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MACROSCOPIC LAWS AND DYNAMICAL SYSTEMS

Objective

Physics provides descriptions of the world at many different scales, yet the relations between such descriptions are poorly understood. In particular, since Boltzmann and Einstein, we interpret the world we see as the product of the microscopic dynamics of a large number of atoms. In spite of this, no satisfactory rigorous derivation of a macroscopic equation (e.g. the heat equation) from such a microscopic physical model exists. This sorry state of affairs is extremely unsatisfactory both from the theoretical point of view and for applications. Indeed, as the technology is entering the mesoscopic scale (nanotechnology), the need for a rigorous understanding of how the phenomenological macroscopic laws emerge and of their limits of validity becomes paramount. We believe that recent advances in the theory of Dynamical Systems and Probability, to which the members of our team have contributed, allow key progresses in the understanding of the above problem. The ultimate goal of this proposal is the derivation of macroscopic evolution laws from a microscopic Hamiltonian evolution. To this end we will consider a series of intermediate models: a) inspired to an anharmonic chain with some noise (of a fixed strength and not itself responsible for the changes in the local energy); b) inspired to hard spheres interacting via elastic collisions and confined by fixed periodic obstacles (gas of geometrically constrained hard spheres). The above project entails the solution of major problems in the fields of Dynamical Systems and Probability. In addition, it would contribute to substantiate Boltzmann's theoretical picture by providing a conclusive rigorous example of non-equilibrium macroscopic behavior arising from an (interacting) microscopic mechanical model.

Field of science

  • /natural sciences/physical sciences/condensed matter physics/soft matter physics

Call for proposal

ERC-2009-AdG
See other projects for this call

Funding Scheme

ERC-AG - ERC Advanced Grant

Host institution

UNIVERSITA DEGLI STUDI DI ROMA TOR VERGATA
Address
Via Cracovia 50
00133 Roma
Italy
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 947 080
Principal investigator
Carlangelo Liverani (Prof.)
Administrative Contact
Giuseppe Novelli (Prof.)

Beneficiaries (2)

UNIVERSITA DEGLI STUDI DI ROMA TOR VERGATA
Italy
EU contribution
€ 947 080
Address
Via Cracovia 50
00133 Roma
Activity type
Higher or Secondary Education Establishments
Principal investigator
Carlangelo Liverani (Prof.)
Administrative Contact
Giuseppe Novelli (Prof.)
UNIVERSITE PARIS DAUPHINE
France
EU contribution
€ 425 640
Address
Place Du Marechal De Lattre De Tass Igny
75775 Paris Cedex 16
Activity type
Higher or Secondary Education Establishments
Administrative Contact
Edith Buser (Ms.)