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Dynamical Chaos and Non-equilibrium
Statistical Mechanics: From Rigorous Results to Applications
in Nano-systems
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Partial list: as at 31 Aug 2006
This two-month program will bring together leading international scientists in the field of mathematics, theoretical, computational, and experimental physics, and local experts from Departments of Physics, Mathematics, Computational Science, Material Science, Mechanical Engineering, Electrical and Computer Engineering, DSO labs, Temasek Labs, and A*Star Institutes. The program participants will review recent developments of dynamical chaos theory and non-equilibrium statistical mechanics and its applications to quantum systems and, in particular, to nanosystems. The participants will discuss basic scientific topics for the understanding of the fundamental laws of physics as well as applications to nano and quantum systems. The program will provide a platform for the participants, in particular the mathematicians and physicists, to dialogue and collaborate in the fast developing field of nano science and technology.
The following areas would be the core issues of the program.
i) Non-equilibrium statistical physics.
An important problem is the understanding of basic issues of nonequilibrium processes like heat transport and generic features of stationary non-equilibrium states. Here a substantial amount of deep mathematical work appeared in the last few years, like the “chaotic principle” extending in the non-equilibrium situation, properties of Sinai-Ruelle-Bowen equilibrium states, or the fluctuation theorem, whose general validity has still to be fully explored. We also mention that recently a large amount of work has shed new lights on the validity (or deviations from it) of heat Fourier law in low dimensional systems: whether this has a role on transport in nanoscale systems is still a completely open problem.
Another important problem is transport in Hamiltonian systems with divided phase space, i.e. in systems where islands of stability coexist with chaotic sea. It has been recently shown that even several islands (not infinitely many as it was thought before) can essentially alter transport properties. This phenomenon together with its universality (universal power law) in systems with a finite number of islands will be discussed at the program with special emphasis on similarity and differences of transport in systems with infinite or finite number of islands.
Basically we would like to stress that a more general approach to randomness of nonlinear dynamics requires new understanding and new tools. For example, zero measure sets in the ergodic theory can not be neglected in applications to realistic systems, in general, since some zero measure domains in the phase space are responsible for anomalous properties of system evolution, particle transport, character of statistical laws, and many other important features of the dynamics. Typical Gaussian type processes, used in kinetic theory, may be a too rough approximation that does not work for a fairly long time.
ii) Directed and anomalous transport in nano-systems
The capability of generating transport properties is one of the most striking features of (even low-dimensional) chaotic systems. Here fundamental issues are still to be clarified, as what are the minimal dynamical requirements that generate non trivial transport properties, or how a mixed phase space determines deviations from normal (Gaussian) transport. Such issues are of deep interest also in well defined physical contexts as plasma confinement in tokomaks, or particle accelerators design.
Recently intensive research, of increasing technological importance, has been devoted to investigations of transport in nano-systems. Prime examples are trans-membrane proton currents through water-filled narrow pores and mechanical friction in carbon nanotubes. Also heat conduction and diffusion in such devices is of great interest and immediately related to the anomalous transport properties mentioned above.
IMS Membership is not required for participation in above activities. For attendance at these activities, please complete the registration form (MSWord|PDF|PS) and fax it to us at (65) 6873 8292 or email it to us at ims@nus.edu.sg.
If you are an IMS member or are applying for IMS membership, you do not need to register for these activities.
The Institute for Mathematical Sciences invites applications for membership for participation in the above program. Limited funds to cover travel and living expenses are available to young scientists. Applications should be received at least three (3) months before the commencement of membership. Application form is available in (MSWord|PDF|PS) format for download.
For enquiries on scientific aspects of the program, please email Baowen Li at phylibw@nus.edu.sg.
Organizing Committee · Confirmed Visitors · Overview · Activities · Membership Application
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