Time: 5pm ~ 6:15pm (JST); 9am ~ 10:15am (CET)

The responses of materials to high intensity light, i.e., nonlinear optical responses, constitute a vast field of physics and engineering. While geometry and topology has been playing a central role in recent studies of condensed matters, geometrical aspects of nonlinear optical effects have not been fully explored so far. In this talk, I will show a few examples of nonlinear optical effects that have geometrical origins. First, I present that the second-order nonlinear optical effects including the shift-current, a candidate mechanism for recently discovered solar cell action in perovskite materials, has a close relationship to the modern theory of polarization, and is described by the Berry connection of Bloch wave function [1]. I will also discuss how electron correlations can enhance/modify shift current response in inversion broken materials. Next, I show that another second-order nonlinear effect, circular photogalvanic effect (CPGE), is governed by Berry curvature and shows quantization in Weyl semimetals [2]. I will report a recent measurement on chiral multifold fermion RhSi that observed a plateau structure in CPGE which is consistent with the expected quantization [3].

5, 11, 17, 23, 29 are prime numbers which form an arithmetic progression of length 5. A famous theorem of Ben Green and Terence Tao in 2008 says there are arbitrarily long arithmetic progressions of prime numbers. Algebraic number theorists are also interested in more general numbers like square roots of integers. Recently, Mimura, Munemasa, Seki, Yoshino and I have established a generalization of the Green-Tao theorem in such a direction.

In the first 50 minutes of my talk, I would like to explain some background and technology behind the Green-Tao theorem. In the second half after a break, I explain the concept of number fields to formulate our generalization of their result. I will also discuss how one of the new difficulties, which I call the norm vs length conflict, is handled by a technique called Geometry of Numbers.

*Please contact Keita Mikami or Hiroyasu Miyazaki's mailing address to get access to the Zoom meeting room.

We offer a beginner’s guide to the functional-analytical techniques in quantum mechanics, and cover its application to the 1D Coulomb problem. It is shown that the wave function at the diverging point of the Coulomb potential is mathematically described by three-parameter family of generalized connection conditions. A scheme is devised to physically implement the generalized conditions, which provides the way to experimentally realize non-Rydberg spectra in 1D Hydrogen atom.

Schedule:
Part 1, Self-adjoint extension of Hilbert space operator
Part 2, 1D Coulomb problem