Confined Quantum Systems (2012, Prolongation from 2011)
Organizers: Weizhu Bao (U.Singapore), Stephane Descombes (U.Nice), Florian Mehats (U.Rennes), H.Christoph Nägerl (Innsbruck), J. Schmiedmayer (WPI c/o TU Wien), H.P. Stimming (WPI c/o Uni Wien),
Rada Weishäupl (U.Wien),
Remi Carles (U. Montpellier), PF Dieter Jaksch (U. Oxford)
Talks
Norbert J. Mauser (WPI c/o Uni Wien) 
WPI, Seminarroom C 714 
Wed, 11. Jul 12, 9:30 
"Modeling and simulation of LOw DImensional QUAntum Systems: The LODIQUAS
project" 
 Thematic program: Confined Quantum Systems (2012, Prolongation from 2011)
 Event: Workshop on "Low dimensional Quantum Systems" (2012)

Yong Zhang (WPI) 
WPI, Seminarroom C 714 
Wed, 11. Jul 12, 11:00 
"Numerical Methods and Analysis for the "low dimensional
SchrödingerPoisson Equations" and their Applications" 
 Thematic program: Confined Quantum Systems (2012, Prolongation from 2011)
 Event: Workshop on "Low dimensional Quantum Systems" (2012)

Francis Nier (CERMICS, Paris) 
WPI, Seminarroom C 714 
Wed, 11. Jul 12, 14:00 
"About the characteristic method" 
Abstract:
This is a part of our most recent work achieved with Z.
Ammari about bosonic quantum mean field dynamics. When mean field problems
are considered, one has to face a transport equation for measures in an
infinite dimensional phasespace. Even when the flow is welldefined
the standard characteristic method is no more available. One solution
(there are other approaches) is given by a probabilistic point of view
used in optimal transport. 
 Thematic program: Confined Quantum Systems (2012, Prolongation from 2011)
 Event: Workshop on "Low dimensional Quantum Systems" (2012)

Andrea Mantile (Reims) 
WPI, Seminarroom C 714 
Wed, 11. Jul 12, 15:30 
"Artificial interface conditions in quantum transport models" 
Abstract:
In a recent collaboration with F.Nier and A.Faraj, it has been shown that
a simple modifcation of the Laplacian through artificial interface
conditions allows an alternative approach to the adiabatic evolution
of quantum resonances.
The use of this modifed framework, may hopefully provide with
effective equations for the nonlinear dynamics of SchrödingerPoisson
systems in the regime of quantum wells in a semiclassical island.
In this perspective, it is important to control the deformations
effects introduced on the spectrum and on the time propagator by such
interface conditions.
In particular we are interested in uniformintime estimates of the perturbed
semigroup. The main difficulty is due to the nonselfadjont character of our
class of operators, involving a lack of accretivity for the
corresponding generator of the quantum dynamics. In this framework, a
standard approach would only provide with finitetime estimates for
the dynamical system. An alternative startegy consists in constructing
intertwining operators leading to a dynamical comparison between the
modified nonselfadjoint model and the corresponding `physical'
Hamiltonian. 
 Thematic program: Confined Quantum Systems (2012, Prolongation from 2011)
 Event: Workshop on "Low dimensional Quantum Systems" (2012)

Fanny Delebecque (Toulouse) 
WPI, Seminarroom C 714 
Thu, 12. Jul 12, 9:45 
"Low dimensional models for the transport of a strongly confined electron gas" 
 Thematic program: Confined Quantum Systems (2012, Prolongation from 2011)
 Event: Workshop on "Low dimensional Quantum Systems" (2012)

Philippe Chartier (INRIA Rennes) 
WPI, Seminarroom C 714 
Thu, 12. Jul 12, 11:00 
"Stroboscopic averaging for the Schrödinger equation" 
 Thematic program: Confined Quantum Systems (2012, Prolongation from 2011)
 Event: Workshop on "Low dimensional Quantum Systems" (2012)

Kristelle Roidot (SISSA Trieste) 
WPI, Seminarroom C 714 
Thu, 12. Jul 12, 14:00 
"Numerical Study of Asymptotic behavior and Blow up phenomena in NLS equations" 
 Thematic program: Confined Quantum Systems (2012, Prolongation from 2011)
 Event: Workshop on "Low dimensional Quantum Systems" (2012)

Mechthild Thalhammer (Innsbruck) 
WPI, Seminarroom C 714 
Thu, 12. Jul 12, 15:15 
Adaptive time integration methods for GrossPitaevskii equations 
 Thematic program: Confined Quantum Systems (2012, Prolongation from 2011)
 Event: Workshop on "Low dimensional Quantum Systems" (2012)

Hans Peter Stimming (WPI Wien) 
WPI, Seminarroom C 714 
Thu, 12. Jul 12, 16:00 
"Dephasing of coherently split quasicondensates" 
 Thematic program: Confined Quantum Systems (2012, Prolongation from 2011)
 Event: Workshop on "Low dimensional Quantum Systems" (2012)

Mohammed Lemou (Rennes) 
WPI, Seminarroom C 714 
Fri, 13. Jul 12, 9:30 
"On micromacro numerical schemes for multiscale kinetic and Schrödinger equations" 
 Thematic program: Confined Quantum Systems (2012, Prolongation from 2011)
 Event: Workshop on "Low dimensional Quantum Systems" (2012)

Florian Mehats (Rennes) 
WPI, Seminarroom C 714 
Fri, 13. Jul 12, 10:45 
"Asymptotic Preserving numerical method for the nonlinear Schrodinger equation in the semiclassical limit" 
 Thematic program: Confined Quantum Systems (2012, Prolongation from 2011)
 Event: Workshop on "Low dimensional Quantum Systems" (2012)

Saut, JeanClaude 
WPI Seminar Room C 714 
Mon, 1. Oct 12, 14:30 
Madelung, GrossPitaevskii and Korteweg 
 Thematic program: Confined Quantum Systems (2012, Prolongation from 2011)
 Event: Workshop on "Complexity in Fluid Mechanics" (2012)

Hillairet, Mathieu 
WPI Seminar Room C 714 
Tue, 2. Oct 12, 9:30 
On the existence of positive solutions to thin film models with surfactant 
 Thematic program: Confined Quantum Systems (2012, Prolongation from 2011)
 Event: Workshop on "Complexity in Fluid Mechanics" (2012)

Renardy, Michael 
WPI Seminar Room C 714 
Tue, 2. Oct 12, 11:00 
On the wellposedness of the hydrostatic limit in fluid mechanics 
 Thematic program: Confined Quantum Systems (2012, Prolongation from 2011)
 Event: Workshop on "Complexity in Fluid Mechanics" (2012)

Vila, JeanPaul 
WPI Seminar Room C 714 
Tue, 2. Oct 12, 14:00 
Cosistency of shallow water models in the limit of wet/dry fronts 
 Thematic program: Confined Quantum Systems (2012, Prolongation from 2011)
 Event: Workshop on "Complexity in Fluid Mechanics" (2012)

GérardVaret, David 
WPI Seminar Room C 714 
Wed, 3. Oct 12, 9:30 
Domain continuity for the Euler and NavierStokes equations 
 Thematic program: Confined Quantum Systems (2012, Prolongation from 2011)
 Event: Workshop on "Complexity in Fluid Mechanics" (2012)

Benzoni, Sylvie 
WPI Seminar Room C 714 
Wed, 3. Oct 12, 11:00 
Tidal bores and superfluids 
 Thematic program: Confined Quantum Systems (2012, Prolongation from 2011)
 Event: Workshop on "Complexity in Fluid Mechanics" (2012)

Olivier, Julien 
WPI Seminar Room C 714 
Wed, 3. Oct 12, 14:00 
A shear band type solution in a model of complex fluids 
 Thematic program: Confined Quantum Systems (2012, Prolongation from 2011)
 Event: Workshop on "Complexity in Fluid Mechanics" (2012)

Chupin, Laurent 
WPI Seminar Room C 714 
Thu, 4. Oct 12, 9:30 
Integral laws for viscoelastic fluids 
 Thematic program: Confined Quantum Systems (2012, Prolongation from 2011)
 Event: Workshop on "Complexity in Fluid Mechanics" (2012)

Martin, Sébastien 
WPI Seminar Room C 714 
Thu, 4. Oct 12, 11:00 
Viscoelastic fluids in thin domains 
 Thematic program: Confined Quantum Systems (2012, Prolongation from 2011)
 Event: Workshop on "Complexity in Fluid Mechanics" (2012)

Noble, Pascal 
WPI Seminar Room C 714 
Thu, 4. Oct 12, 14:00 
Stability of thin films of power law fluids down an incline plane and connection with the derivation of shallow water models 
 Thematic program: Confined Quantum Systems (2012, Prolongation from 2011)
 Event: Workshop on "Complexity in Fluid Mechanics" (2012)

Klein, Christian 
WPI Seminar Room C 714 
Fri, 5. Oct 12, 9:30 
Numerical study of the KadomtsevPetviashvili equation 
 Thematic program: Confined Quantum Systems (2012, Prolongation from 2011)
 Event: Workshop on "Complexity in Fluid Mechanics" (2012)

Bresch, Didier 
WPI Seminar Room C 714 
Fri, 5. Oct 12, 11:00 
Wellposedness and decline curves for PDE's arising in oil production 
 Thematic program: Confined Quantum Systems (2012, Prolongation from 2011)
 Event: Workshop on "Complexity in Fluid Mechanics" (2012)

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. 
Note: You may download the presentation of the talk 
 Thematic program: Confined Quantum Systems (2012, Prolongation from 2011)
 Event: Workshop on "Confined Quantum Systems: Modeling, Analysis and Computation" (2013)

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. 
Note: You may download the presentation of the talk 
 Thematic program: Confined Quantum Systems (2012, Prolongation from 2011)
 Event: Workshop on "Confined Quantum Systems: Modeling, Analysis and Computation" (2013)

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. 
 Thematic program: Confined Quantum Systems (2012, Prolongation from 2011)
 Event: Workshop on "Confined Quantum Systems: Modeling, Analysis and Computation" (2013)

Jörg Schmiedmayer 
WPI Seminar Room C 714 
Mon, 4. Feb 13, 15:50 
Relaxation and prethermlization in a many body quantum system 
 Thematic program: Confined Quantum Systems (2012, Prolongation from 2011)
 Event: Workshop on "Confined Quantum Systems: Modeling, Analysis and Computation" (2013)

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. 
Note: You may download the presentation of the talk 
 Thematic program: Confined Quantum Systems (2012, Prolongation from 2011)
 Event: Workshop on "Confined Quantum Systems: Modeling, Analysis and Computation" (2013)

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

Note: You may download the presentation of the talk 
 Thematic program: Confined Quantum Systems (2012, Prolongation from 2011)
 Event: Workshop on "Confined Quantum Systems: Modeling, Analysis and Computation" (2013)

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. 
 Thematic program: Confined Quantum Systems (2012, Prolongation from 2011)
 Event: Workshop on "Confined Quantum Systems: Modeling, Analysis and Computation" (2013)

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.

Note: You may download the presentation of the talk 
 Thematic program: Confined Quantum Systems (2012, Prolongation from 2011)
 Event: Workshop on "Confined Quantum Systems: Modeling, Analysis and Computation" (2013)

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 
Click here to see the abstract 
 Thematic program: Confined Quantum Systems (2012, Prolongation from 2011)
 Event: Workshop on "Confined Quantum Systems: Modeling, Analysis and Computation" (2013)

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.

 Thematic program: Confined Quantum Systems (2012, Prolongation from 2011)
 Event: Workshop on "Confined Quantum Systems: Modeling, Analysis and Computation" (2013)

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). 
Note: You may download the presentation of the talk 
 Thematic program: Confined Quantum Systems (2012, Prolongation from 2011)
 Event: Workshop on "Confined Quantum Systems: Modeling, Analysis and Computation" (2013)

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.

Note: You may download the presentation of the talk (without movies) 
 Thematic program: Confined Quantum Systems (2012, Prolongation from 2011)
 Event: Workshop on "Confined Quantum Systems: Modeling, Analysis and Computation" (2013)

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 
 Thematic program: Confined Quantum Systems (2012, Prolongation from 2011)
 Event: Workshop on "Confined Quantum Systems: Modeling, Analysis and Computation" (2013)

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 
Note: You may download the presentation of the talk 
 Thematic program: Confined Quantum Systems (2012, Prolongation from 2011)
 Event: Workshop on "Confined Quantum Systems: Modeling, Analysis and Computation" (2013)

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. 
Note: You may download the presentation of the talk 
 Thematic program: Confined Quantum Systems (2012, Prolongation from 2011)
 Event: Workshop on "Confined Quantum Systems: Modeling, Analysis and Computation" (2013)

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. 
Note: You may download the presentation of the talk 
 Thematic program: Confined Quantum Systems (2012, Prolongation from 2011)
 Event: Workshop on "Confined Quantum Systems: Modeling, Analysis and Computation" (2013)

Peter A. Markowich 
WPI Seminar Room C 714 
Thu, 7. Feb 13, 9:30 

 Thematic program: Confined Quantum Systems (2012, Prolongation from 2011)
 Event: Workshop on "Confined Quantum Systems: Modeling, Analysis and Computation" (2013)

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. 
Note: You may download the presentation of the talk 
 Thematic program: Confined Quantum Systems (2012, Prolongation from 2011)
 Event: Workshop on "Confined Quantum Systems: Modeling, Analysis and Computation" (2013)

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. 
Note: You may download the presentation of the talk 
 Thematic program: Confined Quantum Systems (2012, Prolongation from 2011)
 Event: Workshop on "Confined Quantum Systems: Modeling, Analysis and Computation" (2013)

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.

 Thematic program: Confined Quantum Systems (2012, Prolongation from 2011)
 Event: Workshop on "Confined Quantum Systems: Modeling, Analysis and Computation" (2013)

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. 
 Thematic program: Confined Quantum Systems (2012, Prolongation from 2011)
 Event: Workshop on "Confined Quantum Systems: Modeling, Analysis and Computation" (2013)

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 
Note: You may download the presentation of the talk 
 Thematic program: Confined Quantum Systems (2012, Prolongation from 2011)
 Event: Workshop on "Confined Quantum Systems: Modeling, Analysis and Computation" (2013)

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). 
 Thematic program: Confined Quantum Systems (2012, Prolongation from 2011)
 Event: Workshop on "Confined Quantum Systems: Modeling, Analysis and Computation" (2013)

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. 
 Thematic program: Confined Quantum Systems (2012, Prolongation from 2011)
 Event: Workshop on "Confined Quantum Systems: Modeling, Analysis and Computation" (2013)
