A CMA-workshop on

Computational methods for the time-dependent Schroedinger equation

Oslo, Nov. 17-18, 2003

Hosted by:
The Centre of Mathematics for Applications, University of Oslo, Norway

Participants (posted Nov. 24)
List of participansts here.

Introduction:
Recent advances in atomic and molecular physics and solid state physics allow now for studies of isolated quantal systems such as single ions in traps of various geometries under the influence of e.g., time-dependent electromagnetic fields from a Laser.

Such experiments have important consequences for our basic understanding of quantum mechanics and its theoretical foundations. Furthermore, studies of these isolated systems may have important practical applications, spanning from atomic lasers to the construction of quantum gates and tests of quantum information algorithms.

Several methods exist for studying such quantal systems, ranging from partial differential equations to Green's function Monte Carlo methods. The aim of this workshop is to expose possible directions of research based on partial differential equations, discuss eventual limitations and point to links with other methods.

Especially we aim at focussing on

• Interesting physical systems which can be studied with partial differential equation techniques
• Finite element methods for time-dependent Hamiltonians
• Limitations due to increasing degrees of freedom
• Coupling to stochastic differential equations and Monte Carlo methods

Time and place:

The workshop starts on
Monday November 17, 09.00, and ends on
Tuesday November 18, 16.00.

The workshop will take place in the CMA seminar room (B1036) in the Niels Henrik Abel building (mathematics building) on the 10th. floor.

All persons who are interested are welcome to attend this informal workshop.

Preliminary Program (subject to change):

Monday Nov. 17.

0900-1030: Jan Petter Hansen / Sølve Selstø(UiB). Title: "Introduction to the time time-dependent Schroedinger equation and challenges in atomic and solid state physics". Abstract.
1030-1100: Coffee Break.
1100-1200: Simen Kvaal (UiO) Title: "Solving the Time Dependent Schrödinger Equation With Symplectic Integrators
and Finite Element Methods". Abstract.

1200-1400: Lunch.

1400-1500: Per Christian Moan (UiO/CMA). Title: "Time averaging; an approach for overcoming time-step restrictions?". Abstract.
1500-1600: Halvor Møll Nilsen (UiB). Title: "Rotating Bose-Einstein Condensates"
1600-1630: Coffee break
1630-1730: Patrice Bertet (UDelft, Holland). Title: "Experimental Quantum State Manipulation". Abstract.
1730-1900: Discussions

19.00: Dinner

Tuesday Nov. 18

0900-1000: Helge Holden (NTNU/CMA). Title: "On Overgrown Paths - Solvable models in quantum mechanics revisited". Abstract.
1000-1100: Hans Petter Langtangen (Simula Research lab and UiO). Title: "Stochastic ODEs and deterministic PDEs". Abstract.
1100-1130: Coffee break
1130-1230: Snorre Christiansen (UiO/CMA). Title: "Introduction to large scale numerical eigenvalue computation". Abstract.

1230-1400: Lunch.

1400-1430: Hans Munthe-Kaas (UiB). Title: "On geometrical ideas in time integration of dynamical systems". Abstract.
1430-1500: Brynjulf Owren (NTNU). Title: "Fourth order exponential time integrators for a nonlinear Schrodinger
equation". Abstract.

Organizing committee:

Snorre Christiansen (UiO/CMA)
Morten Hjorth-Jensen (UiO/CMA)
Kenneth Hvistendahl Karlsen (UiB/CMA)