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CRM: Mathematical and Computational Methods for Quantum Systems
The goal of the workshop is to gather applied mathematicians, theoretical chemists and physicists, specialists of mathematical and computational methods in relativistic and non-relativistic quantum chemistry and physics, laser physics, cold-matter physics and Bose-Einstein condensates. All these fields of application have in common linear or nonlinear quantum relativistic or non-relativistic wave models, such as the Schroedinger, Gross-Pitaevskii, Klein-Gordon or Dirac equations. The workshop will not only introduce the state-of-the-art in these research fields, but also will address new challenges and the future research trends. The workshop will cover several mathematical areas:
- Numerical and mathematical methods for time dependent linear and nonlinear Dirac and Schroedinger equations.
- Spectral theory applied to quantum Hamiltonians. Spectral pollution. Nonlinear and linear eigenvalue problem for unbounded operators, Dirac operator, Gross-Piatevskii operator. Imaginary time methods, Feit-Fleck exponential method, balanced operators.
- Computational methods for many-body problems. Variational methods.
- Domain decomposition methods, Schwarz waveform relaxation methods, multilevel methods.
- High order operator splitting methods, exponential integrators.
- Multiscale computing in material and cold-matter science.
- High performance computing in quantum and laser physics.
- Application to pair productions, graphene, attosecond science, Bose-Einstein condensate, laser-filamentation, laser-molecule interaction in relativistic regime, quantum imaging, ultrafast laser imaging.