Random matrix theory is the theory of matrices with random number elements. It was invented by mathematical statisticians at the beginning of the 20th century and after World War II introduced to nuclear physics. Now it is transversally applied to many areas, including analytic theory of numbers, combinatorics, elementary particle physics, solid state physics, ecology and financial engineering. Its deep structure and meanings are currently being revealed one after another.
I study random matrices from the viewpoints of both the fundamental theory and various applications. Related research topics are the followings.
It is known that the spectral statistics of quantum systems reflect the features of the underlying classical dynamics. In particular, when the corresponding classical system is chaotic, universal spectral correlations predicted by random matrix theory are observed. In attempt to elucidate the origin of the universality, the following topics are studied.
Antidot superlattices are regular or irregular potential arrays fabricated on semiconductor substrates. The lattice spacing can be made less than 1 micrometer so that the resultant electronic system is in the boundary region between quantum and classical theories. Related research topics are the followings.
Java applet for a single cell antidot system (You can apply a "magnetic field"!)