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Sparber, Christof  Seminarroom C 714  Wed, 24. Sep 08, 9:30 
On the GrossPitaevskii equation for trapped dipolar quantum gases  
I report on a recent joint work together with R. Carles and P. Markowich, where we consider the timedependent GrossPitaevskii equation modeling BoseEinstein condensation of trapped dipolar quantum gases. Existence and uniqueness as well as the possible blowup of solutions are studied. Moreover, we discuss the problem of dimensionreduction for this nonlinear and nonlocal Schrödinger equation.  

Bao, Weizhu  Seminarroom C 714  Wed, 24. Sep 08, 10:45 
Numerical Simulation for Rotating BoseEinstein Condensates  
In this talk, we present efficient and stable numerical methods to compute ground states and dynamics of BoseEinstein condensates (BEC) in a rotational frame. As preparatory steps, we take the 3D GrossPitaevskii equation (GPE) with an angular momentum rotation, scale it to obtain a fourparameter 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.  

Porter, Mason A.  Seminarroom C 714  Wed, 24. Sep 08, 11:30 
BoseEinstein Condensates with Spatially Periodic Scattering Lengths  
We investigate the dynamics of quasionedimensional BoseEinstein condensates (BECs) with spatiallyperiodic scattering lengths. This type of "collisionally inhomogeneous" BEC is described by a GrossPitaevskii (GP) equation with a nonlinearity coefficient that varies periodically in space. For the case of a sinusoidal coefficient, we examine the dynamics of spatiallyextended states (modulated amplitude waves) that we construct analytically using the method of averaging. For the case of piecewiseconstant coefficient, we examine the dynamics of solitary waves that we construct using a "stitching" technique.  

Hunag, Zhongyi  Seminarroom C 714  Thu, 25. Sep 08, 10:00 
Bloch Decomposition Based Method for Lattice BEC  
In this talk, we introduce the Blochdecomposition based timesplitting 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 twoscale asymptotic problem with different scalings of the nonlinearity. In particular we discuss (nonlinear) mass transfer between different Bloch bands and also present threedimensional simulations for lattice BoseEinstein condensates in the superfluid regime. Joint work with Shi Jin, Peter A. Markowich, and Christof Sparber  

Pelinovsky, Dmitry  Seminarroom C 714  Thu, 25. Sep 08, 11:00 
Moving gap solitons in periodic potentials  
I review existence of stationary and moving gap solitons in the GrossPitaevskii equation with a small periodic potential. These solitons are approximated by the explicit solutions of the coupledmode system. We show, however, that exponentially decaying traveling solutions of the GrossPitaevskii 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 coupledmode formalism and are estimated by using techniques of spatial dynamics and local centerstable manifold reductions. Existence of bounded traveling solutions of the GrossPitaevskii equation with a single bump surrounded by oscillatory tails on a large interval of the spatial scale is proven by using these techniques.  

Menotti, Chiara  Seminarroom C 714  Fri, 26. Sep 08, 10:00 
The time dependent GrossPitaesvkii equation: Bogoliubov spectrum and beyond  
Using the continuous and the discrete timedependent GPE, we probe the Bogoliubov spectrum of a BoseEinstein 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 timedependent GPE allows to go beyond the Bogoliubov description by entering the nonlinear regime, where one can observe saturation and selftrapping effects. Finally, we include an external trapping potential to simulate situations closer to the experimental ones.  

Gustavsson, Mattias  Seminarroom C 714  Fri, 26. Sep 08, 11:00 
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 noninteracting particles as a single particle effect. We observe and control manybody matter wave interference, which is driven by nonlinear particle interactions. In a multipath matter wave interferometer the macroscopic manybody wave function of an interacting atomic BoseEinstein 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 spinechotype 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 onedimensional geometry and study Bloch osciallations and transport in a onedimensional gas.  

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