Many phenomena in nature, including multiple chemical and biological processes, are governed by the fundamental property of chirality. An object is called chiral when its mirror image cannot be superimposed with the original object. Many examples of chirality can be found in nature, from seashells to DNA molecules.
This project will address the recently emerged new platform for nanophotonics based on high-index dielectric nanoparticles that opened a whole new realm of all-dielectric Mie-resonant nanophotonics or Mie-tronics. High-index dielectric nanoparticles exhibit strong interaction with light due to the excitation of electric and magnetic dipolar Mie-type resonances.
Many phenomena in nature, including multiple chemical and biological processes, are governed by the fundamental property of chirality. An object is called chiral when its mirror image cannot be superimposed with the original object. Many examples of chirality can be found in nature, from seashells to DNA molecules.
This project will address the recently emerged new platform for nanophotonics based on high-index dielectric nanoparticles that opened a whole new realm of all-dielectric Mie-resonant nanophotonics or Mie-tronics. High-index dielectric nanoparticles exhibit strong interaction with light due to the excitation of electric and magnetic dipolar Mie-type resonances.
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.
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.
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.