The first early career meeting of the South East Mathematical Physics Seminar will be held on Monday 28th July 2014 at the University of Kent. The meeting is partially supported by a London Mathematical Society Joint Research Groups grant.
Non-equilibrium steady states in many-body quantum systems are states which do not change in time, yet are out of equilibrium. Some of the most interesting ones are those where there are constant flows of energy, particles or charge between reservoirs. The full theory is still not understood, so it is crucial to obtain exact results. I will provide an introductory talk overviewing various aspects of this subject, concentrating on exact results in free-field models and in conformal field theory.
In this talk we derive Darboux transformations which are invariant under the action of finite reduction groups. We present Darboux transformations for the NLS equation, the derivative NLS equation and a deformation of the derivative NLS equation. We use the associated Darboux matrices to define discrete Lax pairs and derive discrete integrable systems. Moreover, we use these Darboux matrices to construct 6-dimensional Yang-Baxter maps which can be restricted to completely integrable 4-dimensional YB maps on invariant leaves.
One dimensional Heisenberg spin chains can be used to model certain quasi one dimensional materials. Using the vertex operator approach due to Jimbo and Miwa, it is possible to compute exact results for correlation functions of the spin 1/2 XXZ chain and so calculate the dynamic structure factors of these materials objects measurable in inelastic neutron scattering experiments. I hope to give an overview of the techniques involved and briefly talk about our application of this approach in the spin 1 case, the goal of which being to compute exact form factors.
In a two dimensional, inviscid and steady fluid flow, a hollow vortex is a bounded region of constant pressure with non-zero circulation. It is known that for a single row of hollow vortices, analytical solutions for the flow field and the shape of the hollow vortex boundary can be obtained using conformal mapping methods. In this talk we show how to obtain analytical solutions for the single row of hollow vortices when the flow is weakly compressible. We will also touch upon how to extend these results to a von-Karman street of hollow vortices. (joint work with Darren Crowdy)
Non-abelian monopoles in Euclidean space have been intensively studied since their discovery in the 70's, but explicit solutions are rare. This situation can be improved by moving to a hyperbolic space background, where one can exploit a connection to Euclidean instantons. I will discuss some new techniques based on this approach. The solutions include some examples with Platonic symmetry, as well as one-parameter families analogous to geodesics describing Euclidean monopole scattering.
The Skyrme-Faddeev model is a novel theory which gives string-like solutions that take the form of links and knots. Solutions for a large number of charges are known, however these all take the form of torus knots or links of torus knots. In this talk I shall discuss the search for solutions which take the form of non-torus knots.
We have recently proposed a novel approach to the classification of integrable differential/difference equations in 3D based on the method of deformations of hydrodynamic reductions. This approach is now extended to the fully discrete case: we classify discrete 3D integrable Hirota-type equations within various subclasses. The method can be viewed as an alternative to the conventional multi-dimensional consistency approach. Also, performing elementary numerical simulations, we illustrate the formation of a dispersive shock wave for a particular 3D discrete equation.
Local travel information including maps may be found here.
Train information may be obtained from here. The quickest train from London to Canterbury takes 58 minutes from St Pancras.
Students interested in attending, giving a talk or presenting a poster, please contact Giota Adamopoulou at pma7@kent.ac.uk.
Limited funds are available to help with travel expenses of speakers and other participants with no other source of funding.
Participants planning to stay overnight in Canterbury, please contact Giota to arrange for accommodation (at own expenses).
Lunch and refreshments will be provided.
Giota Adamopoulou (Kent)
Jenny Ashcroft (Kent)
Grego Benincasa (UCL)
Alexander Cockburn (Durham)
Ellen Dowie (Kent)
Benjamin Doyon (King's College London)
Matthew Elliot-Ripley (Durham)
Christoph Fischbacher (Kent)
David Foster (Kent)
Stephen Goatham (Kent)
Mareike Haberichter (Kent)
Christopher Halcrow (Cambridge)
Paul Jennings (Durham)
Sotiris Konstantinou-Rizos (Leeds)
Vikas Krishnamurthy (Imperial College London)
Abera Muhamed (Kent)
George Papamikos (Kent)
Ilia Roustemoglou (Loughborough)
James Smith (Kent)
Chloe Ward (Kent)
Jennifer Willets (Heriot-Watt)
Thomas Winyard (Durham)
In order to claim travel expenses (second class rail, bus, (shared) taxi for local travel) please complete the relevant sections on the claim form that was provided. For quicker payment please put your bank account details on the back of the form. For "Reason for visit" please write "SEMPS, Kent". Return the completed form along with receipts/tickets to Clare Dunning School of Mathematics, Statistics and Actuarial Science Cornwallis Building University of Kent Canterbury CT2 7NF.
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