Kavli Affiliate: Tom Abel
| First 5 Authors: Andrew Eberhardt, Alvaro Zamora, Michael Kopp, Tom Abel,
| Summary:
The classical field approximation is widely used to better understand the
predictions of ultra-light dark matter. Here, we use the truncated Wigner
approximation method to test the classical field approximation of ultra-light
dark matter. This method approximates a quantum state as an ensemble of
independently evolving realizations drawn from its Wigner function. The method
is highly parallelizable and allows the direct simulation of quantum
corrections and decoherence times in systems many times larger than have been
previously studied in reference to ultra-light dark matter. Our study involves
simulation of systems in 1, 2, and 3 spatial dimensions. We simulate three
systems, the condensation of a Gaussian random field in three spatial
dimensions, a stable collapsed object in three spatial dimensions, and the
merging of two stable objects in two spatial dimensions. We study the quantum
corrections to the classical field theory in each case. We find that quantum
corrections grow exponentially during nonlinear growth with the timescale being
approximately equal to the system dynamical time. In stable systems the
corrections grow quadratically. We also find that the primary effect of quantum
corrections is to reduce the amplitude of fluctuations on the deBroglie scale
in the spatial density. Finally, we find that the timescale associated with
decoherence due to gravitational coupling to Baryonic matter is at least as
fast as the quantum corrections due to gravitational interactions. These
results strongly imply that quantum corrections do not impact the predictions
of the classical field theory.
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