Abstract
We study time evolution of Schrödinger-Newton system using the self-consistent Crank-Nicolson method to understand the dynamical characteristics of nonlinear systems. Compactifying the radial coordinate by a new one, which brings the spatial infinity to a finite value, we are able to impose the boundary condition at infinity allowing for a numerically exact treatment of the Schrödinger-Newton equation. We study patterns of gravitational cooling starting from exponentially localized initial states. When the gravitational attraction is strong enough, we find that a small-sized oscillatory solitonic core is forming quickly, which is surrounded by a growing number of temporary halo states. In addition a significant fraction of particles escape to asymptotic regions. The system eventually settles down to a stable solitonic core state while all the excess kinetic energy is carried away by the esca** particles, which is a phenomenon of gravitational cooling.
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Bak, D., Kim, S., Min, H. et al. Patterns of Gravitational Cooling in Schrödinger Newton System. J. Korean Phys. Soc. 74, 756–763 (2019). https://doi.org/10.3938/jkps.74.756
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DOI: https://doi.org/10.3938/jkps.74.756