PT microseminar (archive 2006)
Informal seminar of Doppler Institute
on quantum theory and related topics and methods,
taking place, usually, on the territory of the
Department of Theoretical Physics of the
Nuclear Physics Institute in Rez
The complete list of the talks during 2006
| Date: |
unusual: Wednesday, December 13 |
Time: |
10:30 a. m. |
| Speaker: |
Roland Lombard (IPN Orsay) |
| Title and abstract: |
The size of the He atom
|
|
The mean square radius of the He atom is not an experimental datum. The
best variational wave functions determine this quantity with numerous
digits.
We study this problem by means of the Bertlmann-Martin inequality and
its generalizations. It gives an estimate with an approximated error
of the order of 10 %. Comparison will be made between the results
obtained by the two methods.
|
| Place: |
unusual: Hradec Kralove University, Svobody 331/2, room C7 |
Date and time: |
unusual: Friday, December 8, 11:45 a. m. |
| Speaker: |
Tamas Fulop (NPI & DI) |
| Title and abstract: |
Singular potentials in Quantum Mechanics
|
|
Comprehensive review lecture for 2nd Int. Workshop DI "Spectra, Algorithms and Data Analysis".
|
| Place: |
unusual: Hradec Kralove University, Svobody 331/2, room C7 |
Date and time: |
unusual: Friday, December 8, 9:25 a. m. |
| Speaker: |
Vit Jakubsky (NPI & DI) |
| Title and abstract: |
Non-Hermitian operators in Quantum Mechanics |
|
Comprehensive review lecture for 2nd Int. Workshop DI "Spectra, Algorithms and Data Analysis".
|
| Date (time): |
30. 11. (10.30) |
| Speaker: |
Milos Tater (NPI & DI) |
| Title: |
Asymptotic analysis of spectra of QES Schrodinger operators |
| Abstract: |
We study asymptotic distribution of eigenenergies of the
algebraic part of spectra and properties of roots of the corresponding
eigenpolynomials. Setting of this degenerate exactly-solvable operators in
the general scheme is presented.
|
| Date (time): |
23. 11. (10.30) |
| Speaker: |
Vit Jakubsky (NPI & DI) |
| Title: |
Thermodynamics of pseudo-Hermitian systems in equilibrium |
| Abstract: |
Physical quantities can be derived without an
explicit
evaluation of the spectra and without an
explicit
construction of the metric operator.
|
| Date (time): |
16. 11. (10.30) |
| Speaker: |
Sudhir R. Jain (Utrecht University) |
| Title: |
Resonances |
| Abstract: |
I discuss a study on quantum resonances for simple systems for which analytic results are possible, based on the concept of time-delay. The same ideas are then shown to work for extraction of unflavoured baryon resonances and some exotic systems. From these studies ensue some simple relations describing the density of resonances; we bring them out in the light of adiabatic invariance and Weyl-like laws. |
| Date: |
26. 10. 2006 (10.30) |
| Speaker: |
Hynek Bila (NPI & DI) |
| Title: |
Dirac Equation and its Symmetries III. |
| Abstract: |
The review lecture ctd.
|
| Date (time): |
Thursday 19. 10. 2006 (10.30) |
| Speaker: |
Andrey Sokolov (Sankt Petersburg State University) |
| Title: |
Factorization of non-linear supersymmetry in
one-dimensional Quantum Mechanics |
| Abstract: |
Possible factorizations of supersymmetric (SUSY)
transformations in one-dimensional Quantum Mechanics into
chains of elementary Darboux transformations with non-singular
coefficients and hermitian intermediate Hamiltonians are
investigated. The classification of irreducible (almost)
isospectral transformations and theorems about factorization
of SUSY transformations are presented.
|
| Date: |
2. 10. (exceptionally, Monday) |
| Time: |
10.30, as usual |
| Speaker: |
Alexander
Turbiner
(UNAM, Mexico) |
| Title: |
Anharmonic oscillator and double-well potential:
approximating eigenfunctions |
| Abstract: |
A simple uniform approximation of the logarithmic derivative of the ground
state eigenfunction for both the quantum-mechanical anharmonic oscillator
and the double-well potential given by $V= m^2 x^2+g x^4$ at arbitrary
$g \geq 0$ for $m^2>0$ and $m^2<0$, respectively, is presented. It is
shown that if this approximation is taken as unperturbed problem it
leads to an extremely fast convergent perturbation theory. The case of sextic
oscillator is briefly mentioned. It is shown that quartic and sextic
oscillators are two totally different problems.
|
| Date: |
15. 9. 2006 (exceptionally Friday, 10.30) |
| Speaker: |
Pedro Freitas (University of Lisbon) |
| Title: |
What we do not know about eigevalues |
| Abstract: |
What you always wanted to know but felt afraid to ask |
| Date: |
14. 9. 2006 (10.30) |
| Speaker: |
Vit Jakubsky (NPI & DI) |
| Title: |
Partition functions and PT symmetry |
| Abstract: |
Impressions over the dissertation by A. Ivanov. |
| Date (time): |
24. 8. 2006 (14.00) |
| Speaker: |
Frieder Kleefeld (DI & NPI) |
| Title: |
(Not only) on the paper by Duc Tai Trinh, II |
| Abstract: |
cf. J. Phys. A: Math. Gen. 38 (2005) 3665, continuation. |
| Date (time): |
17. 8. (10.30) |
| Speaker: |
Peter G. L. Leach (Durban, University KwaZulu Natal) |
| Title: |
c-isochronous oscillators and the challenge of consistent
quantisation |
| Abstract: |
Francesco Calogero introduced a class of oscillators
containing a parameter c, which we call c-isochronous oscillators,
to demonstrate that the ground-state energy was dependent upon the
form of the Hamiltonian used even though classically the different
forms are related by canonical transformations. This seems to be
an affront to the physical nature of the system which should be
independent of the mathematical mode of description. We propose a
mathematical solution based upon the algebraic properties of the
Schroedinger Equation.
|
| Date: |
22. 6. 2006 (10.30) |
| Speaker: |
Christian Tanguy (Paris) |
| Title: |
Open problems in the network reliability theory |
| Abstract: |
A few simple algebraically tractable sample networks and the related combinatorial analysis and
matrix recurrences up to dimension 13.
|
| Date: |
1. 6. 2006 (10.30) |
| Speaker: |
Frieder Kleefeld (Erlangen) |
| Title: |
On a paper by Duc Tai Trinh |
| Abstract: |
cf. J. Phys. A: Math. Gen. 38 (2005) 3665. |
| Date: |
25. 5. 2006 (10.30) |
| Speaker: |
Vit Jakubsky (NPI & DI) |
| Title: |
Proca problem once more |
| Abstract: |
Revision of a paper discussed. |
| Date: |
18. 5. 2006 at 10.30 (MHD Dpt. of FZ Rossendorf this time, exceptionally of course). |
| Speaker: |
Miloslav Znojil (NPI & DI) |
| Title: |
Energy-dependent Hamiltonians |
| Abstract: |
A brief review. |
| Date: |
11. 5. 2006 (10.30) |
| Speaker: |
Jaroslav Smejkal (UCF CVUT) |
| Title: |
Proca fields, classical and quantum |
| Abstract: |
Hamilton-Jacobi formulation, Heisenberg picture and all that |
| Date: |
18. 5. 2006 (10.15) |
| Speaker: |
Petr Siegl (FJFI & DI) |
| Title: |
PT-symmetric version of supersymmetry II |
| Abstract: |
Conception and contents of the BSc thesis. |
| Date: |
4. 5. 2006 (exceptionally at 9.00, DI/KM of FJFI CVUT, Trojanova 13, Prague) |
| Speaker: |
Petr Siegl (FJFI & DI) |
| Title: |
PT-symmetric version of supersymmetry |
| Abstract: |
Preliminary version of the BSc thesis |
| Date: |
20. 4. 2006 (10.30) |
| Speaker: |
Milos Tater (NPI & DI) |
| Title: |
Spectra of certain
non-Hermitian Hamiltonians with polynomial
potentials in 2D |
| Abstract: |
Presentation of a numerical study.
|
| Date: |
13. 4. 2006 (10.30) |
| Speaker: |
Hynek Bila (NPI & DI) |
| Title: |
Dirac Equation and its Symmetries II. |
| Abstract: |
The review lecture ctd.
|
| Date: |
6. 4. 2006 (exceptionally at 15.00,
in Brehova 7, room 111, an open-to-public part of the exam) |
| Speaker: |
Vit Jakubsky (NPI & DI) |
| Title: |
Introduction to dissertation |
| Abstract: |
A concise review of a bunch of papers. |
| Date: |
3. 4. 2006 [Monday, 11.15] |
| Speaker: |
Vit Jakubsky (NPI & DI) |
| Title: |
Pre-introduction to dissertation |
| Abstract: |
Preparatory version of the state-exam presenting
a sample of the speaker's PhD-research
results |
| Date: |
30. 3. 2006 (10.30) |
| Speaker: |
Miloslav Znojil (NPI & DI) |
| Title: |
PT-SUSY and exact solvability |
| Abstract: |
Discussion club on the project submitted to GA CR [followed by
its brief presentation
to the (parallel) session of the Sci. Council of NPI]. |
| Date: |
23. 3. 2006 (10.30) |
| Speaker: |
Petr Siegl (FJFI & DI) |
| Title: |
SUSY Quantum Mechanics
|
| Abstract: |
A brief sketch of basic ideas.
|
| Date: |
16. 3. 2006 (10.30) |
| Speaker: |
Hynek Kovarik (Stuttgart) |
| Title: |
Trace formulas in one dimension |
| Abstract: |
Short guide to certain spectral-function estimates. |
| Date: |
9. 3. 2006 (11.00) |
| Speaker: |
Hynek Bila (NPI & DI) |
| Title: |
Green's functions and WKB |
| Abstract: |
A review series, part II: Bender's papers on PT symmetry.
|
| Date: |
6. 3. 2006 (10.30) |
| Speaker: |
Petr Siegl (FJFI & DI) |
| Title: |
Discretizations with instabilities:
PT square well example
|
| Abstract: |
The
instability of the
equidistant-grid version of
the
Weideman's - Weigert's
discretization method
of solving Schroedinger equation
disqualifies its use for the
numerical evaluation of the exceptional points.
|
| Date: |
27. 2. 2006 (13.15) |
| Speaker: |
Hynek Bila (NPI & DI) |
| Title: |
Dirac Equation and its Symmetries. |
| Abstract: |
A review lecture, part I.
|
| Date: |
20. 2. 2006 (13.15) |
| Speaker: |
Miloslav Znojil (NPI & DI) |
| Title: |
What I heared in Polubny |
| Abstract: |
Brief information about the 14th Student's Winter School |
| Date: |
13. 2. 2006 (15.15) |
| Speaker: |
David Krejcirik (NPI & DI) |
| Title: |
The simplest PT-symmetric model? |
| Abstract: |
Pre-publication discussion club.
|
| Date: |
16. 1. 2006 (13.15) |
| Speaker: |
Vit Jakubsky (NPI & DI) |
| Title: |
Proca equation as a pseudo-Hermitian problem |
| Abstract: |
Pre-publication discussion.
|
Reminder:
the list of subjects included
- analytic and algebraic methods
- constructive Quantum Mechanics
- exactly solvable problems
- perturbation expansions
- non-Hermitian quantum models
- computer tricks
- relativistic equations and so on.
|
| the secretaries of the microseminar were |
Vit Jakubsky
and
Miloslav Znojil
|
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