Barak Kol (the Hebrew University of Jerusalem) | The flux-based statistical theory for the three- body problem |


The Newtonian three-body problem is one of the richest, deepest and longest-standing open problems in physics. It is the fertile soil that brought about the paradigm change from the clockwork universe to chaos, and it grew numerous scientific theories including perturbation theory, the symplectic formulation of mechanics, and the mathematical field of topology.

The generic, non-hierarchical, three-body system is known to be chaotic. In fact, it is so chaotic that one expects that a statistical solution is the optimal solution. Yet, despite considerable progress, all extant statistical approaches displayed two flaws. First, probability was equated with phase space volume, thereby ignoring the fact that significant regions of phase space describe regular motion, including post-decay motion. Secondly and relatedly, an adjustable parameter, the strong interaction region, which is a sort of cutoff, was a central ingredient of the theory.

The talk will describe a theory that is based on phase-space flux, rather than phase-space volume, which remedies these flaws. Statistical predictions for the identity of the escaper, and other measurable quantities, will be shown to agree with computerized simulations considerably better than previous theories.

Moreover, the flux-based theory enables to predict the distribution of decay times. This prediction relies on the definition and determination of a regularized phase-volume for the system, and the latter led us to a second aspect of the problem, namely a decomposed formulation of it. Basically, this decomposition separates the motion of the instantanoues plane defined by the three bodies, from the motion of the bodies within the plane.



Youtube movie of a 3 body movement

Based on:

Barak Kol, “Flux-based statistical prediction of three-body outcomes”, Celest. Mech. Dyn. Astron. 133 17 (2021).

Viraj Manwadkar, Barak Kol, Alessandro Trani and Nathan Leigh, “Testing the flux- based statistical prediction of the three-body problem”, MNRAS 506, 692 (2021).

Barak Kol, “Natural dynamical reduction of the three-body problem” arXiv:2107.12372.

Yogesh Dandekar, Barak Kol, Lior Lederer and Subhajit Mazumdar, “Regularized phase-space volume for the three-body problem,” Celest. Mech. Dyn. Astron. 134 55 (2022).

When: January 11, 2023 2:00 PM (Israel Standard Time).

Where: Room 223, Multipurpose Bldg. & over Zoom