New Concept for Studying the Classical and Quantum Three-Body Problem: Fundamental Irreversibility and Time’s Arrow of Dynamical Systems
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 symmetri...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-08-01
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| Series: | Particles |
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| Online Access: | https://www.mdpi.com/2571-712X/3/3/39 |
| _version_ | 1797560359614152704 |
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| author | A. S. Gevorkyan |
| author_facet | A. S. Gevorkyan |
| author_sort | A. S. Gevorkyan |
| collection | DOAJ |
| description | 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 evolution parameter of a dynamical system (<i>internal time</i>) <i>fundamentally irreversible.</i> To describe the motion of three-body system in different random environments, the corresponding stochastic differential equations (SDEs) are obtained. Using these SDEs, Fokker-Planck-type equations are obtained that describe the joint probability distributions of geodesic flows in phase and configuration spaces. The paper also formulates the quantum three-body problem in conformal-Euclidean space. In particular, the corresponding wave equations have been obtained for studying the three-body bound states, as well as for investigating multichannel quantum scattering in the framework of the concept of <i>internal time</i>. This allows us to solve the extremely important <i>quantum-classical correspondence problem</i> for dynamical <i>Poincaré systems.</i> |
| first_indexed | 2024-03-10T17:58:32Z |
| format | Article |
| id | doaj.art-e585542703474021b5bafb7f580c3053 |
| institution | Directory Open Access Journal |
| issn | 2571-712X |
| language | English |
| last_indexed | 2024-03-10T17:58:32Z |
| publishDate | 2020-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Particles |
| spelling | doaj.art-e585542703474021b5bafb7f580c30532023-11-20T09:05:08ZengMDPI AGParticles2571-712X2020-08-013357662010.3390/particles3030039New Concept for Studying the Classical and Quantum Three-Body Problem: Fundamental Irreversibility and Time’s Arrow of Dynamical SystemsA. S. Gevorkyan0Institute for Informatics and Automation Problems, NAS of Armenia, Yerevan 0014, ArmeniaThe 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 evolution parameter of a dynamical system (<i>internal time</i>) <i>fundamentally irreversible.</i> To describe the motion of three-body system in different random environments, the corresponding stochastic differential equations (SDEs) are obtained. Using these SDEs, Fokker-Planck-type equations are obtained that describe the joint probability distributions of geodesic flows in phase and configuration spaces. The paper also formulates the quantum three-body problem in conformal-Euclidean space. In particular, the corresponding wave equations have been obtained for studying the three-body bound states, as well as for investigating multichannel quantum scattering in the framework of the concept of <i>internal time</i>. This allows us to solve the extremely important <i>quantum-classical correspondence problem</i> for dynamical <i>Poincaré systems.</i>https://www.mdpi.com/2571-712X/3/3/39classical three-body problemconformal-geodesic equationsnon-integrable classical systemirreversible classical dynamicsequation of geodesic flowsquantum three-body problem |
| spellingShingle | A. S. Gevorkyan New Concept for Studying the Classical and Quantum Three-Body Problem: Fundamental Irreversibility and Time’s Arrow of Dynamical Systems Particles classical three-body problem conformal-geodesic equations non-integrable classical system irreversible classical dynamics equation of geodesic flows quantum three-body problem |
| title | New Concept for Studying the Classical and Quantum Three-Body Problem: Fundamental Irreversibility and Time’s Arrow of Dynamical Systems |
| title_full | New Concept for Studying the Classical and Quantum Three-Body Problem: Fundamental Irreversibility and Time’s Arrow of Dynamical Systems |
| title_fullStr | New Concept for Studying the Classical and Quantum Three-Body Problem: Fundamental Irreversibility and Time’s Arrow of Dynamical Systems |
| title_full_unstemmed | New Concept for Studying the Classical and Quantum Three-Body Problem: Fundamental Irreversibility and Time’s Arrow of Dynamical Systems |
| title_short | New Concept for Studying the Classical and Quantum Three-Body Problem: Fundamental Irreversibility and Time’s Arrow of Dynamical Systems |
| title_sort | new concept for studying the classical and quantum three body problem fundamental irreversibility and time s arrow of dynamical systems |
| topic | classical three-body problem conformal-geodesic equations non-integrable classical system irreversible classical dynamics equation of geodesic flows quantum three-body problem |
| url | https://www.mdpi.com/2571-712X/3/3/39 |
| work_keys_str_mv | AT asgevorkyan newconceptforstudyingtheclassicalandquantumthreebodyproblemfundamentalirreversibilityandtimesarrowofdynamicalsystems |