https://doi.org/10.1140/epjc/s10052-017-5209-7
Regular Article - Theoretical Physics
The Schrödinger–Poisson equations as the large-N limit of the Newtonian N-body system: applications to the large scale dark matter dynamics
1
Department of Mathematics, Physics and Electrical Engineering, Northumbria University, Newcastle City Campus, Ellison Building D 207, Newcastle upon Tyne, NE1 8ST, UK
2
Istituto Nazionale di Alta Matematica Francesco Severi, Gruppo Nazionale di Fisica Matematica, Città Universitaria, P.le A. Moro 5, 00185, Rome, Italy
* e-mail: briscese.phys@gmail.com
Received:
27
March
2017
Accepted:
7
September
2017
Published online:
19
September
2017
In this paper it is argued how the dynamics of the classical Newtonian N-body system can be described in terms of the Schrödinger–Poisson equations in the large N limit. This result is based on the stochastic quantization introduced by Nelson, and on the Calogero conjecture. According to the Calogero conjecture, the emerging effective Planck constant is computed in terms of the parameters of the N-body system as 
, where is G the gravitational constant, N and M are the number and the mass of the bodies, and 
is their average density. The relevance of this result in the context of large scale structure formation is discussed. In particular, this finding gives a further argument in support of the validity of the Schrödinger method as numerical double of the N-body simulations of dark matter dynamics at large cosmological scales.
© The Author(s), 2017
