutes + discussion
usually in lecture hall S2 or S3
of the University of Hradec Kralove
occasionally also in hybrid form or just
by Zoom
alternatively also in the seminar room (second floor) of the
Department of Theoretical Physics
of the
Nuclear Physics Institute in Rez
note: external interested speakers are always warmly
welcome.
FORTHCOMING SESSIONS:
| Place: | lecture hall S2 of the Department of Physics (UHK) in Hradec Kralove |
| Remark: | hybrid form, with the Zoom access code https://cesnet.zoom.us/j/94011982289 |
| Date: | |
| Time: | 10:45 a.m. (duration: 20 minutes + questions) |
| Speaker: |
|
| Title: |
|
Abstract: | Domain truncations of Schroedinger operators with complex potentials are known to be spectrally exact. However, several examples suggest that additional eigenvalues escaping to infinity seem to be a generic feature. We find conditions on the presence of such eigenvalues and obtain their asymptotic expansions. Our approach also yields asymptotic formulas for diverging eigenvalues in a strong coupling regime for the imaginary part of the potential. |
ARCHIVE:
| Place: | communicated, by Zoom, from the Department of Physics (UHK) in Hradec Kralove |
| Form: | online only |
| Date and time: |
Thursday, April 28th, 2022,
10:45 a.m.
|
| Speaker: | Hassan Hassanabadi (UHK) |
| Title and abstract: |
Investigation of the Dunkl oscillator in the position and momentum
representation
| In this work, first we introduce Dunkl operator and its properties as well as $\nu$-deformed exponential function. Then the Dunkl-Heisenberg relation in the position and momentum representation is obtained by applying the reflection operator for the position and momentum. We then obtain the corresponding eigenfunction and eigenvalue. Based on the $\nu$-deformed Hermite polynomials, we derive the energy levels, ground-state wave functions, and excited wave functions. We expand the method to obtain the related coherent states. |
| Remark: |
participants
|
| Place: | lecture hall S2 of the Department of Physics (UHK) in Hradec Kralove |
| Form: | hybrid form: onsite plus Zoom |
| Date and time: |
Thursday, March 24th, 2022,
10:45 a.m.
|
| Speaker: | Petr Siegl (TU Graz) |
| Title and abstract: |
The damped wave equation with singular damping
|
We analyze the spectral properties and peculiar behavior of solutions of a damped wave equation on a finite interval with a singular damping of the form \alpha/x with a positive \alpha. We establish the exponential stability of the semigroup and determine conditions for the spectrum to consist of a finite number of eigenvalues. As a consequence, we fully characterize the set of initial conditions for which there is extinction of solutions in finite time.
The talk is based on a joint work with P. Freitas (Lisbon) and N. Hefti (Bern). |
| Remark: |
participants
|
| Place: | lecture hall S2 of the Department of Physics (UHK) in Hradec Kralove |
| Form: | hybrid form: onsite plus Zoom |
| Date and time: |
Thursday, March 3rd, 2022,
10:45 a.m.
|
| Speaker: | Anton Galaev (UHK) |
| Title and abstract: |
Holonomy groups and their application
| A short introduction to the holonomy groups of linear connections on smooth manifolds will be given. I will explain the classification results for the Levi-Civita connection on Riemannian and Lorentzian manifolds as well as for the metric connections with skew-symmetric torsion. The importance of these results is shown by the fact that spaces with a broad class of holonomy groups automatically satisfy the Einstein equation and admit parallel spinor fields (supersymmetries). |
| Remark: |
participants
|
| Place: | University of Hradec Kralove, Faculty of Science |
| Form: | online talk, presented by Zoom |
| Date and time: |
Thursday, February 3rd, 2022,
10:45 a.m.
|
| Speaker: | Jan Kriz (UHK) |
| Title and abstract: |
Soft quantum waveguides
| A brief review of the theory of planar quantum waveguides will be provided. The recent results concerning so-called soft waveguides will be discussed in more details. Mathematically, we investigate the existence of discrete spectrum of two-dimensional Schrodinger operators with an attractive potential in the form of a channel of a fixed profile built along an unbounded curve. |
| Remark: |
participants
|
| Place: | University of Hradec Kralove, Faculty of Science, Department of Physics, Building S, lecture hall S2 |
| Form: | talk presented in the hybrid (i.e., Zoom + onsite) form this time |
| Date and time: |
Thursday, January 6th, 2022, 10:45 a.m.
|
| Speaker: | Jiri Lipovsky (UHK) |
| Title and abstract: |
Spectral determinants
|
We introduce a generalization of the notion of the determinant from matrices to operators with infinitely many eigenvalues, which uses the spectral zeta function. We show how to compute it for simple operators and sketch the main difficulties in its definition, especially the dependence of the spectral determinant on the branch cut of the logarithm appearing in the definition of the spectral zeta function.
This is joint work with P. Freitas based on the paper [1]. [1] P. Freitas, J. Lipovsky, Spectral determinant for the damped wave equation on an interval, Acta Physica Polonica A 136 (2019), 817-823 [arXiv: 1908.06862 [math-ph]]. |
| Form: | virtual this time: Jan Kriz (UHK) invited us to join via Zoom |
| Date and time: |
Thursday, December 2nd, 2021, 10:45 a.m.
|
| Speaker: | Marzieh Baradaran (UHK) |
| Title and abstract: |
Spectrum of a Kagome network
|
Spectral properties of quantum graphs in the form of a kagome or a triangular lattice
were investigated
assuming that wave functions at the vertices are matched through conditions which are non-invariant with respect to the time-reversal. While the positive spectrum consists of an infinite number of bands, the negative one has at most three and two bands, respectively. We discussed, in particular, the high-energy behavior of such systems and the probability that a randomly chosen positive number belongs to the spectrum.
This is joint work with Prof. Pavel Exner based on preprint [1]. [1] M. Baradaran, and P. Exner: arXiv:2106.16019 [math-ph] |
| Place: | University of Hradec Kralove, Faculty of Science, Department of Physics, Building S, lecture hall S3 |
| Date and time: |
Thursday, November 4th, 2021, 11:00 a.m.
(triple length: 60 min.) |
| Speaker: | Petr Seba (UHK) |
| Title and abstract: |
Applications of repetitive ballistographic data
| Mathematically processed ballistography signals are used to evaluate various clinically significant markers routinely used in the human diagnostics. |
| Place: | University of Hradec Kralove, Faculty of Science, Department of Physics, Building S, laboratory S19 on the second floor |
| Date and time: | Tuesday, October 12th, 2021, 10:45 a.m. |
| Speaker: |
Andrii Khrabustovskii (UHK) |
| Title and abstract: | Construction of self-adjoint differential operators with prescribed spectral properties |
The objective of the talk is to illustrate how one can construct domains or potentials such that the essential or discrete spectrum of Laplace- and Schroedinger-type operators coincides with a predefined subset of the real line. Another aim is to emphasize that the spectrum of a differential operator on a bounded domain or bounded interval is not necessarily discrete, e.g., eigenvalues of infinite multiplicity or continuous spectrum may be present.
The talk is based on resent works with J. Behrndt (TU Graz). |
| Place (unusual!): | University of Hradec Kralove, Faculty of Science, Department of Physics, Building S, ground floor, room Nr. S13 |
| Date and time: | Thursday, September 16th, 2021, 10:30 a.m. |
| Speaker: |
Miloslav Znojil (UHK) |
| Title and abstract: | Alice in the wanderland of algebraic geometry, and behind quantum catastrophes | A compact reparametrization of the Arnold polynomial potentials of arbitrary degree (known from the classical theory of catastrophes) is introduced and shown useful in quantum phenomenology. Main attention is paid to the specific unstable-localization dynamical regime. In this regime a systematic determination of the observable density distributions proves feasible via 1/N approximation yielding a qualitative classification and approximate description of a new type of quantum phase transitions, tractable as the (avoided) level crossings or, alternatively, as a manifestation of the existence of a fairly close complex exceptional point. |
| Place: | University of Hradec Kralove, Faculty of Science, Department of Physics, Building S, 1st floor, room Nr. 72549 |
| Date and time: | Thursday, June 17th, 2021, 10:30 a.m. |
| Speaker: |
Miloslav Znojil (UHK) |
| Title and abstract: | From Cizek and Dyson to Bender | In the first microseminar organized in UHK the Bender-inspired formulation of quantum mechanics (a.k.a. PT-symmetric quantum mechanics) will be briefly reviewed. With emphasis on the history of the field, five related paradoxes will be formulated. (1) People never noticed the overlap of the theory with the Jiri Cizek's coupled cluster method in which one calculates the real spectrum using realistic Hamiltonians in non-Hermitian representation. (2) Only too late people noticed the overlap of the theory with an analogous Freeman Dyson's recipe. (3) Frequent misunderstandings were evoked by the Bender's claim that his Hamiltonians were non-Hermitian. At present, it is clear that they are only non-Hermitian in an unphysical, auxiliary, irrelevant Hilbert space. In this sense, their proper name should have been quasi-Hermitian Hamiltonians. (4) The main inspiration of the Bender's new theory was the Bessis' imaginary cubic interaction model. In 2012, in a paper by Siegl and Krejcirik, this particular model was proved not to fit the theory. (5) Subsequently, the initial orientation of the theory on the so called closed quantum systems has changed. Today, most people apply the concept of PT symmetry to open quantum systems. |
| Photo of whiteboard: |
|
The archive of the older microseminars:
The list of talks during 2016 - 2020
The list of talks during 2012 - 2015
The list of talks during 2008 - 2011
The list of the talks during 2008
A compactified list of the speakers during 2008
The list of the talks during 2007
A compactified list of the speakers during 2007
The list of the talks during 2006
A compactified list of the speakers during 2006
PS: in parallel, nested seminars of the similar type may be also sought on the webpages of our local
microconferences
devoted to the analytic an algebraic methods in physics
Info for interested speakers:
|
send email to
Miloslav Znojil | |
| propose a talk (Thursdays on 10.30 or 10:45 are preferable) |
|
on any subject related to
|
|
| you should book your term of talk: | not later than 2 or 3 days in advance |
| your talk's length should be | 20 minutes |
| time for subsequent questions: | unlimited |
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