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Non-Markovian statistical mechanics: theory and applications


School of Mathematical Sciences

Wednesday, January 27, 2021 Competition Funded PhD Project (Students Worldwide)

About the Project

The School of Mathematical Sciences of Queen Mary University of London invite applications for a PhD project commencing in September 2021.

This project will be supervised by Dr. Rosemary Harris.

The power of statistical mechanics arises from its ability to predict large-scale and long-time properties of a system from knowledge of the small-scale rules governing individual components. Underlying this is a mathematical description built up using the tools of large deviation theory which quantifies the probability of fluctuations away from the typical values. Within this context the framework of Markovian (memoryless) statistical mechanics has been much-studied over many years. More recently, however, there has been a surge of interest in understanding systems with memory. In particular, statistical physicists have recently studied a variety of memory-dependent random walkers in classical and quantum contexts but much less is known about non-Markovian many-particle systems.

Memory also plays an important role in many “real-life” scenarios, ranging from biology to socio-economics. For example, the persistent or “run-and-tumble” motion of bacteria can be modelled as a type of non-Markovian process. At the other end of the scale, it is obvious that human memory of past experiences affects future decisions; psychological research supports the intuition that extreme events, on one hand, and recent events, on the other, are dominant in our memories (leading to the so-called “peak-end rule”). There is much scope for quantifying the effect of this, and other kinds of memory, on future dynamics.

This PhD project will be concerned with theoretical work on the framework of non-Markovian statistical mechanics (probably with a particular focus on many-particle systems) as well as developing applications in modelling collective behaviour in real systems with memory. The exact balance of topics will depend on the interests and background of the student.

The application procedure is described on the School website. For further inquiries please contact Dr Rosemary Harris at . This project is eligible for full funding, including support for 3.5 years’ study, additional funds for conference and research visits and funding for relevant IT needs. Applicants interested in the full funding will have to participate in a highly competitive selection process.

Funding Notes

For September 2021 entry: Funding may be available through QMUL Principal's Postgraduate Research Studentships, School of Mathematical Sciences Studentships, and EPSRC DTP, in competition with all other PhD applications.

Studentships will cover tuition fees, and a stipend at standard rates for 3-3.5 years.

We welcome applications for self-funded applicants year-round, for a January, April or September start.

The School of Mathematical Sciences is committed to the equality of opportunities and to advancing women’s careers. As holders of a Bronze Athena SWAN award we offer family friendly benefits and support part-time study.

References

• Large deviation approach to nonequilibrium systems, H. Touchette and R. J. Harris, arXiv:1110.5216, chapter for book on "Nonequilibrium Statistical Physics of Small Systems" eds. R. Klages, W. Just and C. Jarzynski (2013).

• Current fluctuations in stochastic systems with long-range memory, R. J. Harris and H. Touchette, J. Phys. A: Math. Theor. 42, 342001 (2009).

• Random walkers with extreme value memory: modelling the peak-end rule, R. J. Harris, New J. Phys. 17 053049 (2015).

• Thermodynamic uncertainty for run-and-tumble type processes, M. Shreshtha and R. J. Harris, EPL (Europhysics Letters) 126, 40007 (2019).

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