Workshop on quantum dynamics and semiclassical methods

Please note that the talk by Daniel Spångberg had to be canceled and the talk by Adam Kirrander is rescheduled to 11:00.

Date

June 15, 2011

Place

Room: Polacksbacken 2345 (House 2, 3rd floor)

Program

  • 09:30-10:00 Magnus Gustafsson: Adaptive discretization of high-dimensional grids for the time-dependent Schrödinger equation
Accurate solution of the time-dependent Schrödinger equation requires massive-scale parallel computing. In particular, the memory requirements for uniform grids with fine enough resolution will become prohibitively large due to the high dimensionality of interesting model problems. We present a block-adaptive framework for spatial discretization that uses high-order finite difference schemes together with summation-by-parts operators with simultaneous approximating term (SBP-SAT) for stable coupling of non-conforming block boundaries. Numerical results will be presented, where we use this discretization technique together with exponential propagation based on the Lanczos algorithm.
  • 10:00-10:30 Anders Szepessy: Molecular dynamics accuracy compared to quantum mechanics
I will show that Born-Oppenheimer molecular dynamics accurately approximates observables based on the time-independent Schrödinger equation, in the limit of large ratio of nuclei and electron masses. The approximation is based on a Hamiltonian system interpretation of the time-independent Schrödinger equation and stability of the corresponding Hamilton-Jacobi equation. I will in particular present the situation with caustic states.
  • 10:30-11:00 coffee break
  • 11:00-11:30 Adam Kirrander: Simulations of electron dynamics in strong fields and spectra of H2
The recently developed Coupled Coherent States (CCS) method for solving the time-dependent Schrodinger equation is a fully quantum method (with semiclassical origins). It has successfully been applied to a number of problems, which require simulation of quantum dynamics in complex multidimensional systems, such as vibrational energy transfer, nonadiabatic dynamics in molecules, dynamics and spectra of small clusters, and tunneling in systems with many degrees of freedom. I will present our efforts towards using this method to simulate the strong field double ionization of helium. The calculated double ionization yield, as a function of laser intensity, reproduces the "shoulder", attributable to electron recollisions. Since the Coherent State representation is guided by classical trajectories, it also provides physical insight into the ionization mechanism. In addition,a new version of the theory which takes explicit account of the exchange symmetry of fermion particles, and uses fermion molecular dynamics to propagate trajectories, is presented.
  • 11:30-12:00 Hans Karlsson: Quantum dynamics for many degrees of freedom - a review of current approaches
In this talk I will review some of the most promising approaches to quantum dynamics of high-dimensional systems. Special focus will be on methods where the potential energy surface can be computed on the fly.
  • 12:00-13:15 lunch break
  • 13:15-14:00 Vasile Gradinaru: Tunneling and spawning with Hagedorn wavepackets
The Hagedorn wavepackets allow an adaptive and boundary-free numerical treatment of some semiclassical models in the quantum dynamics of nuclei. Chances and challenges of their use will be discussed.

Contact

Katharina Kormann

Welcome!