Telluride Workshop on
The Complexity of Dynamics and Kinetics
in Many Dimensions

August 13-24 2007
Camel's Garden Resort HotelTelluride Science Research Center (TSRC)
Telluride, CO, USA

Social Events
August 13: After the today’s workshop
Bear Creek Hiking (2hours)
August 13: 18:00- Opening Reception (15US$ for each)August 14: 18:00-19:15 Pinhead Town Talk
August 16: Photo After the morning session
August 16: 18:00- Picnic at the Garden in Telluride Lodge
August 21: 18:00-19:15 Pinhead Town Talk
“Nuclear Power and Climate Change: Choosing a Course
Beyond Emotions”
Speaker: Professor R. Stephen Berry
August 23: 18:00-Picnic at the Garden in Telluride Lodge

Program
August 13: Setting an agenda of the topics to be discussed

Period of Stay
1st week: Aniruddha Chakraborty, Sergy Grebenshchikov, George Haller,
Manuel Inarrea, Michael E. Kellman, Jesus Palacian, Ana I. Pascual, Vered
Rom-Kedar, Vivian Tyng, Patricia Yanguas (10 people)
Both weeks: Thomas Bartsch, R. Stephen Berry, Johannes-Geert
Hagmann, Jason Green, Charles Jaffe, Tamiki Komatsuzaki, HiroshiTeramoto, Turgay Uzer, Holger Waalkens, Chengju Wang, Tomohiro Yanao,
Laurent Wiesenfeld (15-), Mikito Toda (16-) (13 people)

General Agenda and Several Key Words
What is the underlying principle of complexity in kinetics anddynamics in many-degrees of freedom systems for a wide range ofdiverse systems such as three body systems, clusters, proteins andDNA?
Can we have common language, concepts and methodologies tocover through or bridge among complex systems of different space
and time scales?
Key Concepts: Transition States (TS), Normally Hyperbolic Invariant
Manifold (NHIM)?, Lagrangian Coherent Structure (LCS)? NonlinearTime Series Analysis? Their Quantum Counterparts? Notion ofpotential and free energy Landscape, Billiard problem,…

Related with NHIM:
NHIM (stable against perturbation) and cylindrical invariant
manifolds composed of its stable/unstable invariant manifolds
can mediate chemical reactions even in a sea of chaos
1. Stability of NHIM in dissipative systems & Mechanism of Breakdown ofNHIM: How NHIM can robustly survive under thermal fluctuation?
2. Quantum counterpart of classical NHIM: classical chaotic phase spaceand quantum “regular” structure
3. Local Ergodicity (Phase Space Geometry inside Potential Basins, NHIM
inside Potential Basins): How NHIMs are `connected’ by the stable andunstable manifolds through the entire phase space ?
4. Some experimental evidence to support the versatility of the conceptof NHIM? Ozone Chemistry, Some Chemical Reactions, orHundreds/Thousands of Dimensions?

Related with NHIM:
Ambition to Multiscale Systems such as Proteins, DNA
1. NHIM in dissipative systems: How NHIM can robustly survive underthermal fluctuation?
2. I it possible to find a set of NHIMs for a space of, say, hundreds ofdimensions? In addition, any possible means to address thegeometrical structure of the state space? LCS? Finite Size Liapunov
Exponent? Embedology? …
3. Is there a useful way to find the NHIM of a complex system in termsof a drastically reduced set of variables, e.g. principal coordinates?
4. Can we utilize the concept of NHIM in multi-scale simulation as
an efficient strategy for computations ?
5. Relevance to the implication of Robustness of Biological Functions?

Some other Interesting Topics
1. quantum dynamics is often governed by a particular symmetry. Isthere a consistent way of constructing trajectory-based/TST-type
methods taking symmetry (for example, spatial symmetry) into
account?
2. Is there a consistent way of inclusion of zero-point energy effects in
the TST description of chemical reactions?
3. Can a new paradigm for studying Hamiltonian systems with steep
potentials be of use for studying chemical reactions? Can it be ofuse for identifying the relevant LCS/NHIM for these systems?

Complexity in Kinetics, Dynamics and Energy
Landscapes in proteins and complex systems
1. What kinds of strange kinetics or dynamics are observed in realsystems like clusters and proteins?
2. Is there any new dynamical concept or methodology to dig into
the state space of large systems with multiscale time and spacescales?
3. How can one quantify the complexity of energy landscapes suchas multiple pathways in terms of characteristics of the topographyof multidimensional landscape?

4. If there are multiple pathways between major minima, what is thesignificance--and the signature--of significant interconnectivity orindependence of those pathways?
5. Can we find or invent new, summary variables that can describe thedynamics or kinetics of a system moving on a very high-dimensionallandscape? analogous to the way thermodynamics allows us to workwith a small set of variables?

Is there geometric phase (out of the BO principle) associated to NHIM? See ozone as atrigger for the question, think in terms of Li_3 (RSB)- Advanced topics associated to NHIM:
How can we treat multiscale systems such as proteins or DNA? Is it possible to find a set ofNHIM for a space of hundreds of dimensions? How can we analyze the structure of thegeometric space? Is there a useful way to find the NHIM of a complex system in reduced
coordinates, eg. PC? Implication of robustness for biological systems? How to incorporate
noisy dynamics into analysis of phase space? (TK)
- In a complex systems, can internal modes, through mode coupling, act as a heat bath forthe reaction? (RSB)- Comment: From experiments of small molecules, it is clear that what
you learn from the gas phase remains valid (on a certain timescale) for the solute case.
However, if you put the molecule on a surface, the situation is very different.
-> question of robustness with respect to the environment (MK, TK) special case of nonperturbation of the environment that could be an extension of NHIM to the quantum case:superfluid helium clusters (RSB)- Is it possible to correct TST for the effect of symmetry inthe system? How to describe symmetry in transmission? How to include zero-point energy
in classical trajectories? (SG)- New paradigm for studying Hamiltonian systems with steep
potentials; chemical reactions are very far from being near-integrable, therefore, look at
the billiard limit as a mathematical tool that allows mathematically rigorous studies. NHIM
for the billiard system as an approximation to smooth Hamiltonian systems; include open
billiards (VRK)- More complicated systems: What kinds of strange kinetics on dynamics
have been observed in real systems as clusters or proteins?