scholarly journals Universality in a one-dimensional three-body system

2019 ◽  
Vol 100 (1) ◽  
Author(s):  
Lucas Happ ◽  
Matthias Zimmermann ◽  
Santiago I. Betelu ◽  
Wolfgang P. Schleich ◽  
Maxim A. Efremov
Keyword(s):  
Body System ◽  
One Dimensional ◽  
Three Body

scholarly journals The Dynamics of Digits: Calculating Pi with Galperin’s Billiards

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 509
Author(s):  
Xabier M. Aretxabaleta ◽  
Marina Gonchenko ◽  
Nathan L. Harshman ◽  
Steven Glenn Jackson ◽  
Maxim Olshanii ◽  
...  
Keyword(s):  
Irrational Number ◽  
Type Model ◽  
Hard Wall ◽  
Body System ◽  
Mass Ratio ◽  
Specific Mass ◽  
One Dimensional ◽  
Number Π ◽  
The Masses ◽  
Three Body

In Galperin billiards, two balls colliding with a hard wall form an analog calculator for the digits of the number π . This classical, one-dimensional three-body system (counting the hard wall) calculates the digits of π in a base determined by the ratio of the masses of the two particles. This base can be any integer, but it can also be an irrational number, or even the base can be π itself. This article reviews previous results for Galperin billiards and then pushes these results farther. We provide a complete explicit solution for the balls’ positions and velocities as a function of the collision number and time. We demonstrate that Galperin billiard can be mapped onto a two-particle Calogero-type model. We identify a second dynamical invariant for any mass ratio that provides integrability for the system, and for a sequence of specific mass ratios we identify a third dynamical invariant that establishes superintegrability. Integrability allows us to derive some new exact results for trajectories, and we apply these solutions to analyze the systematic errors that occur in calculating the digits of π with Galperin billiards, including curious cases with irrational number bases.

Multiple impacts and energy transfer in a three-body system for noncollinear collisions

1993 ◽  
Vol 87 (3) ◽  
pp. 195-213 ◽  
Author(s):  
Vladimir M. Azriel ◽  
Lev Yu. Rusin ◽  
Mikhail B. Sevryuk
Keyword(s):  
Energy Transfer ◽  
Body System ◽  
Multiple Impacts ◽  
Three Body

scholarly journals Probing the edge between integrability and quantum chaos in interacting few-atom systems

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 486
Author(s):  
Thomás Fogarty ◽  
Miguel Ángel García-March ◽  
Lea F. Santos ◽  
Nathan L. Harshman
Keyword(s):  
Quantum Chaos ◽  
Cold Atoms ◽  
Quantum Systems ◽  
Particle Interactions ◽  
Body System ◽  
Many Body ◽  
One Dimensional ◽  
The Core ◽  
Emergence Of Chaos ◽  
Number Of Particles

Interacting quantum systems in the chaotic domain are at the core of various ongoing studies of many-body physics, ranging from the scrambling of quantum information to the onset of thermalization. We propose a minimum model for chaos that can be experimentally realized with cold atoms trapped in one-dimensional multi-well potentials. We explore the emergence of chaos as the number of particles is increased, starting with as few as two, and as the number of wells is increased, ranging from a double well to a multi-well Kronig-Penney-like system. In this way, we illuminate the narrow boundary between integrability and chaos in a highly tunable few-body system. We show that the competition between the particle interactions and the periodic structure of the confining potential reveals subtle indications of quantum chaos for 3 particles, while for 4 particles stronger signatures are seen. The analysis is performed for bosonic particles and could also be extended to distinguishable fermions.

scholarly journals Requirements of Orbital Phase Continuity Revisited: A FMO Approach

2021 ◽  
Author(s):  
Yuji Naruse
Keyword(s):  
Orbital Interaction ◽  
Body System ◽  
Orbital Phase ◽  
Three Body

<div> <p>Cyclic orbital interaction, in which a series of orbitals interact with each other so as to make a monocyclic system, affords stabilization if the requirements of orbital phase continuity are satisfied. Initially, these requirements were derived from the consideration of a three-body system. Here I propose that these requirements can be easily derived by considering FMO theory. </p> </div>

scholarly journals Low-energy neutron scattering on light nuclei and $^{19}$B as a $^{17}$B-$n$-$n$ three-body system in the unitary limit

2020 ◽  
Author(s):  
Jaume Carbonell ◽  
Emiko Hiyama ◽  
Rimantas Lazauskas ◽  
Francisco Miguel Marqués
Keyword(s):  
Scattering Length ◽  
Nucleon Nucleon ◽  
Light Nuclei ◽  
Unitary Limit ◽  
Body System ◽  
Resonant States ◽  
Pauli Repulsion ◽  
Nucleus Scattering ◽  
Nucleon Nucleon Interaction ◽  
Three Body

We consider the evolution of the neutron-nucleus scattering length for the lightest nuclei. We show that, when increasing the number of neutrons in the target nucleus, the strong Pauli repulsion is weakened and the balance with the attractive nucleon-nucleon interaction results into a resonant virtual state in ^{18}18B. We describe ^{19}19B in terms of a ^{17}17B-nn-nn three-body system where the two-body subsystems ^{17}17B-nn and nn-nn are unbound (virtual) states close to the unitary limit. The energy of ^{19}19B ground state is well reproduced and two low-lying resonances are predicted. Their eventual link with the Efimov physics is discussed. This model can be extended to describe the recently discovered resonant states in ^{20,21}20,21B.

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