Workshop: Randomness in partial differential equations from first principles?, Anders Szepessy

Date: 2023-12-01

Time: 11:15 - 12:15

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Anders Szepessy


In the study of stochastic partial differential equation one may wonder what is the noise? Often the stochasticity modelled in partial differential equations has  its origin in thermal fluctuations. Starting from a quantum formulation of a  molecular system coupled to a heat bath, I will show that ab initio Langevin dynamics, with a certain rank one friction matrix determined by the coupling, approximates the quantum system more accurately than any Hamiltonian system, for large mass ratio between the system and heat bath nuclei. I will also give an example  of course-graining a stochastic molecular dynamics equation to obtain a continuum stochastic partial differential equation for phase transitions.
This is joint work with Håkon Hoel (Oslo) and Erik von Schwerin (KAUST).