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Atomism and quantization

Presented by: 
J Froehlich ETH Zürich
Monday 27th October 2008 - 17:00 to 18:00
INI Seminar Room 1
Session Chair: 
David Wallace
In this lecture, I will show how the atomistic structure of matter emerges from theories that treat matter as a continuous medium by a process of quantization. The parameter that occupies the role of Planck's constant in the usual quantization of hamiltonian mechanics is a measure of the strength of interactions between "atoms of matter".

I will discuss the examples of Newtonian mechanics of point particles, which can be understood as a quantization of the continuum mechanics described by the Vlasov Equation, and of interacting Bose gases, understood as the quantization of Hartree theory. I will then show how continuum theories of matter emerge from atomistic theories in the mean-field limit where the strength of interactions between "atoms of matter" tends to zero, but the number of such "atoms" tends to infinity.

I will conclude by outlining how the Newtonian mechanics of point particles can also emerge as a theory of solitary wave solutions of some non-linear hamiltonian evolution equations treating matter as a continuous medium.

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    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons