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Soliton gas in Bose-Einstein condensate: when waves act like particles (RDF23/MPEE/CONGY)

   Faculty of Engineering and Environment

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  Dr Thibault Congy, Prof Gennady El  No more applications being accepted  Competition Funded PhD Project (Students Worldwide)

About the Project

Bose-Einstein condensate (BEC) is a state of matter forming when a gas of bosons is cooled to ultra-cold temperatures. At such temperature, a large fraction of bosons occupies a unique low energy-state and microscopic quantum phenomena, such as wave interference, manifest macroscopically. The dynamics of BECs is well modelled by the Schrödinger equation with a nonlinear potential, characterising the interaction between bosons, called the nonlinear Schrodinger equation (NLSE). Remarkably NLSE is a universal equation describing various other physical phenomena ranging from light in fibre optics to oceanic waves.

Solitons are elementary, pulse-shaped wave solutions of NLSE. They play an important role in many physical systems due to a fundamental feature: the wave’s envelope remains unchanged after the collision with another soliton. Such particle-like behaviour has been at the origin of a new mathematical object: the soliton gas, consisting of a collection of solitons for which positions, velocities and amplitudes are randomly distributed [1]. Soliton gases have successfully modelled random nonlinear phenomena such as extreme waves in the ocean and in nonlinear optics. The objective of this project will be to investigate soliton gas in the context of BEC, leveraging recent progress obtained for NLSE [2,3].

Current analytical descriptions of soliton gas do not consider the presence of an external potential, a key component in BECs. Manipulating soliton with an external force will also lead to a better control of the gas thermodynamics. The first steps of the project will be to (i) numerically study NLSE soliton gas in presence of hard-wall boundary conditions or more generally confining potentials, (ii) adapt the gas kinetic theory developed in [2,3]. NLSE is a so-called integrable equation, and you will learn the theory of inverse scattering transform (IST) which can be seen as a nonlinear version of the Fourier transform. It will also be the opportunity to learn established advanced numerical methods for nonlinear partial differential equations (e.g. spectral method), as well as brand-new IST based numerical techniques (e.g. N-soliton solution) using scientific programming languages (e.g. C++, Matlab or Python). At a later stage of the project, these results will be generalised to multi-component BECs for which two or more quantum states are macroscopically populated. These BECs still have soliton solutions in physical regimes, and one model of interest will be the Landau-Lifshitz equation [4].

Applicants with a strong background in mathematics or theoretical physics are strongly encouraged. Numerical skills and a liking for programming will also be beneficial to the project. Besides, throughout the project, the applicant will interact with an international and multidisciplinary team. They will also attend international conferences, give seminars, and publish results in international peer-reviewed journals to communicate on the progress.

Academic Enquiries

This project is supervised by Dr Thibault Congy. For informal queries, please contact [Email Address Removed]. For all other enquiries relating to eligibility or application process please use the email form below to contact Admissions. 

Funding Information

Home and International students (inc. EU) are welcome to apply. The studentship is available to Home and International (including EU) students and includes a full stipend at UKRI rates (for 2022/23 full-time study this is £17,668 per year) and full tuition fees. Studentships are also available for applicants who wish to study on a part-time basis over 5 years (0.6 FTE, stipend £10,600 per year and full tuition fees) in combination with work or personal responsibilities).  

Please also see further advice below of additional costs that may apply to international applicants.

Eligibility Requirements:

  • Academic excellence of the proposed student i.e. 2:1 (or equivalent GPA from non-UK universities [preference for 1st class honours]); or a Masters (preference for Merit or above); or APEL evidence of substantial practitioner achievement.
  • Appropriate IELTS score, if required.
  • Applicants cannot apply for this funding if they are already a PhD holder or if currently engaged in Doctoral study at Northumbria or elsewhere.

 Please note: to be classed as a Home student, candidates must meet the following criteria:

  • Be a UK National (meeting residency requirements), or
  • have settled status, or
  • have pre-settled status (meeting residency requirements), or
  • have indefinite leave to remain or enter.

If a candidate does not meet the criteria above, they would be classed as an International student.  Applicants will need to be in the UK and fully enrolled before stipend payments can commence, and be aware of the following additional costs that may be incurred, as these are not covered by the studentship.

  • Immigration Health Surcharge https://www.gov.uk/healthcare-immigration-application
  • If you need to apply for a Student Visa to enter the UK, please refer to the information on https://www.gov.uk/student-visa. It is important that you read this information very carefully as it is your responsibility to ensure that you hold the correct funds required for your visa application otherwise your visa may be refused.
  • Check what COVID-19 tests you need to take and the quarantine rules for travel to England https://www.gov.uk/guidance/travel-to-england-from-another-country-during-coronavirus-covid-19
  • Costs associated with English Language requirements which may be required for students not having completed a first degree in English, will not be borne by the university. Please see individual adverts for further details of the English Language requirements for the university you are applying to.

How to Apply

For further details of how to apply, entry requirements and the application form, see


For applications to be considered for interview, please include a research proposal of approximately 1,000 words and the advert reference (e.g. RDF23/…).

Deadline for applications: 27 January 2023

Start date of course: 1 October 2023 tbc

Northumbria University is committed to creating an inclusive culture where we take pride in, and value, the diversity of our doctoral students. We encourage and welcome applications from all members of the community. The University holds a bronze Athena Swan award in recognition of our commitment to advancing gender equality, we are a Disability Confident Employer, a member of the Race Equality Charter and are participating in the Stonewall Diversity Champion Programme. We also hold the HR Excellence in Research award for implementing the concordat supporting the career Development of Researchers.


[1] G. El, J. Stat. Mech. 11, 114001 (2021).
[2] G. El and A. Tovbis, Phys. Rev. E 101, 052207 (2020).
[3] T. Congy, G. El and G. Roberti, Phys. Rev. E 103, 042201 (2021).
[4] S.K. Ivanov, A.M. Kamchatnov, T. Congy and N. Pavloff, Phys. Rev. E 96, 062202 (2017).

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