Warwick Dumas

Dr Warwick Dumas was a PhD student in the Applied Mathematics department at the University of Leicester from 2005 to 2010, and also taught the MA1061 Probability course in 2009.

W M Dumas

 

 

My PhD supervisor was Professor Michael Tretyakov.  

My thesis essentially contains results relating to improvements in functional integration using Monte Carlo methods. You can download my thesis here:

 On Conditional Wiener Integrals and the Fermion Sign Problem

Some completed work, that forms part of my thesis, relates to the numerical error encountered when evaluating Conditional Wiener integrals. The following paper has been accepted for publication in the IMA Journal of Numerical Analysis.

Computing Conditional Wiener Integrals of Functionals of a General Form

A program is available for download which gives (unannotated) illustrations of some of the objects in this paper. Graphical program

More recently, my research focused on the fermion sign problem. In order to find the expectation of an observable for a system of fermions at finite temperature via Path Integral Monte Carlo, it is necessary to evaluate a signed functional integral. In conditions where the propensity for quantum exchange is high, there is near-cancellation between the positive and negative contributions to the integral, and this gives rise to an exponential increase in monte carlo variance. 

My method for dealing with the sign problem is based on a resampling over paths which samples together those paths with countersigned, strongly covariant contributions. This method includes the well-known exact solution in 1D as a special case. In an experiment performed with 2 2D fermions, the cost saving compared with linear translation is substantial and grows exponentially. In the thesis some discussion is made of how to extend the method to n 3D fermions.

Another result from my thesis explains how to find excited states for a quantum system, consisting of either all bosons or all fermions, by taking a particular arrangement of interacting system copies.

If you are a researcher (or PhD student) working on related problems and would like to discuss something with me, please feel free to contact me.

I also provide consultancy on statistical analysis and mathematical modelling.

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Department of Mathematics
University of Leicester
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Leicester LE1 7RH
United Kingdom

Tel.: +44 (0)116 229 7407

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