Bulletin of the American Physical Society
APS March Meeting 2024
Monday–Friday, March 4–8, 2024; Minneapolis & Virtual
Session M55: Statistical and Nonlinear Physics I
8:00 AM–9:36 AM,
Wednesday, March 6, 2024
Room: 204AB
Sponsoring
Unit:
GSNP
Chair: Enkeleida Lushi, New Jersey Institute of Technology
Abstract: M55.00004 : Role of Topology in Relaxation of One-Dimensional Stochastic Processes*
8:36 AM–8:48 AM
Presenter:
Taro Sawada
(Univ of Tokyo)
Authors:
Taro Sawada
(Univ of Tokyo)
Kazuki Sone
(Univ of Tokyo)
Ryusuke Hamazaki
(RIKEN iTHEMS)
Yuto Ashida
(University of Tokyo)
Takahiro Sagawa
(University of Tokyo)
In this talk, we will see the topological characterization of relaxation phenomena of one-dimensional stochastic processes with the aid of recent studies on the spectral theory of non-Hermitian topological phases accompanied by the non-Hermitian skin effect. To this end, we define a winding number of a master equation under the periodic boundary condition and theoretically show that it corresponds to a nonzero spectral gap under the open boundary condition (OBC) in the thermodynamic limit. We numerically confirm that the winding number corresponds to the system-size dependence of the divergent OBC relaxation time and the unconventional transient behavior called a cutoff phenomenon, where the relaxation does not occur until a certain time and then rapidly proceeds. These unconventional relaxation phenomena can be understood in terms of the so-called gap-discrepancy problems.
*This work is supported by MERIT-WINGS and Institute of AI and Beyond of the University of Tokyo, JSPS KAKENHI Grant No. JP21J20199, JP19K23424, JP19H05796, JST ERATO-FS Grant No. JPMJER2204, JST ERATO Grant No. JPMJER2302, and JST CREST Grant Number JPMJCR20C1.
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