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Open positions

Students who are interested in theoretical quantum dynamics at ultra-high intensities and computational physics are encouraged to apply for Ph.D. positions or a Bachelor or a Master Thesis in the division «Quantum Dynamics in Intense Laser Fields». In particular, there are the following open positions:

We are also open for unsolicited applications try to take into account students' interests.

Ph.D. studentship – Relativistic light-matter interactions

Recent progress in laser technology allows to study light-matter interactions at high intensities of about 1022 W/cm2, even higher intensities will be available in the near future. At ultra-high intensities relativistic effects can no longer be neglected. This opens the door to the study of many new quantum phenomena: high harmonic generation and above-threshold ionization at relativistic intensities, non-dipole effects, spin effects, pair production, short-time physics, high-energy physics, and others.

Perturbative methods are no longer adequate if light and matter interact at ultra-high intensities. In fact, the theoretical description of light-matter interaction at relativistic intensities and its complex quantum dynamics requires the numerical solution of the Dirac equation. We are seeking a Ph.D. student to address relativistic light-matter interactions by numerical methods. The Ph.D. candidate is expected to carry out numerical model calculations using existing codes as well as to develop and to implement new numerical schemes.

The candidate should have a master or equivalent degree in physics and be highly motivated to work on a challenging theoretical project. He or she should be interested in numerical simulation, sound knowledge of at least one programming language is inevitable. A solid background in theoretical physics is desirable and experience in theoretical atomic, optical or plasma physics is an advantage. Fluency in English and good interpersonal communication skills are required.

The research project will be carried out at the Max Planck Institute for Nuclear Physics, Postfach 103980, 69029 Heidelberg, Germany. Please send your application, including CV, list of publications/scientific contributions and M.Sc. certificate by e-mail to . Equal opportunity is a cornerstone policy of the Max Planck Society, and women as well as disabled people are particularly encouraged to apply. This position is open and applicants are invited as of now.

Projects for a Bachelor Thesis or a Master Thesis

Recent progress in laser technology allows to study light-matter interactions at high intensities of about 1022 W/cm2, and even higher intensities will be available in the near future. At ultra-high intensities relativistic effects can no longer be neglected. This opens the door to the study of many new quantum phenomena: high harmonic generation and above-threshold ionization at relativistic intensities, non-dipole effects, spin effects, pair production, short-time physics, high-energy physics, and others.

Perturbative methods are no longer adequate if light and matter interact at ultra-high intensities. In fact, the theoretical description of light-matter interaction at ultra-high intensities and its complex quantum dynamics requires the numerical solution of quantum mechanical wave equations (Schrödinger, Dirac, or Klein-Gordon equation) of the type

Schrrödinger type equation

Solving the time-dependent Schrödinger equation numerically has a long history in physics and computational chemistry. Various methods have been developed to solve this equation numerically and the numerical properties of these methods are quite well understood.

Project I: Evaluation of numerical methods for the time-dependent Dirac-equation

Many approaches for the solution of the non-relativistic Schrödinger equation can be generalized to relativistic wave equations, i.e., the Dirac equation and the Klein-Gordon equation. However, it is not well understood how these methods perform if they are applied to the Dirac equation or the Klein-Gordon equation.

The task of the proposed Bachelor or Master thesis project is to evaluate different numerical schemes (e.g., the split operator method, the Cayley propagator, and others) for the numerical solution of the Dirac equation and/or the Klein-Gordon equation in terms of numerical accuracy, stability, computational performance, and parallelization properties. This project is suited for any student who has a good general physics background and is interested in computational physics. Some experience in C++ or some other programming language is required. For more information, please contact Dr. .

Project II: Krylov subspace methods in relativistic quantum dynamics

Krylov subspace methods allow to solve various numerical tasks in a very efficient manner by a series of matrix-vector multiplications. The Arnoldi-Lanczos propagator is a Krylov subspace method for the numerical propagation of quantum wave functions which has been applied to the Schrödinger equation with great success, see J. Comp. Phys., 94, 59-80 (1991) or J. Phys. A: Math. Gen. 39 (2006) 1691-1699.

The task of the proposed Bachelor or Master thesis project is to implement the Arnoldi-Lanczos propagator (or some other Krylov subspace propagator) for the Dirac equation and to evaluate this method in terms of numerical accuracy, stability, computational performance, and parallelization properties. This project is suited for any student who has a good general physics background and is interested in computational physics. Some experience in C++ or some other programming language is required. For more information, please contact Dr. .

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