Understanding the dynamics of molecules at energies where chemical bonds
break or are formed is not only of academic importance but basically
it is the foundation of chemistry with all the consequences that implies
for our continuously advancing technological world. The progress obtained
in quantum chemistry, non-linear mechanics and in the correspondence of
classical to quantum mechanics [1] in
the last forty years has unveiled the complexity of the interactions among
the nuclei in a molecule and their internal motions.
The simple statistical theory
named RRKM [2], which is based on the ergodic hypothesis, is inadequate to
explain detailed experimental results now available from single molecule
spectroscopy and molecular beams [3].
Numerous studies show that the polyatomic molecules seen as a set of
non-linear coupled oscillators is not an ergodic system, but instead,
they form a mixed phase space with regular and chaotic regions [4,5].
The motions in two or more degrees of freedom may come into resonances,
thus being adiabatically separated from the other
degrees of freedom. This leads to the localization of energy. Transitions from
normal modes (extended motions) to local modes were first observed
spectroscopically in molecules. From the non-linear mechanics point of view
the transition from normal to local modes can be described as an elementary
pitchfork bifurcation of those periodic orbits which correspond to normal
modes with the increase of the energy of the molecule [6].
Another elementary bifurcation frequently observed in non-linear systems is the
saddle-node. Its importance for the dynamics of the molecules was early
pointed out [7]. Systematic studies mainly in triatomic molecules have
shown that the route to a bond breaking or formation with the increase of
energy is paved by a cascade of such bifurcations [4,5].
The appearance of saddle-node bifurcations demonstrate that
some degrees of freedom come into a resonance with the simultaneous
appearance of two or
more new periodic orbits. Via saddle-node bifurcations the energy can flow
into regions of phase space that normal mode type motions can not penetrate.
These studies revealed that elementary chemical reactions such as
isomerization and dissociation occur via saddle-node bifurcations [4,5].
The energy in the resonance
zones dictated by the saddle-node bifurcations is mainly localized in the bond
or angle which is about to break. Spectroscopic signatures of this type
of bifurcations
have recently been recorded. HCP was the first molecule for which
characteristics of the high energy vibrational spectra could be explained by
periodic orbits analysis and exact quantum mechanical calculations [4].
Acetylene is another example of a small polyatomic molecule where
normal to local mode transitions in vibrational spectra are explained
by combining quantum and classical mechanical calculations [8,9,10].
Independently, while the studies in localization of energy and bifurcations of
motions were carried out in small polyatomic molecules, another research
community has done
important advances in studying localization and coherent phenomena in extended
physical, chemical and biological systems.
The key ingredients are the existence of an underlying spatial lattice
and the nonlinearity of the equations of motion which describe the
evolution of atoms. Spatially localized excitations are found
to be generic to these systems, with the internal dynamics in the
core of the excitation being periodic or nearly periodic in time.
The core is typically consisting of a very
limited number of atoms of
the extended system. Theoretically,
large systems are represented by models of infinite regular lattices of one,
two and three dimensions with non-linear interactions among neighboring sites.
Using simple interaction potentials numerical calculations, models and
in a few cases rigorous mathematical theorems prove the existence of
``Intrinsic Localized Modes (ILM)'' or ``Discrete Breathers (DB)'' [11].
DB have been used to understand the molding of light in
non-linear photonic crystals,
localized excitations in
superconducting Josephson junction arrays,
many-phonon bound states in solids, complex dynamics of micromechanical
cantilever systems
and protein spectroscopy
[12,13,14,15]. Thus, using atomistic models to study DB it is possible
to bridge the gap
between small and large space scales.
Biological macromolecules such as DNA and proteins are complex systems in
which large conformational changes and
electron transfer are responsible for their macroscopic behaviour and
structures. DNA transcription through bubble opening, protein folding and
biological machines involve bond breaking/formation and reveal a high degree
of ** selectivity** and ** specificity** in conformational changes.
Spectroscopic techniques
(vibrational relaxation spectroscopy, NMR, laser spectroscopy) have been
applied to study these phenomena. DNA ``breathing'' has been known by
biologists for a long time, and it is a highly localized, large amplitude
distortion of the molecule, which might be well described by a localized mode
[16].
Evidence for the existence of localized modes in model compounds having the
same peptide bonds as proteins has been obtained by non-linear spectroscopy [17].
Simple models have been proposed but modeling these systems at the
atomistic level remains a challenging task, which is important
to demonstrate the validity of the results obtained in highly
simplified non-linear lattice models. By joining the forces of
the two communities, the small and large molecules, we expect to
further advance the field of energy localization.
The two groups share common theoretical and numerical techniques for modeling
localization phenomena. This is particularly true when classical mechanics
are applied. Small molecules are amenable to rigorous quantum mechanical
studies, something which is not feasible for large molecules.
On the other hand,
the breather community has developed statistical mechanical methods to study
complex systems. Currently, intense research is carried out on quantum
non-linear localization, and the role of quantum diffusion of breathers
due to tunneling.

Both research groups are looking for localized coherent motions in non-linear excited systems. To some extent they share the same theoretical tools and numerical techniques and apply spectroscopy in their experimental search for localization phenomena. The breather community can offer methods and models to study large biological macromolecules whereas the small molecule community can provide detailed knowledge for a few degrees of freedom systems both in classical and in quantum mechanics. Since we study localized phenomena these few degrees of freedom models may serve as good approximations to breathers. The main objective of the proposed workshop will be to bring together the two research groups which up to now have been working practically independently. Emphasis will be given to applications in the field of chemical reactions, dynamics of biomolecules, and to the theoretical tools and methods of analyzing the underlying models both in the classical and quantum regime. The fact that two communities have been accumulating knowledge rather independently will guarantee a success in mutual exchange of ideas, methods and results. Both groups will benefit from each other's experience but most importantly the participation of spectroscopists will enable us to examine characteristics of the localized motions which can be traced spectroscopically. Now the study of localized phenomena in association to the non-linear mechanics is a matured field of research with several applications. The three days meeting we are planning to organize does not allow us to cover all areas of potential interest. Thus, one additional objective of this meeting will be the planning of a regular conference or a longer workshop. The possibility of preparing a new European proposal to give us a chance to pursue some collaboration will also be examined.

{1} M.C. Gutzwiller, * Chaos in Classical and Quantum Mechanics*, Vol. 1, Springer-Verlag, Berlin, (1990).

{2} R.G. Gilbert and S.C. Smith, * Theory of Unimolecular and Dissociation Recombination Reactions*, Blackwell Scientific Publications, Oxford, (1990).

{3} See articles in, * Molecular Dynamics and Spectroscopy by Stimulated Emission Pumping*, edited by H.-L. Dai and R. Field, World Scientific, Singapore, (1995).

{4} H. Ishikawa, R. W. Field, S. C. Farantos, M. Joyeux, J. Koput, C. Beck and
R. Schinke, * Ann. Rev. Phys. Chit.*, ** 50**, 443 (1999).

{5} M. Joyeux, S.C. Farantos and R. Schinke, * J. Phys. Chem. A*, ** 106**, 5407 (2002).

{6}{A. A. Ovchinnikov, N. S. Erikhman and K. A. Pronin, * Vibrational -
Rotational Excitations in Non-linear Molecular Systems*, (Kluwer Academic/Plenum
Publishers, New York, 2001).}

{7} S. C. Farantos, * Int. Rev. Phys. Chem.*, ** 15**, 345 (1996).

{8}{M.~P. Jacobson, J.~P. O'Brien, R.~J. Silbey and R.~W. Field, * J. Chem. Phys.*, ** 109**, 121 (1998).

{9} M.~P. Jacobson, C.~Jung, H.~S. Taylor and R.~W. Field, *J. Chem. Phys.* ** 111**, 600 (1999).

{10} R. Prosmiti and S. C. Farantos, * J. Chem. Phys.*, ** 118**, 8275, (2003).

{11} A. J. Sievers and J. B. Page, in * Dynamical Properties
of Solids VII Phonon Physics The Cutting Edge*, Eds. G. K. Horton and
A. A. Maradudin (Elsevier, Amsterdam, 1995);
S. Aubry, * Physica D* ** 103**, 201 (1997);
S. Flach and C. R. Willis, * Phys. Rep.* ** 295,** 181 (1998),
and references therein.

{12} H. S. Eisenberg, Y. Silberberg et al, * Phys. Rev. Lett.* **
81**, 3383 (1998); J. W. Fleischer, M. Segev et al, * Nature* **
422**, 147 (2003).

{13} E. Trias, J. J. Mazo and T. P. Orlando, * Phys. Rev. Lett.*
** 84**, 741 (2000); P. Binder et al, * Phys. Rev. Lett.* ** 84**,
745 (2000).

{14} B. I. Swanson et al, * Phys. Rev. Lett.* ** 82**, 3288 (1998);
M. Sato et al, * Phys. Rev. Lett.* ** 90**, 044102 (2003).

{15} A. Xie, L. van der Meer, W. Hoff and R. H. Austin, * Phy. Rev. Lett.* ** 84,** 5435 (2000).

{16} M. Gueron, M. Kochoyan and J. L. Leroy, * Nature* ** 328**, 89 (1987))

{17} J. Edler and P. Hamm, * J. Chem. Phys.* ** 117**, 2415 (2002).