Using methods of quantum many-body theory to describe elementary processes in atoms and molecules interacting with strong electromagnetic fields.

The project studies possibility of the coherent control (i.e. manipulating properties of a quantum system, such as charge density, levels populations, etc., using a suitably tailored laser pulse) for a quantum mechanical model of a molecule.

We apply the most advanced quantum-mechanical modeling to resolve electron motion in atoms and molecules on the atto-second (one quintillionth of a second) time scale.  Our theoretical modeling, based on a rigorous, quantitative description of correlated electron dynamics, provides insight into new physics taking place on the atomic time scale.

Dissipative solitons are generated due to the balance between gain and loss of energy as well as to the balance between input and output of matter. Their existence requires continuous supply of energy and matter that is available in open systems. The model explains variety of phanomena in biology and physics.

The concept of rogue waves was born in nautical mythology, entered the science of ocean waves and gradually moved into other fields: optics, matter waves, superfluidity. This project will allow students to enter the front edge of modern science.

A reading course on the connections between the representation theory of Lie groups and the properties of fundamental particles within quantum field theory, using Howard Georgi's "Lie Groups in Particle Physics: from Isospin to Unified Theories".

The standard correspondence principle implies that quantum theory reduces to classical theory in the limit of the vanishing Planck constant. This project is devoted to a new type connection between quantum and classical systems which holds for arbitrary finite values of the Planch constant.

Conformal Field Theory (CFT) in two-dimensions describes physics of the second order transitions in statistical mechanics and also plays important role in string theory, which is expected to unify the theory of strong interaction with quantum gravity. The project aims to explore and further develop mathematical techniques of CFT.  

A reading course on the connections between the representation theory of Lie groups and the properties of fundamental particles within quantum field theory, using Howard Georgi's "Lie Groups in Particle Physics: from Isospin to Unified Theories".

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.

Using methods of quantum many-body theory to describe elementary processes in atoms and molecules interacting with strong electromagnetic fields.

It is well known that the quasiclassical quantisation of the harmonic oscillator leads to its exact quantum mechanical spectrum. Remarkably, this result can be generalized to various anharmonic systems via mysterious connections to Conformal Field Theory.

Dissipative solitons are generated due to the balance between gain and loss of energy as well as to the balance between input and output of matter. Their existence requires continuous supply of energy and matter that is available in open systems. The model explains variety of phanomena in biology and physics.

A separation of variables is a standard technique in classical mechanics which allows to reduce a complicated dynamics with many degrees of freedom to a set of one-dimensional problems. Surprisingly this method finds its natural generalization in the theory of quantum integrable systems. This project aims to study such systems and apply results to the theory of special functions in one and several variables.

The project studies possibility of the coherent control (i.e. manipulating properties of a quantum system, such as charge density, levels populations, etc., using a suitably tailored laser pulse) for a quantum mechanical model of a molecule.

The concept of rogue waves was born in nautical mythology, entered the science of ocean waves and gradually moved into other fields: optics, matter waves, superfluidity. This project will allow students to enter the front edge of modern science.

This project aims to develop and employ the full power of the theory of integrable quantum systems to new models of quantum many-body spin systems in string theory.

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.

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.

We apply the most advanced quantum-mechanical modeling to resolve electron motion in atoms and molecules on the atto-second (one quintillionth of a second) time scale.  Our theoretical modeling, based on a rigorous, quantitative description of correlated electron dynamics, provides insight into new physics taking place on the atomic time scale.

It appears that the scattering amplitudes in Quantum Chromodynamics (theory of strong interactions) can be exactly calculated in certain limiting cases (e.g. in the so-called multi-Redge kinematics). This is possible due to remarkable connections of this problem to the theory of integrable systems based on the Yang-Baxter equation. 

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.