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(Quantum) Wave equations (2022/2023)

Organizers: PF Jean-Claude Saut (U. Paris Sud and ICP), Mechthild Thalhammer (U. Innsbruck), Christoph Nägerl (WPI c/o U. Innsbruck),

Talks


Christian Lubich (U. Tübingen) HS13, 2nd floor Fak Math Oskar Morgensternplatz 1 Tue, 27. Sep 22, 14:00
Time integration of tree tensor networks
I first report on recent numerical experiments with time-dependent tree tensor network algorithms for the approximation of quantum spin systems. I will then describe the basics in the design of time integration methods that are robust to the usual presence of small singular values, that have good structure-preserving properties (norm, energy conservation or dissipation), and that allow for rank (= bond dimension) adaptivity and also have some parallelism. This discussion of basic concepts will be done for the smallest possible type of tensor network differential equations, namely low-rank matrix differential equations. Once this simplest case is understood, there is a systematic path to the extension of the integrators and their favourable properties to general tree tensor networks. This talk is based on joint work with many colleagues and former and present students, among which I wish to single out Othmar Koch for the first mathematical work on dynamical low-rank approximation (DLRA) in 2007, Ivan Oseledets for jointly finding the first robust DLRA integrator (the projector-splitting integrator) in 2014, Gianluca Ceruti for jointly finding the Basis Update & Galerkin (BUG) integrators in 2021, and him and Hanna Walach and Dominik Sulz for the recent systematic extension from low-rank matrices to general tree tensor networks.
  • Thematic program: (Quantum) Wave equations (2022/2023)

Jean-Claude Saut (U. Paris-Saclay) WPI, OMP 1, Seminar Room 08.135 Mon, 17. Oct 22, 14:30
Old and new on Boussinesq systems
  • Thematic program: (Quantum) Wave equations (2022/2023)
  • Event: Workshop on "Nonlinear dispersive equations - Inverse scattering and PDE methods" (2022)

Rémi Carles (CNRS Rennes) WPI, OMP 1, Seminar Room 08.135 Mon, 17. Oct 22, 15:45
Time dependent Hartree approximation in quantum dynamics
  • Thematic program: (Quantum) Wave equations (2022/2023)
  • Event: Workshop on "Nonlinear dispersive equations - Inverse scattering and PDE methods" (2022)

Jakob Möller (U. Wien) WPI, OMP 1, Seminar Room 08.135 Mon, 17. Oct 22, 16:45
Semiclassical limit of Pauli-Poisswell by WKB and Wigner methods
  • Thematic program: (Quantum) Wave equations (2022/2023)
  • Event: Workshop on "Nonlinear dispersive equations - Inverse scattering and PDE methods" (2022)

Christian Klein (U. Bourgogne) WPI, OMP 1, Seminar Room 08.135 Tue, 18. Oct 22, 9:15
Complex geometric optics for the Davey-Stewartson-II equation
  • Thematic program: (Quantum) Wave equations (2022/2023)
  • Event: Workshop on "Nonlinear dispersive equations - Inverse scattering and PDE methods" (2022)

Patrick Gerard (U. Paris-Saclay) WPI, OMP 1, Seminar Room 08.135 Tue, 18. Oct 22, 10:45
Doubly periodic solutions of the Benjamin-Ono equation
  • Thematic program: (Quantum) Wave equations (2022/2023)
  • Event: Workshop on "Nonlinear dispersive equations - Inverse scattering and PDE methods" (2022)

Petar Topalov (Northeastern U. College of Science) WPI, OMP 1, Seminar Room 08.135 Tue, 18. Oct 22, 14:00
Spatially quasi-periodic solutions of the Euler equation
  • Thematic program: (Quantum) Wave equations (2022/2023)
  • Event: Workshop on "Nonlinear dispersive equations - Inverse scattering and PDE methods" (2022)

Jiao He (U. Paris-Saclay) WPI, OMP 1, Seminar Room 08.135 Tue, 18. Oct 22, 15:30
Some work in progress on integrability of the Kadomtsev-Petviashvili-II equation
  • Thematic program: (Quantum) Wave equations (2022/2023)
  • Event: Workshop on "Nonlinear dispersive equations - Inverse scattering and PDE methods" (2022)

Benoit Grebert (U. Nantes) WPI, OMP 1, Seminar Room 08.135 Wed, 19. Oct 22, 9:15
Dynamics of Hamiltonian PDEs at low regularity
  • Thematic program: (Quantum) Wave equations (2022/2023)
  • Event: Workshop on "Nonlinear dispersive equations - Inverse scattering and PDE methods" (2022)

Anton Arnold (TU Wien) WPI, OMP 1, Seminar Room 08.135 Wed, 19. Oct 22, 10:45
All relative entropies for the Fokker-Planck equation
  • Thematic program: (Quantum) Wave equations (2022/2023)
  • Event: Workshop on "Nonlinear dispersive equations - Inverse scattering and PDE methods" (2022)

Nikola Stoilov (U. Bourgogne) WPI, OMP 1, Seminar Room 08.135 Wed, 19. Oct 22, 14:00
Numerical studies of the Zakharov-Kuznetsov family of equations
  • Thematic program: (Quantum) Wave equations (2022/2023)
  • Event: Workshop on "Nonlinear dispersive equations - Inverse scattering and PDE methods" (2022)

Douglas Svensson (NTNU) WPI, OMP 1, Seminar Room 08.135 Wed, 19. Oct 22, 15:30
Asymmetric traveling waves for the gravity -capillary Whitahm equation
  • Thematic program: (Quantum) Wave equations (2022/2023)
  • Event: Workshop on "Nonlinear dispersive equations - Inverse scattering and PDE methods" (2022)

Peter Perry (U. Kentucky) WPI, OMP 1, Seminar Room 08.135 Thu, 20. Oct 22, 9:15
Towards Inverse Scattering for the intermediate long wave equation
  • Thematic program: (Quantum) Wave equations (2022/2023)
  • Event: Workshop on "Nonlinear dispersive equations - Inverse scattering and PDE methods" (2022)

Ken McLaughlin (Tulane) WPI, OMP 1, Seminar Room 08.135 Thu, 20. Oct 22, 10:45
Analysis of soliton interactions and random matrix theory
  • Thematic program: (Quantum) Wave equations (2022/2023)
  • Event: Workshop on "Nonlinear dispersive equations - Inverse scattering and PDE methods" (2022)

Erik Wahlen (U. Lund) WPI, OMP 1, Seminar Room 08.135 Thu, 20. Oct 22, 14:00
Large amplitude solitary waves for the Whitham equation
  • Thematic program: (Quantum) Wave equations (2022/2023)
  • Event: Workshop on "Nonlinear dispersive equations - Inverse scattering and PDE methods" (2022)

Jannis Körner (TU Wien) WPI, OMP 1, Seminar Room 08.135 Thu, 20. Oct 22, 15:30
WKB scheme for the 1D stationary Schrödinger equation in the highly oscillating regime
  • Thematic program: (Quantum) Wave equations (2022/2023)
  • Event: Workshop on "Nonlinear dispersive equations - Inverse scattering and PDE methods" (2022)

Nana Liu (INS – U. Michigan - Shanghai Jiao Tong Univ.) WPI Seminar room Tue, 31. Jan 23, 12:00
Quantum simulation of partial differential equations via Schrödingerisation
In this talk, I’ll introduce a simple new way – called „Schrödingerisation“ – to simulate general linear partial differential equations via quantum simulation. Using a simple new transform, referred to as the „warped phase transformation“, any linear partial differential equation can be recast into a system of Schrödinger’s equations – in real time — in a straightforward way. This can be seen directly on the level of the dynamical equations without more sophisticated methods. This approach is not only applicable to PDEs for classical problems but also those for quantum problems – like the preparation of quantum ground states, Gibbs states and the simulation of quantum states in random media in the semiclassical limit.
Note:   External webpage: www.nanaliu.weebly.com
  • Thematic program: (Quantum) Wave equations (2022/2023)

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