Dynamics of correlations for integrable and non-integrable systems - A two levels formulation of laws of nature

by Prof. Ilya Prigogine (Université Libre, Bruxelles, 1977 Nobel Laureate of Chemistry)

Thursday 24 Jan 2002, 16:30 → 17:30 Europe/Zurich

500/1-001 - Main Auditorium (CERN)

Hamiltonian systems can be classified according to Poincaré into integrable and non-integrable systems. On the other hand, our previous work introduced a formulation of dynamics based on the evolution of correlations. It is shown that for integrable systems this method is equivalent to the diagonalisation problem of the Hamiltonian for integrable systems but our method can be easily extended to non-integrable systems through analytic continuation. This leads to a description of unstable dressed excited states, as well as to excitations for interacting fields. The mechanism of the formation of dressed objects will be analysed in terms of two different time scales. The analogy with these dissipative structures will be emphasized. We may distinguish two levels in the formulation of laws of nature. The first is in terms of Hamiltonian dynamics, the second, necessary for classes of non-integrable systems, arises from limiting processes and leads to time symmetry breaking and to an intrinsically probabilistic description. Kinetic theories and thermodynamics correspond to an extension of dynamics and not to some approximation scales. Background information Ilya Prigogine received the Nobel Prize for Chemistry in 1977 for contributions to non-equilibrium thermodynamics, especially the theory of dissipative structures. His theoretical work extended the work of Lars Onsager by developing thermodynamic methods of understanding irreversible processes as well as the classical reversible reactions that were supposed to result in states of equilibrium. Prigogine was born in Moscow on January 25, 1917. He received his Ph.D. in 1942 at the Free University in Brussels, where he accepted the position of professor in 1947. In 1962 he became director of the International Institute of Physics and Chemistry, Solvay, Belgium. He also served as director of the Center for Statistical Mechanics and Thermodynamics at the University of Texas, Austin, from 1967. The Science & Society seminar is part of a new seminar series in the framework of the Geneva Research Collaboration in which participate researchers from the University of Geneva, CERN and different research groups at banks in the Geneva region. The main objective of the Geneva Research Collaboration is to establish an international, open, and creative research framework for developing and disseminating new mathematical and physical models in social science, in general, and in finance and environmental sciences, in particular. The collaboration involves researchers at the University of Geneva and CERN, other Swiss and foreign research institutions, practitioners from banks in the Geneva area, as well as selected individual researchers, who will interact through the organization of different types of research seminars. The topics of interest to the Geneva Research Collaboration include models related to financial engineering, financial time series, investment strategies, risk management, technical analysis, dynamics of biological and environmental systems, climate change, data analysis, stochastic processes, optimization methods, statistical mechanics, and quantum mechanics.

Organiser(s): James Gillies / ETT Division

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