microseminar archive 2012 - 2015
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.
Talks during 2012 - 2015:
| Date and time: |
Thursday, December 17th,
2015,
10:30 a.m.
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| Speaker: |
Markus Holzmann (INM TU Graz, Austria)
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| Title and abstract: |
Approximation of Schroedinger operators with delta-interactions
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Schroedinger operators with singular delta-interactions (or ``delta-potentials'') are used as idealized models to solve the spectral
problem for classical Schroedinger operators H=T+V. Namely, if V has relatively large values around a set $\Sigma$ and small values
elsewhere, the potential V is often replaced by a weighted delta-distribution $\alpha \delta_\Sigma$ supported on $\Sigma$.
Here, $\Sigma$ can be, for instance, a set of points, a curve or a plane.
From the mathematical point of view it is not trivial to show that this idealization is justified, i.e.
that Hamiltonians with delta-potentials have similar spectral properties
as H=T+V, and how to choose the interaction strength $\alpha$ to get good approximations.
We are going to discuss some physical models, where Schroedinger operators with delta-interactions are used,
including applications from quantum
mechanics and the theory of electromagnetic waves and photonic crystals. For these models, we outline the correspondence of the
idealized delta-operators and the real physical operators and we show results, how physical properties of the underlying
systems can be deduced from our theoretical construct.
This talk is based on joint works with J. Behrndt, P. Exner and V. Lotoreichik.
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| Date and time: |
Thursday, December 10th,
2015,
10:30 a.m.
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| Speaker: |
Vaclav Zatloukal (FJFI CVUT Praha and Freie Universitat Berlin, Germany)
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| Title and abstract: |
Pais-Uhlenbeck oscillator -- a prototype of fourth-order-derivative theory
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In my talk I will discuss the Pais-Uhlenbeck oscillator --- a model based on an
action with second-order derivatives, which leads to fourth-order-derivative
equations of motion. I start with the classical theory in Lagrangian and Hamiltonian
framework, and then discuss quantisation using canonical as well as path-integral
methods. My concern will be mainly with ghosts states, which show up to disgrace the
ensuing quantum theory. Finally, I will discuss analogy between the Pais-Uhlenbeck
oscillator and conformal theory of gravity.
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| Date and time: |
Thursday, May 29th, 2014,
10:30 a.m.
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| Speaker: |
prof. Z. Riecanova (Math. Dept., Slovak Tech. University, Bratislava)
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| Title and abstract: |
A few remarks on algebras of unbounded operators.
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One of the standard formulations of quantum theory was inspired by Birkhoff and von Neumann (1936) who promoted the use of the language of suitable generalizations of Boolean algebras. A brief review of the mathematical aspects of these developments will be provided, with particular emphasis on the study of unbouded operators of "effects".
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| Date and time: |
Thursday, May 15th, 2014,
10:30 a.m.
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| Speaker: |
Jiri Janda (Masaryk University, Brno)
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| Title and abstract: |
Quantum structures.
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Recently, much effort has been invested into development of purely algebraic theory of quantum structures. Especially in Slovakia and Czech republic (Olomouc, Brno, Praha) this research is quite popular, some of the leading algebraists are working in this field. The purpose of my talk is to give an overview of some latest concepts and generalizations (e.g. dynamic effect algebras) together with their mathematical motivations, and to provide some background for discussion of possible physical relevance of the concepts.
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| Date and time: |
Monday, November 4th, 2013,
10:30 a.m.
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| Speaker: |
Julien Royer (Math. Dept., Univ. of Toulouse)
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| Title and abstract: |
Energy decay for the Schroedinger equation on a dissipative wave guide.
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We prove that the norm of the solution for the Schroedinger equation on a dissipative wave guide decays exponentially. For this we use uniform resolvent estimates on a strip around the real axis.
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| Date and time: |
Thursday, October 24, 2013,
10:30 hours
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| Speaker: |
Martin Himmel (Mainz University)
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| Title and abstract: |
Geometry of Planar Flows
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My talk is about dynamical systems, more precisely ordinary differential equations in the plane, and their multipliers. The latter are skalar-valued functions preserving the smoothness of the corresponding vector field. With their help one can characterize properties of the underlying dynamical system such as integrabiity or existence of periodic orbits. We discuss the Flow Curvature Method by Jean-Marc Ginoux, which has applications to fixed points stability, invariant sets, center manifolds, local bifurcations, integrability of dynamical systems and many other interesting topics and is in some sense an alternative approach to geometric singular pertubation theory. If there is enough time, we mention connections to the Cauchy transform and the notion of curvature of a measure that goes back to Mark Melnikov and Xavier Tolsa. Most of my research is joint work with Francois Dulac. The talk will stay on an elementary level and is addressed to any scientist with some basic knowledge in calculus and linear algebra.
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| Date and time: |
Friday, July 26, 2013,
10:30 hours
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| Speaker: |
Francisco Correa (CECS Valdivia, Chile)
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| Title and abstract: |
Black Holes and Solitons in Three Dimensions
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In this talk I will introduce the basic notions about three dimensional gravity and discuss some properties of black holes, scalar hairy black holes and soliton solutions.
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| Date and time: |
Thursday, May 16, 2013,
10:30 hours
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| Speaker: |
Frantisek Stampach (KM FJFI & KAM FIT)
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| Title and abstract: |
Introduction to the Moment Problem
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A brief review of main results concerning the moment problem. In particular, we provide a necessary and sufficient conditions for a real sequence to be a moment sequence of a positive Borel measure. Then we discuss the question on uniqueness of such a measure. In the case when there exists more measures with the same moments, we present a nice parametrization of the set of such measures discovered by Rolf Nevanlinna.
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| Date and time: |
Friday, April 26, 2013,
11:30 hours
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| Speaker: |
Amru Hussein (Inst. f. Math.,
Johannes Gutenberg Universitaet, Mainz, Germany)
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| Title and abstract: |
Non-self-adjoint graphs
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Self-adjoint Laplace operators on metric graphs are a well-studied subject.
For non-self-adjoint Laplace operators on graphs some difficulties are
discussed in terms of examples. Furthermore, a way how to construct, in
specific situations, similarity transforms to self-adjoint Laplace operators
is presented and illustrated by examples.
The talk is based on the joint work with David Krejcirik and Petr Siegl
conducted during the speaker's stay in Rez.
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| Date and time: |
Monday, March 18th, 2013,
10:30 hours
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| Speaker: |
Amru Hussein (Inst. f. Math.,
Johannes Gutenberg Universitaet, Mainz, Germany)
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| Title and abstract: |
Differential Operators on metric graphs with changing sign
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The aim of the talk is to discuss model problems for second order differential operators on graphs. These are related to the ordinary differential expressions
-\frac{d^2}{dx^2},
-\frac{d}{dx} \sgn (x) \frac{d}{dx},
-\sgn (x) \frac{d^2}{dx^2},
-\sgn (x) \frac{d}{dx} \sgn (x) \frac{d}{dx}.
Each is exemplary for certain methods and difficulties. The spectral properties are discussed and compared to each other taking into account the role of the sign.
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| Date and time: |
Thursday, February 14th, 2013,
10:30 hours
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| Speaker: |
Anatoly G. Nikitin (Institute of Mathematics of Nat. Acad. Sci. of Ukraine, Kyiv)
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| Title and abstract: |
Quantum superintegrable systems with spin
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Superintegrable quantum systems described by two coupled Schroedinger equations are presented. The related first and second order integrals of motion are specified. Physically, the discussed systems simulate fermions with non-trivial dipole moment, interacting with the external electromagnetic field.
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| Date and time: |
Thursday, January 31st, 2013,
14:30 hours
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| Speaker: |
Matej Tusek (KM, FNSPE CTU Prague)
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| Title and abstract: |
On thin quantum layers with magnetic fields
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Let $\Sigma$ be a surface in $R^3$ and $-\Delta_g$ the corresponding Laplace-Beltrami operator. Furthermore, define $\Omega_\epsilon$ as the layer of the width $\epsilon$ constructed around $\Sigma$. Then it is well known for some time that the Laplace operator on $\Omega_\epsilon$ converges (after subtracting the divergent transverse energy term) to $-\Delta_{g}+K-M^2$ in the weak sense. Here $K$ and $M$ denote the Gauss and the mean curvature of $\Sigma$, respectively. In my talk the norm resolvent convergence, that implies also convergence of the respective eigenvalues and eigenfunctions, will be proved. Moreover we will consider more general configuration including a magnetic field.
The talk was based on a joint work with David Krejcirik and Nicolas Raymond.
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| Date and time: |
Friday, October 26, 2012,
10:30 hours
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| Speaker: |
Gabriela Malenova (NPI)
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| Title and abstract: |
Chebfun and Beyond
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Chebfun is a collection of algorithms, and a software system in object-oriented MATLAB, which extends familiar powerful methods of numerical computation involving numbers to continuous or piecewise-continuous functions. The origin goes back to 2002, when professor Lloyd Nick Trefethen launched the project at Oxford University. The mathematical basis of the system combines tools of Chebyshev expansions, fast Fourier transform, barycentric interpolation, recursive zero-finding, and automatic differentiation.
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| Date and time: |
Thursday, September 20th, 2012,
10:30 hours
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| Speaker: |
Yahia Saadi (University Ferhat Abbas - Setif, Algeria)
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| Title and abstract: |
Geometrical aspects of S matrix
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A connection between the scattering matrix and the geometric phase is outlined in both the adiabatic and non adiabatic regime. The generalized adiabatic theorem and the invariant theory are used in the first and second case, respectively. For illustration, the scattering by Poeschl-Teller potential is worked out in detail.
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| Date and time: |
Thursday, June 28th, 2012,
10:30 hours
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| Speaker: |
Francisco Correa (CECS Valdivia, Chile)
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| Title and abstract: |
Self-isospectral tri-supersymmetry in PT-symmetric quantum systems with pure imaginary periodicity
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We study a reflectionless PT-symmetric quantum system described by the pair of complexified Scarf II potentials mutually displaced in the half of their pure imaginary period. Analyzing the rich set of intertwining discrete symmetries of the pair, we find an exotic supersymmetric structure based on three matrix differential operators that encode all the properties of the system, including its reflectionless (finite-gap) nature. The structure we revealed particularly sheds new light on the splitting of the discrete states into two families, related to the bound and resonance states in Hermitian Scarf II counterpart systems, on which two different series of irreducible representations of sl(2,C) are realized.
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| Date and time: |
Wednesday, May 9th, 2012,
14:30 hours
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| Speaker: |
Miloslav Znojil (NPI)
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| Title and abstract: |
Stationary quantum evolution operators from non-stationary Hamiltonians
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The standard unitary evolution of a quantum system is assumed controlled by a complicated self-adjoint Hamiltonian which is, in addition, manifestly time-dependent, h = h(t). A simpler non-Hermitian instantaneous representation H(t) of this operator is assumed obtainable via a suitable crypto-unitary map Omega(t) at any time t. In the new representation the generator of the time evolution (denoted as G(t)) is different from H(t). Its form depends on our choice of the (ambiguous) mapping Omega(t). We intend to show that without making the construction non-linear, this enables us to require the full time-independence of G(t)= G(0). The physical unitarity requirement is still preserved in an ad hoc representation of the physical Hilbert space of states of the system in question.
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| Date and time: |
Wednesday, March 21st, 2012,
10:30 a. m.
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| Speaker: |
Julien Royer (Univ. of Toulouse)
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| Title and abstract: |
Damped wave equation and uniform resolvent estimates for the Helmholtz equation
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I will present the problem of the local energy decay for the damped wave equation on R^d. After a Fourier transform the problem reduces to proving uniform resolvent estimates for the corresponding Helmholtz equation. I will explain some of the ideas used to obtain such estimates, especially for high frequencies.
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| Date and time: |
Wednesday, February 8th, 2012,
10:30 a. m.
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| Speaker: |
Stephan Schmitz (IfM, JGU Meinz)
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| Title and abstract: |
On indefinite Differential Operators of second order
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Let \(\Omega\subset \mathbb{R}^n\) be a bounded open set with \(C^2\) boundary. Let \(A(\cdot)\) be a symmetric, not necessarily definite \(n\times n\) matrix with entries in \( L^\infty(\Omega)\), such that the inverse \(A(\cdot)^{-1}\) has entries in \( L^\infty(\Omega)\) again and \(\int_\Omega A(x)^{-1}dx\) is invertible.
We show, that under these assumptions, there is a unique self-adjoint operator associated with the indefinite quadratic form
\[\left\langle \grad u, A(\cdot) \grad u\right\rangle_{L^2(\Omega)^n}\]
with domain lying in the domain of the gradient.
This operator has a compact resolvent and its spectral properties are studied as well.
The talk was based on a joint work with A. Hussein, D. Krejcirik and V. Kostrykin.
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| Date and time: |
Tuesday, January 3rd, 2012,
10:30 a. m.
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| Speaker: |
Tomas Brauner (Universitaet Bielefeld )
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| Title and abstract: |
Number of Nambu-Goldstone bosons and its relation to charge densities
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I review some recent results concerning the counting of Nambu-Goldstone bosons in norelativistic system. Further details can be found in the papers 1109.6327 and 1112.3890 written together with Haruki Watanabe.
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The archive of the older microseminars:
The complete list of the talks delivered 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 potential/interested external speakers:
| you would be always welcome by: |
all of us
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| you may choose any date and time |
though Thursdays on 10.30 are preferred
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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.
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| 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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