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Quantum Variational Principle and Discrete Integrable Systems

PGR-P-189

Key facts

Type of research degree
PhD
Application deadline
Ongoing deadline
Country eligibility
International (open to all nationalities, including the UK)
Funding
Competition funded
Supervisors
Professor Frank Nijhoff
Schools
School of Mathematics
Research groups/institutes
Applied Mathematics
<h2 class="heading hide-accessible">Summary</h2>

The project deals with a novel quantum theory that is based on the mathematical structure behind so-called integrable systems, i.e., models that on the classical level are described by certain (mostly nonlinear) differential or difference equations and that exhibit the aspect of `exact solvability&#039; - the fact that they are amenable to exact (rather than approximate or numerical) methods for their solution. Such systems possess a rich mathematical structure (e.g. connections to infinite-dimensional Lie algebras and quantum groups). A key feature is the notion of `multidimensional consistency&#039;, the property that such models can be extended to compatible systems of equations in spaces of arbitrary dimension. In 2009 Lobb &amp;amp; Nijhoff proposed a novel variational (i.e., least-action) principle that describes this remarkable feature within a Lagrangian formalism.<br /> <br /> The new principle forms potentially a paradigm for a new type of fundamental physics.<br /> <br /> Recently, the ideas behind this new approach were extended to the quantum realm, and the first steps were taken to formulate a quantum version of this variational principle. The project for a PhD student is to continue this work into the quantum variational principle, elaborating various (integrable) model systems aimed at building a coherent framework together with the development of some new mathematical methodologies.<br /> <br /> The project is embedded in the activities of a wider research group in Integrable Systems within the School of Mathematics, comprising several permanent staff, postdocs and postgraduate students. The group runs its own weekly seminar, and entertains close connections with other research groups in the School, e.g. in Algebra, Geometry and Analysis, as well as with the Quantum Information group in Physics.

<h2 class="heading">How to apply</h2>

<p>Formal applications for research degree study should be made online through the&nbsp;<a href="https://www.leeds.ac.uk/info/130206/applying/91/applying_for_research_degrees">University&#39;s website</a>. Please state clearly in the research information section&nbsp;that the research degree you wish to be considered for is &lsquo;Quantum Variational Principle and Discrete Integrable Systems&rsquo; as well as&nbsp;<a href="https://physicalsciences.leeds.ac.uk/staff/68/professor-frank-nijhoff">Prof Frank Nijhoff</a>&nbsp;as your proposed supervisor.</p> <p>If English is not your first language, you must provide evidence that you meet the University&#39;s minimum English language requirements (below).</p> <p><em>We welcome applications from all suitably-qualified candidates, but UK black and minority ethnic (BME) researchers are currently under-represented in our Postgraduate Research community, and we would therefore particularly encourage applications from UK BME candidates. All scholarships will be awarded on the basis of merit.</em></p>

<h2 class="heading heading--sm">Entry requirements</h2>

Applicants to research degree programmes should normally have at least a first class or an upper second class British Bachelors Honours degree (or equivalent) in an appropriate discipline. The criteria for entry for some research degrees may be higher, for example, several faculties, also require a Masters degree. Applicants are advised to check with the relevant School prior to making an application. Applicants who are uncertain about the requirements for a particular research degree are advised to contact the School or Graduate School prior to making an application.

<h2 class="heading heading--sm">English language requirements</h2>

The minimum English language entry requirement for research postgraduate research study is an IELTS of 6.0 overall with at least 5.5 in each component (reading, writing, listening and speaking) or equivalent. The test must be dated within two years of the start date of the course in order to be valid. Some schools and faculties have a higher requirement.

<h2 class="heading">Funding on offer</h2>

<p><strong>Self-Funding Students are welcome to apply.</strong></p> <p><strong>UK&nbsp;students</strong>&nbsp;&ndash;&nbsp;The&nbsp;<a href="https://phd.leeds.ac.uk/funding/138-leeds-doctoral-scholarships-2021-january-deadline">Leeds Doctoral Scholarship (January deadline)</a>&nbsp;and the&nbsp;<a href="https://phd.leeds.ac.uk/funding/142-william-wright-smith-scholarship-2021">William Wright Smith Scholarship&nbsp;</a>are available to UK applicants. &nbsp;<a href="https://phd.leeds.ac.uk/funding/60-alumni-bursary">Alumni Bursary</a> is available to graduates of the University of Leeds.</p> <p><strong>Non-UK students</strong>&nbsp;&ndash; The&nbsp;<a href="https://phd.leeds.ac.uk/funding/48-china-scholarship-council-university-of-leeds-scholarships-2021">China Scholarship Council - University of Leeds Scholarship</a>&nbsp;is available to nationals of China. The&nbsp;<a href="https://phd.leeds.ac.uk/funding/73-leeds-marshall-scholarship">Leeds Marshall Scholarship</a>&nbsp;is available to support US citizens.&nbsp; <a href="https://phd.leeds.ac.uk/funding/60-alumni-bursary">Alumni Bursary</a> is available to graduates of the University of Leeds.</p>

<h2 class="heading">Contact details</h2>

<p>For further information please contact Doctoral College Admissions by&nbsp;email:&nbsp;<a href="mailto:EMAIL@leeds.ac.uk">m</a><a href="mailto:maps.pgr.admissions@leeds.ac.uk">aps.pgr.admissions@leeds.ac.uk</a>, or by telephone: +44 (0)113 343 5057</p>


<h3 class="heading heading--sm">Linked research areas</h3>