IAS Benjamin Meaker Visiting Professor Eugene Bogomolny, CNRS, Paris-SUD, France

Bogomolny

Whispering galleries for light: beyond the two-dimensional approximation

2 January - 31 March 2018

Biography

Professor Bogomolny received his PhD at the Institute of Theoretical and Experimental Physics  (ITEP) in Moscow. He then worked at the L. D. Landau Institute of Theoretical Physics, first as research fellow and later as research director. In 1992 he moved to Orsay near Paris where he received a CNRS research director position at the Université Paris-Sud in the Laboratory of Theoretical Physics and Statistical Models (LPTMS). These are prestigious positions in France that allow scientists to work purely on their research. In 2011 he was promoted to a CNRS research director of the exceptional class.

Summary

Whispering gallery waves are not restricted to sound waves and in recent times they have found prominence in micro- and nano-optics. Light can be confined in the form of whispering gallery waves to small micron-sized disks or spheres that are made of transparent dielectric (nonconductive) material. This confinement is due to an effect called total internal reflection that keeps light rays from escaping when they bounce along the boundary at shallow angles, and it has a large range of applications. Among them are the construction of miniature lasers, filters or switches in optical communication, detectors for nanoparticles and molecules and on the theoretical side, the calculation of whispering gallery waves in thin dielectric disks relies on treating a disk as a two-dimensional object and taking account of its thickness only in a material constant. Although commonly used, this approximation cannot be justified rigorously and no error estimates can be given, and its validity was questioned by some recent experimental results. We intend to go beyond the two-dimensional approximation and investigate its validity for some simple geometries where rigorous methods, called Wiener-Hopf methods, can be applied.

During his stay in Bristol Professor Bogomolny will be hosted by Dr Martin Sieber (Mathematics)

Below are some of the lectures and seminars that Professor Bogomolny will be involved with (dates/times tbc):

Public lecture: Quantum chaos, ideas and methods 
Synopsis: a mini-review of ideas and methods of quantum chaos and their applications for different models ranging from nuclear physics to number theory.

Departmental lecture: Intermediate spectral statistics
Synopsis: It is well established that spectral statistics of general quantum systems depend on properties of their classical limits. Classically integrable systems exhibit Poisson statistics of quantum eigenvalues whereas classically chaotic systems display statistics of standard random matrix ensembles. Much less is known for systems whose classical analogues are neither integrable nor chaotic. This lecture will address a special subclass of dynamical systems, namely pseudo-integrable models. It appears that their spectral statistics differs from both, Poisson and random matrix statistics. This type of statistics is called intermediate statistics and it is characterized by a level repulsion as for random matrices and by an exponential decrease of the nearest-neighbour distribution as for Poisson statistics. Another unusual property of practically all models with intermediate statistics is a non-trivial fractal dimension of their wave functions. Many different models with such properties will be discussed

Graduate student seminar: Functions, hypergeometric, elliptic and Painlevé
Synopsis: the origin and main properties of various classes of functions that are rarely discussed in standard courses but which are very important in modern theoretical physics.