skip to content

Atomism and quantization

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.

The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons