Solving the Vlasov equation in two spatial dimensions with the Schrödinger method

I present recent progress (Kopp, Vattis & Skordis 1711.00140) to solve the Vlasov equation via the so-called Schrödinger method (Widrow & Kaiser 1993). This technique consists of solving the Schrödinger-Poisson equation, together with a prescription to construct a phase space distribution from the wave function.

For the first time, we implemented the Schrödinger method in two spatial dimensions, extending the one-dimensional previous studies.

We performed a quantitative comparison of our code and the state-of-the-art Vlasov solver ColDICE (Sousbie & Colombi 1509.07720), finding excellent agreement.

I review how the fully fledged phase space dynamics is encoded in a wave function with its mere 2 spatial degrees of freedom, and how the cumulants of the phase space distribution, including vorticity and velocity dispersion, can be easily decoded from the wave function in a way that completely avoids the cumbersome high-dimensional phase space.

As an application we evaluate the background pressure induced by the non-linearity of large scale structure formation, thereby estimating the magnitude of cosmological backreaction. We find that it is negligibly small and has time dependence and magnitude compatible with expectations from the effective field theory of large scale structure.

Speaker: Michael Kopp, Czech Academy of Sciences

Editor's Note: This event was originally scheduled for December 15.

Monday, 12/11/17


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