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The classical field approximation of ultra light dark matter: quantum breaktimes, corrections, and decoherence

Published 11 Oct 2023 in astro-ph.CO and hep-ph | (2310.07119v1)

Abstract: 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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  47. |z→⟩f=\sum@⁢\slimits@{n}⁢nt⁢o⁢t!⁢\bigotimes@⁢\slimits@i=1M⁢zinini!⁢|ni⟩subscriptket→𝑧𝑓\sum@subscript\slimits@𝑛subscript𝑛𝑡𝑜𝑡\bigotimes@superscriptsubscript\slimits@𝑖1𝑀superscriptsubscript𝑧𝑖subscript𝑛𝑖subscript𝑛𝑖ketsubscript𝑛𝑖\mathinner{|{\vec{z}}\rangle}_{f}=\sum@\slimits@_{\set{n}}\sqrt{n_{tot}!}% \bigotimes@\slimits@_{i=1}^{M}\frac{z_{i}^{n_{i}}}{\sqrt{n_{i}!}}\mathinner{|{% n_{i}}\rangle}start_ATOM | over→ start_ARG italic_z end_ARG ⟩ end_ATOM start_POSTSUBSCRIPT italic_f end_POSTSUBSCRIPT = start_POSTSUBSCRIPT { start_ARG italic_n end_ARG } end_POSTSUBSCRIPT square-root start_ARG italic_n start_POSTSUBSCRIPT italic_t italic_o italic_t end_POSTSUBSCRIPT ! end_ARG start_POSTSUBSCRIPT italic_i = 1 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_M end_POSTSUPERSCRIPT divide start_ARG italic_z start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_n start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT end_POSTSUPERSCRIPT end_ARG start_ARG square-root start_ARG italic_n start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT ! end_ARG end_ARG start_ATOM | italic_n start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT ⟩ end_ATOM.
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