[Vortraege] Vortragsankündigungen der komm. Woche (KW 39)

[Dekanat für Mathematik]

Sehr geehrte Fakultätsmitglieder,

anbei die Vortragsankündigungen für die nächste Woche, im Anhang finden 
Sie den Text auch als PDF Datei.

Mittwoch, 24. September, WPI – Wolfgang Pauli Institute, Seminar Room C 
714, Nordbergstr. 15, 1090 Wien, 9:30 Uhr
Workshop "The Gross-Pitaevskii equation and its application for BEC in 
optical lattices" (2008)
Sparber Christof
„On the Gross-Pitaevskii equation for trapped dipolar quantum gases“
I report on a recent joint work together with R. Carles and P. 
Markowich, where we consider the time-dependent Gross-Pitaevskii 
equation modeling Bose-Einstein condensation of trapped dipolar quantum 
gases. Existence and uniqueness as well as the possible blow-up of 
solutions are studied. Moreover, we discuss the problem of 
dimension-reduction for this nonlinear and nonlocal Schrödinger equation.

Mitwoch, 24. September, 10:45 Uhr
Pelinovsky, Dmitry
„Moving gap solitons in periodic potentials“
I review existence of stationary and moving gap solitons in the 
Gross--Pitaevskii equation with a small periodic potential. These 
solitons are approximated by the explicit solutions of the coupled-mode 
system. We show, however, that exponentially decaying traveling 
solutions of the Gross--Pitaevskii equation do not generally exist in 
the presence of a periodic potential due to bounded oscillatory tails 
ahead and behind the moving solitary waves. The oscillatory tails are 
not accounted in the coupled-mode formalism and are estimated by using 
techniques of spatial dynamics and local center-stable manifold 
reductions. Existence of bounded traveling solutions of the 
Gross--Pitaevskii equation with a single bump surrounded by oscillatory 
tails on a large interval of the spatial scale is proven by using these 
techniques.

Mittwoch, 24. September, 11:30 Uhr
Porter Mason A.
„Bose-Einstein Condensates with Spatially Periodic Scattering Lengths“
We investigate the dynamics of quasi-one-dimensional Bose-Einstein 
condensates (BECs) with spatially-periodic scattering lengths. This type 
of "collisionally inhomogeneous" BEC is described by a Gross-Pitaevskii 
(GP) equation with a nonlinearity coefficient that varies periodically 
in space. For the case of a sinusoidal coefficient, we examine the 
dynamics of spatially-extended states (modulated amplitude waves) that 
we construct analytically using the method of averaging. For the case of 
piecewise-constant coefficient, we examine the dynamics of solitary 
waves that we construct using a "stitching" technique.

Donnerstag, 25. September, 10:00 Uhr
Hunag, Zhongyi
„Bloch Decomposition Based Method for Lattice BEC“
In this talk, we introduce the Bloch-decomposition based time-splitting 
spectral method to conduct numerical simulations of the dynamics of 
(non)linear SchrÄodinger equations subject to periodic and confining 
potentials. We consider this system as a two-scale asymptotic problem 
with different scalings of the nonlinearity. In particular we discuss 
(nonlinear) mass transfer between different Bloch bands and also present 
three-dimensional simulations for lattice Bose-Einstein condensates in 
the superfluid regime. Joint work with Shi Jin, Peter A. Markowich, and 
Christof Sparber.

Donnerstag, 25. September, 11:00 Uhr
Bao, Weizhu
„Numerical Simulation for Rotating Bose-Einstein Condensates“
In this talk, we present efficient and stable numerical methods to 
compute ground states and dynamics of Bose-Einstein condensates (BEC) in 
a rotational frame. As preparatory steps, we take the 3D 
Gross-Pitaevskii equation (GPE) with an angular momentum rotation, scale 
it to obtain a four-parameter model and show how to reduce it to 2D GPE 
in certain limiting regimes. Then we study numerically and 
asymptotically the ground states, excited states and quantized vortex 
states as well as their energy and chemical potential diagram in 
rotating BEC. Some very interesting numerical results are observed. 
Finally, we study numerically stability and interaction of quantized 
vortices in rotating BEC. Some interesting interaction patterns will be 
reported. This talk is based on joint work with Qiang Du, Peter 
Markowich, Hanquan Wang and Yanzhi Zhang. 

Freitag, 26. September, 10:00 Uhr
Menotti, Chiara 
„The time dependent Gross-Pitaesvkii equation: Bogoliubov spectrum and 
beyond“
Using the continuous and the discrete time-dependent GPE, we probe the 
Bogoliubov spectrum of a Bose-Einstein condensate in a 1D optical 
lattice. The presence of the optical lattice not only reduces the sound 
velocity, but is also responsible for phenomena which arise due to the 
interplay of interactions and periodic potential, like dynamical 
instabilities for a moving condensate. Moreover, the time-dependent GPE 
allows to go beyond the Bogoliubov description by entering the 
non-linear regime, where one can observe saturation and self-trapping 
effects. Finally, we include an external trapping potential to simulate 
situations closer to the experimental ones.

Freitag, 26. September, 11:00Uhr
Nägerl, H. Christoph
„Interference of Matter Waves with Tunable Interactions“
The phenomenon of matter wave interference lies at the heart of quantum 
physics. It has been observed in many contexts in the limit of 
non-interacting particles as a single particle effect. We observe and 
control many-body matter wave interference, which is driven by nonlinear 
particle interactions. In a multipath matter wave interferometer the 
macroscopic many-body wave function of an interacting atomic 
Bose-Einstein condensate develops a regular interference pattern, 
allowing us to directly visualize the effect of interaction induced 
phase shifts as time progresses. We demonstrate coherence for the 
nonlinear phase evolution in a matter wave spin-echo-type experiment 
when we stop and reverse the interaction driven evolution by first 
nulling the strength of the interaction and then driving the multipath 
phase shifts with opposite signs by means of an external potential. 
Alternatively, we balance the effect of interactions by means of the 
external potential and observe persistent Bloch oscillations. If time 
permits, we discuss experiments in which we confine the matter wave 
sample to a one-dimensional geometry and study Bloch osciallations and 
transport in a one-dimensional gas.


Mit freundlichen Grüßen

Margit Honkisz

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