PhD position in quantum integrability and KAM theory

Job description

Integrability represents a fundamental area within mathematical and physical sciences, despite its absence from the standard (undergraduate and graduate) curricula. Being a subfield of dynamical systems, it connects to nearly every area of modern mathematics and mathematical physics, including algebra, geometry, and number theory, classical and celestial mechanics, string theory, and cosmology.

The pioneering works on integrability were written by Birkhoff and later Kolmogorov, Arnol’d, Moser (and also Smale), who also laid the foundation of classical KAM (Kolmogorov-Arnol’d-Moser) theory. This theory applies to systems close to complete integrability and is widely used in celestial mechanics, providing robust predictions regarding the motion of celestial bodies. It is also indispensable to the study of simple atomic and molecular systems, such as the hydrogen atom in external fields.

This PhD project is primarily focused on quantum KAM theory, i.e. the study of systems close to quantum integrability. A particular one-million question in this context concerns the existence of monodromy in such systems. Here we mainly refer to the so-called Hamiltonian monodromy which appears as the first obstruction to the existence of global action-angle variables for integrable systems and can suitably be generalised to the context of quantum KAM. If successful, the PhD project will shed light on the spectral properties of various real-life physical and chemical systems.

The objective of the temporary position is the production of a number of research articles in peer-reviewed scientific journals and conference proceedings, which together will form the basis of a thesis leading to a PhD degree (Dr) at the University of Groningen.

*The PhD project is part of the NWO VIDI grant “Finding monodromy in perturbation of classical and quantum integrable systems” of one of the supervisors.

Organisation

Founded in 1614, the University of Groningen enjoys an international reputation as a dynamic and innovative institution of higher education offering high-quality teaching and research. Flexible study programmes and academic career opportunities in a wide variety of disciplines encourage the 35,000 students and researchers alike to develop their own individual talents. As one of the best research universities in Europe, the University of Groningen has joined forces with other top universities and networks worldwide to become a truly global centre of knowledge.

Within the Faculty of Science and Engineering, a 4-years PhD position is available at the Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence with the topic of integrability and quantum KAM theory.

The candidate would become a member of the Dynamical Systems, Geometry and Mathematical Physics group of the Bernoulli Institute.

Qualifications

The successful candidate should have

• A Master’s degree in Mathematics, Mathematical Physics or related area with excellent results.
• An interest in Dynamical Systems and Quantum Mechanics.
• Demonstrable ability to learn a new subject.
• Experience in teaching and academic writing in English is a plus.

Organisation

Conditions of employment

We offer you, following the Collective Labour Agreement for Dutch Universities

• A salary of € 2,901 gross per month in the first year, up to a maximum of € 3,707 gross per month in the fourth and final year for a full-time working week.
• A holiday allowance of 8% gross annual income and an 8.3% year-end bonus.
• Teaching: employed PhD candidates are expected to spend 10% of their working hours on teaching and/or supervising candidates.
• A full-time position (1.0 FTE). The successful candidate will first be offered a temporary position of one year with the option of renewal for another three years. Prolongation of the contract is contingent on sufficient progress in the first year to indicate that a successful completion of the PhD thesis within the next three years is to be expected. A PhD training programme is part of the agreement and the successful candidate will be enrolled in the Graduate School of Science and Engineering.