An introduction to combinatorial physics and stochastic mechanics
- Event time: 11:30am
- Event date: 4th March 2015
- Speaker: Nicolas Behr (School of Informatics)
- Location: Room 4309, James Clerk Maxwell Building (JCMB) James Clerk Maxwell Building Peter Guthrie Tait Road Edinburgh EH9 3FD GB
A standard result in the theory of chemical reaction systems states that the dynamics of the system is described by the so-called master equation, a first order ODE, derived based on the assumption of mass-action kinetics. Albeit an interpretation of this equation in terms of concepts from combinatorics had in principle been known since the early 1970s from the work of Navon and Katriel, it has only become apparent much more recently due to the work of [Duchamp et al.] that in fact there exists a very fundamental link between (ODEs of the type of) the master equation one the one hand, and so-called evolutionary groups and boson normal ordering on the other hand, which in turn are amongst the core concepts of modern combinatorics. Duchamp and coworkers chose to call this research field "combinatorial physics".
In this talk, I will give an introduction to combinatorial physics and present its ties with so-called "stochastic mechanics" (cf. [Baez et al.]), i.e. the modern formulation of chemical reaction systems in the language of creation and annihilation operators acting on a particular type of bosonic Fock space. I will not assume any particular previous knowledge from the audience, albeit colleagues with a background in quantum mechanics will presumably find it amusing to see that the construction of stochastic mechanics is remarkably analogous to that of quantum mechanics!
As an illustrative example, I will present a few reaction systems for which an analytical solution is attainable within this framework. Time permitting, I will also comment briefly on the even more recent development of so-called "combinatorial field theory", a direct analogue of (zero-dimensional) quantum field theory.
* Gérard Henry Edmond Duchamp et al. "Ladder operators and endomorphisms in combinatorial physics.", arXiv:0908.2332 (2009).
* John C. Baez and Jacob Biamonte. "A course on quantum techniques for stochastic mechanics.", arXiv:1209.3632 (2012).
This is a roughly weekly series of didactical blackboard talks focussing on some theoretical aspect of Condensed Matter, Biological, and Statistical Physics..