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Dieter Jaksch  WPI Seminar Room C 714  Mon, 4. Feb 13, 10:00 
Magnetic monopoles and synthetic spinorbit coupling in Rydberg macrodimers  
We show that sizeable Abelian and nonAbelian gauge fields arise in the relative quantum motion of two dipoledipole interacting Rydberg atoms. Our system exhibits two magnetic monopoles for adiabatic motion in one internal twoatom state. These monopoles occur at a characteristic distance between the atoms that is of the order of one micron. The deflection of the relative motion due to the Lorentz force gives rise to a clear signature of the broken symmetry in our system. In addition, we consider nonadiabatic transitions between two neardegenerate internal states and show that the associated gauge fields are nonAbelian. We present quantum mechanical calculations of this synthetic spinorbit coupling and show that it realizes a velocitydependent beamsplitter.  
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Martin Bruderer  WPI Seminar Room C 714  Mon, 4. Feb 13, 11:35 
Impurities immersed in BoseEinstein condensates  
The study of impurities immersed in a BoseEinstein condensate (BEC) has become an active field of research during the past few years both on the theoretical and experimental side. In my talk I will present theoretical results on the behaviour of impurities obtained within the framework of coupled GrossPitaevskiiSchrödinger (GPS) equations. This approach describes effects on the impurity such as selftrapping, breathing oscillations and induced impurityimpurity interactions. I will show that variational and numerical solutions of the coupled GPS equations provide an intuitive physical picture of the statics and dynamics of the impurity and the BEC.  
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Thorsten Schumm  WPI Seminar Room C 714  Mon, 4. Feb 13, 14:30 
Nonlinear atom optics with BoseEinstein condensates  
Realizing building blocks of photon quantum optics for matter waves is a longstanding goal. We present an efficient source for twinatom beams, in analogy to parametric downconversion in nonlinear optics. The source shows strong nonclassical correlations in the population of the two beams,  10dB below the classical limit. We also realized an integrated MachZehnder interferometer for matter waves by combining a spatial beam splitter for BEC, a gravitydependent phaseshifter and a recombined based on a pulsed Josephson tunnel junction. The intrinsic nonlinearity of the matter waves leads to number squeezing in the splitting process and to fundamental phase diffusion in the interferometer sequence. We will discuss performance limits towards matter wave metrology.  

Jörg Schmiedmayer  WPI Seminar Room C 714  Mon, 4. Feb 13, 15:50 
Relaxation and prethermlization in a many body quantum system  

JeanClaude Saut  WPI Seminar Room C 714  Tue, 5. Feb 13, 9:30 
Dispersive blowup for Schrödinger type equations  
I will present results (obtained with Jerry Bona and Christof Sparber) on the dispersive blowup phenomenum for various Schrödinder type equations (both linear and nonlinear). Those results might be one explanation to optical rogue waves formation.  
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Florian Mehats  WPI Seminar Room C 714  Tue, 5. Feb 13, 10:50 
High order averaging for the GrossPitaevskii equation  
In this talk, I will present an averaging procedure, – namely Stroboscopic averaging –, for highlyoscillatory evolution equations posed in a Hilbert space, typically partial differential equations (PDEs) in a highfrequency regime where only one frequency is present. A high order averaged system is constructed, whose solution remains exponentially close to the exact one over long time intervals, possesses the same geometric properties (structure, invariants, . . . ) as compared to the original system, and is nonoscillatory. The results will illustrated numerically in the case of the GrossPitaesvkii equation. Joint works with: F. Castella, P. Chartier, A. Murua, Y. Zhang and N. Mauser  
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Phillippe Chartier  WPI Seminar Room C 714  Tue, 5. Feb 13, 11:40 
Averaging for evolution equations: the multifrequency case  
In this work, I will discuss the extension of stroboscopic averaging to quasiperiodic highlyoscillatory differential equations and envisage their application to partial differential equations (PDEs) in a highfrequency regime where only a finite number of frequencies are present. The application of these resuts to GrossPitaesvkii equation will be envisaged.  

Han Pu  WPI Seminar Room C 714  Tue, 5. Feb 13, 14:30 
Ground state and expansion dynamics of a onedimensional Fermi gas  
Lower dimensional physical systems often exhibit stronger quantum behavior in comparison with high dimensional ones. Quantum gases of cold atoms can be confined in traps with effectively low spatial dimension. In this talk, I will discuss the properties of a 1D gas of twocomponent fermions. When the population in the two components are unequal, such a system supports a ground state that is the analog of the socalled FuldeFerrelLarkinOvchinnikov state, an exotic superfluid state with finitemomentum Cooper pairs. Through both a meanfield Bogoliubovde Gennes study and an essentially exact numerical investigation (TEBD), we show how FFLO can manifest itself in the expansion dynamics of the gas.  
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ILiang Chern  WPI Seminar Room C 714  Tue, 5. Feb 13, 15:50 
Exploring Ground States and Excited States of Spin1 BoseEinstein Condensates with/without external magnetic field  
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Yong Zhang  WPI Seminar Room C 714  Tue, 5. Feb 13, 16:40 
Dimension reduction of the schrodinger equation with coulomb and anisotropic confining potentials  
We present a rigorous dimension reduction analysis for the three dimensional (3D) Sch"{o}dinger equation with the Coulombic interaction and an anisotropic confining potential to lower dimensional models in the limit of infinitely strong confinement in two or one space dimensions and obtain rigorously the surface adiabatic model (SAM) or surface density model (SDM) in two dimensions (2D) and the line adiabatic model (LAM) in one dimension (1D). Efficient and accurate numerical methods for computing ground states and dynamics of the SAM, SDM and LAM models are presented based o n efficient and accurate numerical schemes for evaluating the effective potential in lower dimensional models. They are applied to find numerically convergence and convergence rates for the dimension reduction from 3D to 2D and 3D to 1D in terms of ground state and dynamics, which confirm some existing analytical results for the dimension reduction in the literatures. In particular, we explain and demonstrate that the standard SchPoisson system in 2D is not appropriate to simulate a ``2D electron gas" of point particles confined into a plane (or more general a 2D manifold), whereas SDM should be the correct model to be used for describing the Coulomb interaction in 2D in which the square root of Laplacian operator is used instead of the Laplacian operator. Finally, we report ground states and dynamics of the SAM and SDM in 2D and LAM in 1D under different setups.  

Romain Duboscq  WPI Seminar Room C 714  Wed, 6. Feb 13, 9:30 
Development of accurate and robust numerical methods for fast rotating and strongly interacting BoseEinstein condensates  
The aim of this talk is to develop some robust and accurate computational methods for solving BoseEinstein condensates. Most particularly, we are interested in the case where fast rotations arise as well as strong nonlinear interactions. We consider single and multi components BEC. Furthermore, we will give some numerical examples computed by GPELab which is a freely available Matlab toolbox currently developed in collaboration with Xavier Antoine and JeanMarc SacEpée (IECL).  
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Mechthild Thalhammer  WPI Seminar Room C 714  Wed, 6. Feb 13, 10:50 
Adaptive integration methods for Gross–Pitaevskii equations: Theoretical and practical aspects  
In this talk, I shall primarily address the issue of efficient numerical methods for the space and time discretisation of nonlinear Schrödinger equations such as systems of coupled timedependent Gross–Pitaevskii equations arising in quantum physics for the description of multicomponent Bose–Einstein condensates. For the considered class of problems, a variety of contributions confirms the favourable behaviour of pseudospectral and exponential operator splitting methods regarding efficiency and accuracy. However, in the absence of an adaptive local error control in space and time, the reliability of the numerical solution and the performance of the space and time discretisation strongly depends on the experienced scientist selecting the space and time grid in advance. I will illustrate the reliable time integration of Gross–Pitaevskii equations on the basis of a local error control for splitting methods and indicate the main tools for a stability and error analysis justifying the use of the employed space and time discretisations.  
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Christophe Besse  WPI Seminar Room C 714  Wed, 6. Feb 13, 11:40 
An asymptotic preserving scheme based on a new formulation for the nonlinear Schrödinger equation in the semiclassical limit  

Rada Weishäupl  WPI Seminar Room C 714  Wed, 6. Feb 13, 14:30 
A twocomponent nonlinear Schrödinger system with linear coupling  
Click here to see the abstract  
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Zhongyi Huang  WPI Seminar Room C 714  Wed, 6. Feb 13, 15:50 
Bloch decomposition based method for quantum dynamics with periodic potentials  
In this talk, we give a review of our Blochdecomposition based timesplitting spectral method to conduct numerical simulations of the dynamics of (non)linear Schroedinger equations subject to periodic and confining potentials. We consider this system as a twoscale asymptotic problem with different scalings of the nonlinearity. Moreover we demonstrate the superiority of our method over the classical pseudospectral method in many physically relevant situations. We also extended/coupled with other methods to the simulation of other wave type equations with periodic coefficients.  
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Benson Muite  WPI Seminar Room C 714  Wed, 6. Feb 13, 16:40 
Spectral methods for investigating solutions to partial differential equations  
Fourier series serve as a powerful tool for finding approximate numerical solutions to partial differential equations. This talk will discuss the use of collocation methods to investigate solutions to partial differential equations, including the KohnMuller, AvilesGiga and KleinGordon equations. Of particular interest is asymptotic behavior when there is a large or small coefficient. The implementation of these methods on parallel computers will also be addressed.  
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Peter A. Markowich  WPI Seminar Room C 714  Thu, 7. Feb 13, 9:30 

Othmar Koch  WPI Seminar Room C 714  Thu, 7. Feb 13, 11:40 
Adaptive Full Discretization of Nonlinear Schrödinger Equations  
We discuss the time integration of nonlinear Schrödinger equations by highorder splitting methods. The convergence is analyzed first for the semidiscretization in a general Banach space framework. For the GrossPitaevskii equation with rotation term, a generalized LaguerreFourierHermite method is employed for the full discretization. The convergence of this method is established theoretically and illustrated by numerical examples. To obtain efficient integrators, adaptive timestepping is introduced. As a basis, two classes of local error estimators based on embedded pairs of splitting formulae and the defect correction principle are put forward and their asymptotical correctness is demonstrated. Numerical examples illustrate the success of the solution approach.  
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Hans P. Stimming  WPI Seminar Room C 714  Thu, 7. Feb 13, 14:30 
Absorbing boundaries: Exterior Complex Scaling versus Perfectly Matched Layers  
Exterior Complex Scaling and Perfectly Matched Layers are two related methods for artificial absorption on bounded computational domains. The differences in the theory of both methods are discussed and the consequences of these for applicability, stability and accuracy of both methods.  
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Mohammed Lemou  WPI Seminar Room C 714  Thu, 7. Feb 13, 15:50 
Uniformly accurate numerical schemes for highly oscillatory Schrödinger equation  
This work is devoted to the numerical simulation of nonlinear Schrödinger equations. We present a general strategy to construct numerical schemes which are uniformly accurate with respect to the oscillation frequency. This is a stronger future than the usual so called "Asymptotic preserving" property, the last being therefore satisfied by our scheme in the highly oscillatory limit. Our strategy enables to simulate the oscillatory problem without using any mesh or time step refinement, and the order of the scheme is preserved in all regimes. In other words, since our numerical method is not based on the derivation and the simulation of asymptotic models, it works in the regime where the solution does not oscillate rapidly, in the highly oscillatory limit regime, and in the intermediate regime as well. The method is based on a "doublescale" reformulation of the original equation, with the introduction of an additional variable. Then a link is made with classical strategies based on ChapmanEnskog expansions in kinetic theory despite of the dispersive context of the Schrödinger equation.  

Gilles Vilmart  WPI Seminar Room C 714  Thu, 7. Feb 13, 16:40 
Multirevolution composition methods for highly oscillatory problems  
We introduce a new class of geometric numerical integrators for the time integration of highly oscillatory systems of differential equations using large time steps. These methods are based on composition methods and can be considered as numerical homogenization integrators. We prove error estimates with error constants that are independent of the oscillatory frequency. Numerical experiments, in particular for the nonlinear Schrödinger equation, illustrate the theoretical results and the versatility of the methods. This is joint work with P. Chartier, J. Makazaga, and A. Murua.  

George N. Makrakis  WPI Seminar Room C 714  Fri, 8. Feb 13, 9:30 
Uniformization by Wignerization  
We analyse a concrete example to show how to uniformize a twophase WKB function by applying an appropriate "asymptotic surgery" of its Wigner transform  
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François Golse  WPI Seminar Room C 714  Fri, 8. Feb 13, 10:50 
On the propagation of monokinetic measures with rough momentum profiles  
This work is motivated by the description of the classical limit of the Schrodinger equation in terms of Wigner measures. Specifically, we study the structure of the Wigner measure at time t corresponding to a WKB ansatz for the initial wave function. We also provide information on the number of folds in the Lagrangian manifold associated to the propagated measure. Our theory applies to situations where the momentum profile is continuous with derivatives in some appropriate Lorenz space. Finally we give information on the evolution under the dynamics of the Schrodinger equation in classical scaling of a WKB ansatz that cannot be attained with the usual WKB theory for lack of regularity on the initial phase function. (Work in collaboration with C. Bardos, P. Markowich and T. Paul).  

Claude Bardos  WPI Seminar Room C 714  Fri, 8. Feb 13, 11:40 
About the VlasovDiracBenney equation  
This variant of the Vlasov equation is dubbed VlasovDiracBenney because the original potential is replaced by a Dirac mass and because it is very similar to the Benney equation used in water waves. Beside shaving a broad range of applications it is really at the cross road of different techniques in partial differential equations ranging from non linear hyprbolic problems to spectral theory, integrability and semi classical limit.  

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