Mikito Toda

Address

• Complex System Laboratory, Department of Physucs, Faculty of Science
• Nara Women's University
• Nara, 630-8506, Japan

Research Topics

1. Multi-Dimensional Chaos
2. Quantum Chaos and Quantum Information
3. Foundation of Statistical Physics
4. Dynamics of Chemical Reactions
5. Nonequilibrium Aspects of Life

Lectures(2009)

1. Statistical Physics I
2. Statistical Physics II
3. Pattern Formation
4. Introduction to Nonlinear Science
5. Foundation of Statistical Mechanics : Post Graduate Cource

Key Papers

• Random Matrix Theory of Singular Values of Rectangular Complex Matrices I:Exact Formula of One-Body Distribution Function in Fixed-Trace Ensemble
  Accepted and to be published in Annals of Physics,
  S.Adachi, H.Kubotani and M.Toda.
  
• Exact Formula of the Distribution of Schmidt Eigenvalues for Dynamical Formation of Entanglement in Quantum Chaos,
  Phys.Rev.Lett.,100,240501(4 pages), 2008,
  H.Kubotani, S.Adachi and M.Toda.
  
• Bifurcation of no-return transition states in many-body chemical reactions,
  J.Chem.Phys.,130,124116(7 pages), 2009
  C-B Li, M.Toda and T.Komatsuzaki.
  
• Fractional Behavior in Multi-dimensional Hamiltonian Systems Describing Reactions,
  Phys.Rev.,E76,056205(14 pages), 2007,
  A.Shojiguchi, C-B Li, T.Komatsuzaki and M.Toda.
  
• Dimension Reduction for Extracting Geometrical Structure of Multidimensional Phase Space: Application to Fast Energy Exchange in the Reaction ${\rm O(1D)}+{\rm N}_2{\rm O}\rightarrow{\rm NO}+{\rm NO}$,
  Phys.Rev.,A75,022714(11 pages), 2007,
  S.Kawai, Y.Fujimura, O.Kajimoto, T.Yamashita, C-B Li, T.Komatsuzaki and M.Toda.
  
• Universality in Dynamical Formation of Entanglement in Quantum Chaos,
  Phys.Rev.,A74,032314(5 pages), 2006,
  H.Kubotani, M.Toda and S.Adachi.
  
• Definability of No-return Transition States in High Energy Regime above Reaction Threshold,
  Phys.Rev.Lett.,97,028302(4 pages), 2006,
  C-B Li, A. Shojiguchi, M.Toda and T.Komatsuzaki.
  
• Wavelet Analysis and Arnold Web Picture for Detecting Energy Transfer in a Hamiltonian Dynamical System,
  Laser Physics, Vol.17, 1097-1106, 2006,
  A.Shojiguchi, C-B. Li T.Komastuzaki and M.Toda.
  
• Global Aspects of Chemical reactions in Multidimensional Phase Space
  Advances in Chemical Physics vol.130(2005)Part A,337-399
  M.Toda
  
• Dynamics of Chemical Reactions and Chaos
  Advances in Chemical Physics vol.123(2002)153-198
  M.Toda
  
• Crisis in Chaotic Scattering of a Highly Excited van der Waals Complex
  Physical Review Letters Vol.74(1995)2670-2673
  M.Toda
  
• Phase Retrieval Problem in Quantum Chaos and Its Relation to the Origin of Irreversibility I
  Physica D59(1992)121-141
  M.Toda
  
• Dynamical Aspects of Quantum-Classical Correspondence in Quantum Chaos
  Progress of Theoretical Physics Supplement vol.98(1989)323-375
  M.Toda,S.Adachi and K.Ikeda
  
  

Books

• Geometric Structures of Phase Space in Multi-Dimensional Chaos:
  Applications to Chemical Reactions in Complex Systems
  Advances in Chemical Physics vol.130(2005)Part A&B
  Edited by M.Toda, T.Komatsuzaki, T.Konishi, R.S.Berry and S.A.Rice
  
  These volumes are the proceeding of the YITP international symposium
  explained as follows.
  

Other Recent Papers

• Dynamical Foundation and Limitaions of Statsistical Reaction Thoery,
  Communications in Nonlinear Science and Numerical Simulation,Vol.13,857-867, 2008,
  A.Shojiguchi, C-B Li, T.Komatsuzaki and M.Toda.
  
• Fractional Behavior in Nonergodic Reaction Processes of Isomerization,
  Phys.Rev.,E75,035204(R), 4 pages, 2007,
  A.Shojiguchi, C-B Li, T.Komatsuzaki and M.Toda.
  
• Dynamical Hierarchy in Transition States of Reactions,
  Few Body Systems, Vol 38,173-179, 2006,
  C-B. Li. A.Shojiguchi, M.Toda and T.Komatsuzaki.
  
• Phase Space Reaction Network on a Multisaddle Energy Landscape:HCN Isomerization
  Journal of Chemical Physics 123(2005)184301
  Chun-Biu Li, Y.Matsunaga, M.Toda, T.Komatsuzaki
  

5th Dynamics Days Asia Pacific (DDAP5 )
From 5th to 12th Sept. 2008 at Nara Prefectual New Public Hall:
Homepage of DDAP5

YITP INTERNATIONAL SYMPOSIUM ON
Geometrical Structures of Phase Space in Multi-Dimensional Chaos:
Applications to Chemical Reaction Dynamics in Complex Systems

• Date
  26th Oct. 2003 1st Nov. 2003
• place
  Kyoto University, Yukawa Institute
• Organizing Comettee
  Mikito Toda(Nara Women's Univ.),Tamiki Komatsuzaki(Kobe Univ.), Tetsuro Konishi(Nagoya Univ.)
  R.S.Berry(Chicago University),S.A.Rice(Chicago University)
• Abstract
  Chemical reactions are dynamical phenomena where nonlinear oscillations are strongly coupled with each other.
  Therefore, chaos in dynamical systems plays a crucial role in studying chemical reactions. In particular, reactions
  involving macromolecules such as protein folding are important examples of dynamical systems with many degrees of freedom.
  Thus, studies of these reactions from this point of view shed a new light in understanding their efficiency and seeking
  the possibility of manipulating these reactions.
  
  In this conference, we will focus on the following subjects.
  
  (1) transition state theory revisited from dynamical point of view, a historical perspective of the study.
  
  (2) how to analyze the phase space structure of Hamiltonian systems with many degrees of freedom, in particular, normally hyperbolic
  invariant manifolds, heteroclinic intersections between their stable and unstable manifolds and Arnold Webs.
  
  (3) how to relate the phase space structure of the system to the reaction dynamics.
  
  (4) dynamics of systems with internal degrees of freedom, in particular, bottleneck of energy flow due to the mismatch of time scales.
  
  (5) how to understand many dimensional dynamics of clusters, liquid and biological molecules from viewpoint of dynamical
  system theories. e.g., how to extract information of complex dynamics from a given time series information.
  
  
• Web cite