Global PhD Scholarship in Physics
The University of St Andrews is pleased to offer a scholarship funded by St Leonard’s Postgraduate College, to support an exceptional student undertaking doctoral research in the following project:
Collective Behaviour of Driven Many-Body Quantum Systems
Quantum mechanics provides a framework to understand physics ranging from the states of atoms, to the existence of macroscopic behaviour such as superfluidity of liquid helium, or superconductivity of some materials. These macroscopic quantum states — superfluidity and superconductivity — also require understanding collective behaviour, involving large numbers of particles. A triumph of twenty-first century physics has been the ability to understand and predict such behaviour in thermal equilibrium. However, when used in real applications, materials are not necessarily in thermal equilibrium, as one needs to allow currents to flow, or fields to change in time. Moreover, recent pioneering experiments have hinted that one can use driving with electromagnetic radiation to engineer collective quantum states, including results suggesting the existence of superconductivity at room temperature, albeit for a small fraction of a second. Such driven systems are intrinsically non-equilibrium, and so require a theory of collective behaviour in driven systems. As such, understanding how to control and use driven quantum states provide a revolutionary approach to engineering materials for the modern world. This project seeks to develop the theoretical tools that will allow us to understand such states.
Modelling quantum systems is hard because naively, the number of degrees of freedom grows exponentially with the number of quantum particles. Combined with challenges of non-equilibrium physics, this generally restricts “brute force” approaches to modelling of order ten or twenty coupled particles. However, there has been a recent revolution in how such problems can be addressed. “Matrix product state” (MPS) methods allow one to target only those quantum states which are important for realistic situations. This massively reduces the size of space we must search for a solution, from exponential to nearly linear in the number of particles. We will combine Professor Kollath’s and Dr Keeling’s expertise in these methods. Professor Kollath is an expert in large scale applications of MPS methods and applications to time dependent problems. Dr Keeling has used MPS methods to describe coupling quantum systems to realistic environments, through the “TEMPO” algorithm.
So far, much of the theoretical work on collective behaviour in driven quantum systems questions has involved pen-and-paper calculations, which rely on approximations which are often hard to test. Our goal is to extend MPS methods to directly numerically model phase transitions and collective states in these driven systems.
This doctoral project will have various aspects:
- Phase transitions in driven networks of superconducting qubits and microwave resonators. MPS methods can very well model the hyperbolic lattices that have recently been realised in experiment. Considering these lattices will provide a novel approach to understanding phase transitions and collective behaviour.
- Realistic models of damping and their effect on collective behaviour. Most work on non-equilibrium collective behaviour has considered very crude approximations of external environments, effectively assuming them to be featureless, and to just provide irreversible (Markovian) dissipation. We will build on our TEMPO algorithm to develop methods capable of treating phase transitions in realistic models of the environment.
- Phase transitions in driven models with long-range interactions. Professor Kollath has very recently developed methods capable of tackling models which have both short range and long range interactions, such as those mediated by light. We will extend these and combine with the methods above to consider phase transitions in such models.
The successful candidate will be supervised by Dr Jonathan Keeling in the School of Physics and Astronomy at the University of St Andrews and by Professor Corinna Kollath in the Institute for Physics at the University of Bonn.
Informal enquiries regarding this scholarship may be addressed to Dr Jonathan Keeling – email email@example.com
Domicile for fee status
Level of study
Postgraduate Research (Doctoral)
Year of entry
2020-2021 academic year; applicants must be able to start their degree in September 2020.
School of Physics and Astronomy
Applicants must not already (i) hold a doctoral degree; or (ii) be matriculated for a doctoral degree at the University of St Andrews or another institution.
What does it cover?
Duration of award
Up to 3.5 years. The student will be expected to spend approximately half of the award term at the University of St Andrews and half at the University of Bonn. The successful candidate will be expected to have completed the doctorate degree by the end of the award term. The award term excludes the continuation period and any extension periods.
Value of award
The award covers full tuition fees for the period of time spent at the University of St Andrews. For this period, the student will also receive a stipend payable at the standard UK Research council rate (the 2019-2020 annual rate is £15,009). For the period spent at the University of Bonn the student may receive funding to help with living and maintenance costs.
Tuition or maintenance award
Tuition and maintenance.
About St Andrews
Doctoral Research at St Andrews
As a doctoral student at the University of St Andrews you will be part of a growing, vibrant, and intellectually stimulating postgraduate community. St Andrews is one of the leading research-intensive universities in the world and offers a postgraduate experience of remarkable richness.
St Leonard’s Postgraduate College is at the heart of the postgraduate community of St Andrews. The College supports all postgraduates and aims to provide opportunities for postgraduates to come together, socially and intellectually, and make new connections.
St Leonard’s Postgraduate College works closely with the Postgraduate Society which is one of the most active societies within the Students’ Association. All doctoral students are automatically welcomed into the Postgraduate Society when they join the University.
In addition to the research training that doctoral students complete in their home School, doctoral students at St Andrews have access to GRADskills – a free, comprehensive training programme to support their academic, professional, and personal development.
How to apply
Apply for admission as a doctoral student – please see the advice on applying for research degree programmes.
Please indicate in your application that you wish to be considered for this Global St Andrews scholarship (reference Keeling).
Please contact us should you have any questions regarding the scholarship: firstname.lastname@example.org
When do applications open?
Scholarship application deadline
13 February 2020
When will I hear if my application has been successful?
Late February/early March 2020. Awards are subject to final signatures between the parties.