informal seminar of Doppler Institute
on quantum theory and related topics and methods,

usually on Thursdays at 10.30 a.m. in Rez, on the territory of the
Department of Theoretical Physics of the Nuclear Physics Institute.

       Enthusiastic visitors and/or speakers are always welcome.

     Forthcoming sessions:

Place: OTF seminar room (second floor)

     Tuesday, October 25th, 2016

Time (in the afternoon!):                12:30 (20 minutes + questions)

     Hafida Moulla (University of Constantine 1, Constantine, Algeria)


     The q-deformed harmonic oscillator

Language of the talk:

     French (plus the projection of transparencies provided in English)

It is known that the q-deformed version of the operator of "particle position" - which is an observable quantity - is not selfadjoint in L2(R). The resolution of the paradox is provided using the standard three-Hilbert-space theory due to Freeman Dyson. Firstly, the inner product in the Hilbert space of states is properly redefined. Secondly, a few consequences are discussed via the q-deformed version of the usual harmonic oscillator.


Date and time: Tuesday, October 11th, 2016, 12:30 p.m.
Speaker: Ilhem Leghrib (University of Constantine 1, Constantine, Algeria)
Title and abstract: Swanson model
A q-deformed generalization of the well known non-Hermitian Swanson's Hamiltonian is introduced and studied. In the dynamical regime of small deformations (i.e., with q close to one) the methods of perturbation theory are employed.

Note: The language of the talk was French, the transparencies were in English.

Date and time: Thursday, August 18th, 2016, 2:30 p.m.
Speaker: Ondrej Turek (OTF UJF in Rez and BLTP JINR in Dubna, Russia)
Title and abstract: A generalization of the circulant Hadamard conjecture
The circulant Hadamard conjecture says that circulant Hadamard matrices exist only of order n=1 and n=4. The conjecture, which dates back to a book of Ryser (1963), is partially proved in the symmetric case (Johnsen 1964). The general case, however, remains open to this day. In 1976, Stanton and Mullin showed that circulant conference matrices exist only of order n=2. With regard to their result, we consider circulant matrices C of order n>1 with diagonal entries $d \geq 0$, off-diagonal entries $\pm 1$ and mutually orthogonal columns. Matrices C generalize circulant Hadamard (d=1) and conference (d=0) matrices. We demonstrate that the parameter d and the order of C obey the relation n=2(d+1), whenever d is different from an odd integer, as well as when C is symmetric. The formula n=2(d+1) generalizes the theorems of Stanton, Mullin and Johnsen and reveals a suprising connection between circulant Hadamard and conference matrices. Furthermore, we conjecture that the relation n=2(d+1) is valid also when d is an odd integer, which generalizes the circulant Hadamard conjecture.

The talk was based on a joint work with D. Goyeneche.

Date and time: Tuesday, June 21st, 2016, 10:30 a.m.
Speaker: Artur Ishkhanyan (Institute for Physical Research of the National Academy of Sciences of Armenia, Ashtarak)
Title and abstract: Heun functions and Schroedinger equation
We shall review the cases for which the Schroedinger equation is solved in terms of general and confluent Heun functions. We present the possible choices for the coordinate transformation that provide energy-independent potentials that are proportional to an energy independent continuous parameter and have a shape independence of that parameter. We present several examples of explicit solutions for the latter potentials.

Date and time: Wednesday, June 1st, 2016, 14:30 a.m. (triple length)
Speaker: Alexander Turbiner (Stony Brook and UNAM, Mexico)
Title and abstract: 3-body quantum Coulomb problem: where we are
Current status of 3-body Coulomb problem of charge Z and two electrons (Z; e; e): hydrogen ion H-, helium atom, lithium ion, $H^+_2$ ion etc, is given. Major emphasis is given to a question of stability vs. Coulomb charge Z and to analytic structure of the ground state energy vs. Z. Celebrated 1/Z expansion is reviewed. Two critical charges, physical (corresponding to phase-transition type discontinuity) and unphysical (with associated square-root branch point) are described and calculated. The 2nd excited, weakly-bound state of $H^-$ is predicted.

Date and time: Thursday, January 21st, 2016, 10:30 a. m.
Speaker: Vladimir Lotoreichik (OTF)
Title and abstract: A spectral isoperimetric inequality for cones
Spectral isoperimetric inequalities are one of the most famous issues in spectral geometry, the first rigorous results dating almost a century back to the papers of {Faber} and {Krahn}. Recently such inequalities appeared in the context of Schr\"odinger operators with singular potentials used as models of `leaky quantum wires' and similar systems. In particular, for the 2-D Schroedinger operator with a $\delta$-potential of a fixed strength supported on a loop of a given length it was shown by {Exner}, {Harrell} and {Loss} that its principal eigenvalue is maximal when the loop is a circle. The corresponding problem in 3-D is more involved. For closed simply connected surfaces of a fixed area the sphere gives a local maximum of the ground-state eigenvalue, however, the result does not have a global validity.

Nevertheless, there are 3-D Schroedinger operators with singular interactions supported on surfaces for which one is able to derive a spectral isoperimetric inequality that holds not only locally. The aim of my talk is to discuss one such class considered in our preprint (arXiv:1512.01970). The surfaces in question are of a conical shape, both finite and infinite.

The proofs rely on the Birman-Schwinger principle and on the fact that circles are unique minimisers for a class of energy functionals. The main novel idea consists in the special choice of the test function for the Birman-Schwiner principle.

Joint work with Pavel Exner.

Date and time: Thursday, January 7th, 2016, 13:30 a.m. (irregular time)
Speaker: Ondrej Turek (OTF UJF in Rez and BLTP JINR in Dubna, Russia)
Title and abstract: The effect of edge lengths ratio on the spectrum of a hexagonal lattice
We analyze the spectrum of a Laplacian operator on a dilated honeycomb lattice. The lattice is assumed to be dilated along its axis of symmetry and supporting $\delta$ potentials of strength $\alpha \neq 0$ in its vertices. It turns out that the qualitative properties of the spectrum depend on number-theoretic properties of edge lengths ratio $\theta$. We will show that the number of spectral gaps is infinite for any rational or well approximable $\theta$, whereas there are only finitely many gaps in the spectrum if $\theta$ is badly approximable and the potential strength $\alpha$ in the vertices is small compared to the Markov constant of $\theta$.

This talk is based on joint works with P. Exner.

The archive of the older microseminars:

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


devoted to the analytic an algebraic methods in physics

Info for potential/interested external speakers:

you would be always welcome by: all of us
you may choose any date and time though Thursdays on 10.30 are preferred
and any subject related to
  • analytic and algebraic methods
  • constructive Quantum Mechanics
  • exactly solvable problems
  • perturbation expansions
  • non-Hermitian quantum models
  • computer tricks
  • relativistic equations
  • and so on.

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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