microseminar

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 session:

Place:	NPI seminar room (ground floor)
Date:	Thursday, ... , 2013
Time:	10:30 a. m.
Speaker:	t. b. a. (...)
Title:	t. b. a.
Abstract:	t. b. a.

Archive:

Date and time:	Thursday, January 31st, 2013, 14:30 hours
Speaker:	Matej Tusek (KM, FNSPE CTU Prague)
Title and abstract:	On thin quantum layers with magnetic fields
	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.

Date and time:	Friday, October 26, 2012, 10:30 hours
Speaker:	Gabriela Malenova (NPI)
Title and abstract:	Chebfun and Beyond
	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.

Date and time:	Thursday, September 20th, 2012, 10:30 hours
Speaker:	Yahia Saadi (University Ferhat Abbas - Setif, Algeria)
Title and abstract:	Geometrical aspects of S matrix
	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.

Date and time:	Thursday, June 28th, 2012, 10:30 hours
Speaker:	Francisco Correa (CECS Valdivia, Chile)
Title and abstract:	Self-isospectral tri-supersymmetry in PT-symmetric quantum systems with pure imaginary periodicity
	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.

Date and time:	Wednesday, May 9th, 2012, 14:30 hours
Speaker:	Miloslav Znojil (NPI)
Title and abstract:	Stationary quantum evolution operators from non-stationary Hamiltonians
	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.

Date and time:	Wednesday, March 21st, 2012, 10:30 a. m.
Speaker:	Julien Royer (Univ. of Toulouse)
Title and abstract:	Damped wave equation and uniform resolvent estimates for the Helmholtz equation
	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.

Date and time:	Wednesday, February 8th, 2012, 10:30 a. m.
Speaker:	Stephan Schmitz (IfM, JGU Meinz)
Title and abstract:	On indefinite Differential Operators of second order
	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.

Date and time:	Tuesday, January 3rd, 2012, 10:30 a. m.
Speaker:	Tomas Brauner (Universitaet Bielefeld )
Title and abstract:	Number of Nambu-Goldstone bosons and its relation to charge densities
	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.

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
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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