Mathematical physics group

Department of Fundamental & Theoretical Physics

Variational approach to many-body problems

In recent years there was a large boost in development of advanced variational methods which play an important role in analytic and numerical studies of  1D and 2D quantum spin systems. Such methods are based on the ideas coming from the renormalization group theory which states that  physical properties of  spin systems become scale invariant near criticality. One of the most powerful variational algorithms is the corner-transfer matrices (CTM) method which allows to predict properties of large systems based on a simple iterative algorithm.

Dr Vladimir Mangazeev

Stochastic dynamics of interacting systems and integrability

There are many interesting physical statistical systems which never reach thermal equilibrium. Examples include surface growth, diffusion processes or traffic flow. In the absence of general theory of such systems a study of particular models plays a very important role. Integrable systems provide examples of such systems where one can analyze time dynamics using analytic methods.

Dr Vladimir Mangazeev

Combinatorics and integrable systems

We will study links between integrable systems in statistical mechanics, combinatorial problems and special functions in mathematics. This area of research has attracted many scientist's attention during the last decade and revealed unexpected links to other areas of mathematics like enumeration problems and differential equations.

Dr Vladimir Mangazeev, Professor Vladimir Bazhanov

Introduction to quantum integrable systems

The aim of this project is to introduce quantum integrable systems which play a very important role in modern theoretical physics. Such systems provide one of very few ways to analyze nonlinear effects in continuous and discrete quantum systems.

Dr Vladimir Mangazeev

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