Funded (UK/EU and international students)

Project code



School of Mathematics and Physics

Start dates

October 2021

Application deadline

4 May 2021

Applications are invited for a fully-funded three year PhD to commence in October 2021. 

The PhD will be based in the School of Mathematics and Physics and will be supervised by Dr Arseni Goussev, Dr Jaewoo Joo and Dr Andrew Burbanks.

Candidates applying for this project may be eligible to compete for one of a small number of bursaries available; these cover tuition fees at the UK rate for three years and a stipend in line with the UKRI rate (£15,609 for 2021/22). Bursary recipients will also receive a £1,500 p.a. for project costs/consumables. 

The work on this project could involve:

  • Research in foundations of quantum theory
  • Applications of quantum computing
  • Design of experimental realisation of quantum backflow

The laws of quantum mechanics allow for a moving particle to temporarily reverse the direction of its motion even in the absence of any external force. One manifestation of this counterintuitive phenomenon is the so-called quantum backflow effect, whereby the probability of finding a particle “on the left” increases with time despite the particle velocity pointing “to the right".

Quantum backflow is a genuinely quantum effect without classical parallel. It is weak and fragile, and has not been yet observed experimentally. Recently [Goussev, “Quantum backflow in a ring”, arXiv:2008.08022] it has been shown that the effect becomes much more pronounced and robust, and better amenable to experimental observation, if instead of letting the particle move along a straight line one forces it to move in a circular ring. This opens a new possibility for the first experimental observation of the effect, and raises new questions on the theoretical side. Investigation of these questions is the objective of the advertised PhD project.

The successful candidate will explore the effect of quantum backflow using a range of techniques from mathematical analysis, numerical simulations, and quantum computing.

Entry requirements

You'll need a good first degree from an internationally recognised university (minimum upper second class or equivalent, depending on your chosen course) or a Master’s degree in an appropriate subject. In exceptional cases, we may consider equivalent professional experience and/or qualifications. English language proficiency at a minimum of IELTS band 6.5 with no component score below 6.0.

You should have a solid background in theoretical physics and applied mathematics. Some experience in scientific computing is also desirable.

How to apply

We’d encourage you to contact Dr Arseni Goussev ( to discuss your interest before you apply, quoting the project code.

When you are ready to apply, you can use our online application form. Make sure you submit a personal statement, proof of your degrees and grades, details of two referees, proof of your English language proficiency and an up-to-date CV. Our ‘How to Apply’ page offers further guidance on the PhD application process. 

If you want to be considered for this funded PhD opportunity you must quote project code SMAP6000521 when applying.