Subject areas:
Mathematics.
Funding type:
Bench Fees / Research Training & Support Grant.
Study costs.
Awarding body:
King's College London.
Fully-funded PhD studentship available to start in 2025.
Award details
Context: Thermodynamics is a very powerful theory to describe systems at equilibrium. But what happens out of equilibrium? Can we describe in a universal fashion the motion at large scales of space and time? This is relevant, as what we observe in many experiments are aggregate effects of many small degrees of freedom (atoms, spins, waves, etc.). Describing the large-scale dynamics of many-body systems is one of the most important questions of modern physics.
Project: The general principles of hydrodynamics give a powerful framework to understand large-scale behaviours, much beyond hydrodynamics from textbooks. For instance, in integrable systems, which admit many more conservation laws than the usual energy and momentum, the hydrodynamic equations are very different - the theory is called Generalised Hydrodynamics. Most interestingly, in general, there are powerful ``hydrodynamic field theories" to describe fluctuations, which show unusual non-equilibrium effects. The project will explore correlations and fluctuations at large scales using and extending these powerful new theories. After starting with applications to interesting models in order to gain familiarity, the main goals will be to understand the quantum effects, including entanglement, and the higher orders in the hydrodynamic expansion. The projects will delve into fundamental aspects of statistical mechanics, and may involve a variety of analytical methods including integrability such as the Bethe ansatz and classical inverse scattering theory, as well as numerical methods such as Monte Carlo.
The PhD candidate will be supported by EPSRC under grant UNIHYPE: Universal hydrodynamic principles and emergent physics, EP/Z534304/1.
Skills: I seek for a very motivated student with a solid background in either theoretical physics or applied mathematics, preferably with some basic knowledge of coding for numerical simulations.
Award value
Funding is available for 4 years, covering:
- Stipend;
- Bench Fees;
- Tuition fees (full home or overseas tuition fees).
Eligibility criteria
Award open to UK and international students.
Applicants should have a 2:1 or first-class undergraduate degree, or an MMath, MSci or Master’s degree with Merit and high grades in modules relating to the research area. A solid background in either theoretical physics or applied mathematics is expected.
Application process
To be considered for the position, candidates must apply via King’s Apply online application system. Details are available at https://www.kcl.ac.uk/mathematics/postgraduate/research-degrees.
Please apply for “Applied Mathematics Research: Disordered Systems/Financial Mathematics/Probability MPhil/PhD“, indicate Benjamin Doyon as the supervisor and quote the project title in your application and all correspondence.
Please ensure to add the following code “UKRIECRUniHypDoyon1” in the Funding section of the application form. Please select option 5: ‘I am applying for a funding award or scholarship administered by King’s College London’ and type the code into the ‘Award Scheme Code or Name’ box. Please copy and paste the code exactly.
The selection process will involve a pre-selection on documents and, if selected, will be followed by an invitation to an interview. If successful at the interview, an offer will be provided in due course.
Contact Details:
For further information please contact, or if you require support with the application process please contact mathematics-pgr@kcl.ac.uk.
For more details on the project feel free to contact Professor Benjamin Doyon benjamin.doyon@kcl.ac.uk.