Tokyo Metropolitan University

Nonlinear Physics Group

Workshop on Chaos and Diffusion in Leaky Systems

Welcome to our workshop on "Chaos and Diffusion in Leaky Systems". Thank you everyone for your participation!!

Date: February 21st and February 22nd, 2017
Place: Tokyo Metropolitan University, building number 12, room number 201


Dynamical systems with leakage naturally appear in physics. Examples comprise ionization of atoms, light emission from microlasers, or leakage of sound from a concert hall. In particular, when the internal dynamics of these system is chaotic or diffusive, recent years have witnessed a significant progress in theory and experiment. In our workshop we represent a glimpse of these developments, by inviting young researchers who significantly contributed to the understanding of chaotic and diffusive dynamics in leaky systems.

Topics include:
- chaotic systems with leaks
- optical microlasers
- dynamical reaction theory
- anomalous diffusion
- escape rates in the Henon map
- dynamical tunneling

We particularly welcome young students and generally curious non-experts from neighboring fields. For this reason all speakers have been asked to include a long introduction and give pedagogical lectures.

Invited speakers

Altmann, Eduardo (University of Sydney)
Sunada, Satoshi (Kanazawa University)
Akimoto, Takuma (Keio University)
Lippolis, Domenico (Jiangsu University)
Teramoto, Hiroshi (Center for Exploratory Research, Research & Development Group, Hitachi, Ltd.)
Hanada, Yasutaka (Tokyo Metropolitan University)


Feb 21 (Tue) Speaker title
09:30-11:00 Altmann, Eduardo Chaotic Systems with Holes and Leaks
11:30-13:00 Sunada, Satoshi Chaotic billiard lasers
14:30-16:00 Akimoto, Takuma Distributional reproducibility in anomalous diffusion processes from continuous-time random walk to laser cooling
18:00 banquet
Feb 22 (Wed) Speaker title
09:30-11:00 Lippolis, Domenico Counting statistics of chaotic resonances at optical frequencies: theory and experiments
11:30-13:00 Teramoto, Hiroshi Dynamical Reaction Theory Beyond Perturbation
14:30-16:00 Hanada, Yasutaka Quantum tunneling in the classically chaotic system
18:00 inofficial dinner and more discussions

Titles and Abstracts

-- Tuesday, February 21st, 2017 --

Speaker: Altmann, Eduardo
Title: Chaotic Systems with Holes and Leaks
Examples of physical situations in which a hole or leak is introduced in an otherwise closed dynamical system appear in room accoustics, fluid dynamics, optical microcavities, and planetary astronomy. After a revision of basic concepts of transient chaos theory, usually applied to natural open systems, I will discuss interesting issues that arise when this theory is applied to closed systems with holes. In particular, I will show how an extension of the usual transient chaos theory of open system is needed in order to consider billiards in which trajectories are partially absorbed and partially reflected at the collisions in the boundary. In particular, generalized escape-rate and fractal-dimension formulas will be derived from a new transfer operator, introduced to describe true-time maps with partial absorption.
E. G. Altmann, J. S. E. Portela, and Tamas Tel "Leaking Chaotic Systems", Rev. Mod. Phys. 85, 869-918 (2013); "Chaotic explosions", Europhys. Lett. 109, 30003 (2015).

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Speaker: Sunada, Satoshi
Title: Chaotic billard lasers
Dynamical billiards have been used as simple and standard models for classical and quantum chaos studies, and they have been nowadays realized as actual optical devices, i.e., optical resonant cavities, by advanced processing technologies. The internal ray is repeatedly reflected by the boundary and result in a variety of motion, depending on its shape. Among various optical cavities, optical chaotic billiards, i.e., chaotic cavities, in which ray motions are chaotic, have attracted much interest over the past decades because they can offer an ideal experimental stage for studying wave/quantum chaos in open systems. Moreover, studies on chaotic cavities have motivated the development of novel laser devices using chaotic cavities, which can exhibit a variety of nonlinear dynamics by interplay between chaotic cavities and active materials. Here, I will introduce several theoretical and experimental results on chaotic cavities and its applications to microlasers. Then, I will discuss a manifestation of ray chaos in microlasers and the possibility of its applications.
T. Harayama and S. Shinohara, Laser Photonics Rev. Vol. 5 247 (2011). S. Sunada et al., Phys. Rev. Lett.116, 203903 (2016).

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Speaker: Akimoto, Takuma
Title: Distributional reproducibility in anomalous diffusion processes from continuous-time random walk to laser cooling
Reproducibility is a key property in experiments. If a result obtained from an experiment is not reproducible, the result is not reliable. However, such a reproducibility may be broken in anomalous diffusion process, which is a ubiquitous phenomenon in nature. In continuous-time random walk (CTRW), which is a stochastic model of anomalous diffusion, it has been shown that time-averaged mean square displacement (MSD) crucially depends on realizations. In other words, the diffusion coefficients are intrinsically random. In this talk, I will review irreproducible properties in anomalous diffusion processes. Here, I will provide a brief lecture on a key theory (renewal theory). This theory can be applied to the CTRW as well as quenched trap model. Thus, I will show distributional limit theorem for time-averaged MSDs. If I have a time, I will provide a distributional behavior for a time-averaged observable in a stochastic model of laser cooling.

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-- Wednesday, February 22nd, 2017 --

Speaker: Lippolis, Domenico
Title: Counting statistics of chaotic resonances at optical frequencies: theory and experiments
A deformed dielectric microcavity is used as an experimental platform for the analysis of the statistics of chaotic resonances, in the perspective of testing fractal Weyl laws at optical frequencies. In order to surmount the difficulties that arise from reading strongly overlapping spectra, we exploit the mixed nature of the phase space at hand, and only count the high-Q whispering-gallery modes directly. That enables us to draw statistical information on the more lossy chaotic resonances, coupled to the high-Q regular modes via dynamical tunneling.

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Speaker: Teramoto, Hiroshi
Title: Dynamical Reaction Theory Beyond Perturbation
It was 1914 that chemical reaction dynamics met dynamical systems theory when Marcelin represented chemical reaction by a motion of a point, i.e., a trajectory, in phase space. Since then, one of the main purposes of studies on chemical reaction dynamics are to understand mechanisms of how a system evolves from a reactant to a product. In this talk, we give an introduction to chemical reaction dynamics in terms of dynamical system theory along with our recent trial to verify them experimentally.

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Speaker: Hanada, Yasutaka
Title: Quantum tunneling in the classically chaotic systems
Quantum phenomena can be understood by the associated classical dynamics through the semiclassical theory. Tunneling, which is to penetrate into the classically forbidden region, could be also expressed by the classical dynamics in the complex domain. Theory for tunneling has been constructed by the knowledge of integrable systems such as the one degree of freedom. On the other hand, the chaotic orbits appear in Hamiltonian systems with 1.5 or 2 degrees of freedom. It is still an issue of debate whether the nonintegrability is necessary to understand the tunneling phenomena in higher dimensional systems or not. We will talk about the recent analysis of the tunneling in the classically chaotic systems and the surrounding background.

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place: Tokyo Metropolitan University, building number 12, room number 201 (changed a room from 202)

Enter from the main gate and follow the corridor to the 8th building (left-hand side) or 11th building (right-hand side).
(see the photo guides ja, en)
The 12th building is over the 11th building (right-hand side).
Please note that it takes 15 minutes from Minami-Osawa station to the place!!

Minami-Osawa Campus: ja, en
Access to the University: ja en


Normann Mertig, Yasutaka Hanada, and Akira Shudo