# 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

## Scope

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)

## Program

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 |

Lunch | ||

14:30-16:00 | Akimoto, Takuma | Distributional reproducibility in anomalous diffusion processes from continuous-time random walk to laser cooling |

discussion | ||

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 |

Lunch | ||

14:30-16:00 | Hanada, Yasutaka | Quantum tunneling in the classically chaotic system |

discussion | ||

18:00 | inofficial dinner and more discussions |

## Titles and Abstracts

-- Tuesday, February 21st, 2017 --

**Speaker**: Altmann, Eduardo

**Title**: Chaotic Systems with Holes and Leaks

**Abstract**:

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.

**References**:

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).

**Speaker**: Sunada, Satoshi

**Title**: Chaotic billard lasers

**Abstract**:

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.

**References**:

T. Harayama and S. Shinohara, Laser Photonics Rev. Vol. 5 247 (2011).
S. Sunada et al., Phys. Rev. Lett.116, 203903 (2016).

**Speaker**: Akimoto, Takuma

**Title**: Distributional reproducibility in anomalous
diffusion processes from continuous-time random walk to laser cooling

**Abstract**:

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.

**Speaker**: Lippolis, Domenico

**Title**: Counting statistics of chaotic resonances at
optical frequencies: theory and experiments

**Abstract**:

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.

**Speaker**: Teramoto, Hiroshi

**Title**: Dynamical Reaction Theory Beyond Perturbation

**Abstract**:

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.

**Speaker**: Hanada, Yasutaka

**Title**: Quantum tunneling in the classically chaotic
systems

**Abstract**:

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.

## Access

**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!!

References:

Minami-Osawa Campus: ja,
en

Access to the University:
ja
en