Stochastic processes are widely used to model systems in which one or more variables fluctuate randomly. Problems arise when large sets of random variables are allowed to interact with each other, as is often the case with physical and biological systems. Stochastic operators provide a convenient framework for describing the interactions and evolution of the random variables. In this talk, I will discuss techniques and methods typically used in spin systems to deal with stochastic operators and their spectral analysis in the context of random processes. I will briefly review their properties and applications to biological systems. As practical examples, I will present some results of my research in infectious diseases and migration of glioma cells.

This workshop aims to present recent investigations related to mathematical modeling of COVID-19 spread and impacts, and to foster the use of data assimilation techniques in future studies. It also aims to facilitate interactions and discussions among researchers from different fields such as epidemiology, economics, and mathematics. This workshop is jointly hosted by RIKEN Data Assimilation Research Team and by Nagoya University Graduate School of Mathematics, and supported by FY2021 RIKEN President's Discretionary Funds for COVID-19. A hybrid meeting is planned, but depending on the situation, an online version will be organized. Young researchers and students are encouraged to attend.

Program:
13:00 - 13:10 Opening
13:10 - 14:00 Hiroshi Nishiura (Kyoto University)
(35 min + 15 min Q&A) TBD

14:00 - 14:50 Catherine Beauchemin (RIKEN iTHEMS)
(35 min + 15 min Q&A) The straight line: simple and effective

14:50 - 15:10 Break

15:10 - 16:00 Taisuke Nakata (The University of Tokyo)
(35 min + 15 min Q&A) Balancing NPIs and Economic Activities

16:00 - 16:50 Qiwen Sun (RIKEN Data Assimilation Research Team, Nagoya University)
(35 min + 15 min Q&A) Analysis of COVID-19 in Japan with Extended SEIR model and ensemble Kalman filter

16:50 - 17:30 Discussion

15:00- Talk by Prof. Tetsuya Nagata
16:05- 2021 MACS Result Briefing
16:30- Discussion

False vacuum decay is a non-perturbative phenomenon in quantum field theory and important quantum process in cosmology. It has relied on the Euclidean formalism developed by Coleman, but there are several subtle issues in cosmological application as a negative mode problem or ambiguity in the definition of the decay rate in the presence of the gravity. Instead of the Euclidean path integral, we directly evaluate the Lorentzian path integral to discuss false vacuum decay and estimate the decay probability. To make the Lorentzian path integral convergent, the deformation of an integral contour is performed on the basis of the Picard-Lefschetz theory. We show that the nucleation probability of a critical bubble, for which the corresponding bounce action is extremized, has the same exponent as the Euclidean approach. We also extend our computation to the nucleation of a bubble larger or smaller than the critical one to which the Euclidean formalism is not applicable.

In condensed matter physics, transport measurement has played crucial roles in understanding fascinating phenomena such as superconductivity and quantum Hall and Kondo effects. In this talk, we discuss the usefulness of spin transport as a probe for many-body properties in ultracold atoms. In the first part, we focus on the conductivity of alternating spin current, which includes information on superfluid gap, pseudogap, and topological phase transition. In the latter part, we consider mesoscopic spin transport between two Fermi gases weakly connected with each other. Our analysis suggests that the spin current is sensitive to whether the gases have pseudogaps, which are gap-like structures in densities of states just above the superfluid transition temperature. In this talk, we also mention similarities of ultracold atoms to neutron star matter.

We calculate the renormalization group flows of all renormalizable interactions in the three dimensional Ginzburg--Landau potential for the chiral phase transition of three flavor quantum chromodynamics [1]. On the contrary to the common belief we find a fixed point in the system that is able to describe a second order phase transition in the infrared. This shows that longstanding assumptions on the transition order might be false. If the transition is indeed of second order, our results can also be interpreted as indirect evidence that the axial anomaly restores at the transition temperature.

In the February RIKEN Day, we will have a talk with Naritaka Oshita, a researcher who is researching on the theme of "Listening to the Ringing of a Black Hole."

See related links for details.