# New Concept for Studying the Classical and Quantum Three-Body Problem: Fundamental Irreversibility and Time’s Arrow of Dynamical Systems

@inproceedings{Gevorkyan2020NewCF, title={New Concept for Studying the Classical and Quantum Three-Body Problem: Fundamental Irreversibility and Time’s Arrow of Dynamical Systems}, author={Ashot Gevorkyan}, year={2020} }

The article formulates the classical three-body problem in conformal-Euclidean space (Riemannian manifold), and its equivalence to the Newton three-body problem is mathematically rigorously proved. It is shown that a curved space with a local coordinate system allows us to detect new hidden symmetries of the internal motion of a dynamical system, which allows us to reduce the three-body problem to the 6th order system. A new approach makes the system of geodesic equations with respect to the…

## Figures from this paper

## References

SHOWING 1-10 OF 127 REFERENCES

The Three-body Problem in Riemannian Geometry. Hidden Irreversibility of the Classical Dynamical System

- Mathematics, PhysicsLobachevskii Journal of Mathematics
- 2019

The classical three-body problem is formulated as a problem of geodesic flows on a Riemannian manifold. It is proved that a curved space allows to detect new hidden symmetries of the internal motion…

On reduction of the general three-body Newtonian problem and the curved geometry

- Mathematics
- 2014

In the framework of an idea of separation of rotational and vibrational motions, we have examined the problem of reducing the general three-body problem. The class of differentiable functions…

On the motion of a three-body system on hypersurface of proper energy

- Mathematics, Physics
- 2013

Based on the fact that for hamiltonian system there exists equivalence between phase trajectories and geodesic trajectories on the Riemannian manifold, the classical three-body problem is formulated…

On the motion of classical three-body system with consideration of quantum fluctuations

- Physics, Mathematics
- 2015

We obtained the systemof stochastic differential equations which describes the classicalmotion of the three-body system under influence of quantum fluctuations. Using SDEs, for the joint probability…

Chaos in classical and quantum mechanics

- Physics
- 1990

Contents: Introduction.- The Mechanics of Lagrange.- The Mechanics of Hamilton and Jacobi.- Integrable Systems.- The Three-Body Problem: Moon-Earth-Sun.- Three Methods of Section.- Periodic Orbits.-…

A geometric setting for classical molecular dynamics

- Physics
- 1987

In studying the « internal » motions of a molecule (a many-particle system), use has been made of the Eckart frame, relative to which the molecule moves without rotation. This paper shows, on the…

A New Approach To The Evaluation Of The S-Matrix In Atom-Diatom Quantum Reactive Scattering Theory

- Physics
- 2006

A new approach is described to the evaluation of the S-matrix in three-dimensional atom-diatom reactive quantum scattering theory. The theory is developed based on natural collision coordinates where…

The quantum dynamics of three particles in hyperspherical coordinates

- Physics
- 1983

A derivation of the quantum mechanical wave equation for the three body problem expressed in hyperspherical coordinates is presented. The coordinates, due to Smith and Whitten and later modified by…

The entropy formula for the Ricci flow and its geometric applications

- Mathematics
- 2002

We present a monotonic expression for the Ricci flow, valid in all dimensions and without curvature assumptions. It is interpreted as an entropy for a certain canonical ensemble. Several geometric…

Poincaré and the Three-Body Problem

- Mathematics
- 2015

The Three-Body Problem has been a recurrent theme of Poincare’s thought. Having understood very early the need for a qualitative study of “non-integrable” differential equations, he developed the…