What is liquid? Lyapunov instability reveals symmetry-breaking irreversibilities hidden within Hamilton's many-body equations of motion
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
What is liquid? Lyapunov instability reveals symmetry-breaking irreversibilities hidden within Hamilton's many-body equations of motion
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| Creator |
Hoover, Wm.G.
Hoover, C.G. |
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| Description |
Typical Hamiltonian liquids display exponential "Lyapunov instability", also called "sensitive dependence on initial conditions". Although Hamilton's equations are thoroughly time-reversible, the forward and backward Lyapunov instabilities can differ, qualitatively. In numerical work, the expected forward/backward pairing of Lyapunov exponents is also occasionally violated. To illustrate, we consider many-body inelastic collisions in two space dimensions. Two mirror-image colliding crystallites can either bounce, or not, giving rise to a single liquid drop, or to several smaller droplets, depending upon the initial kinetic energy and the interparticle forces. The difference between the forward and backward evolutionary instabilities of these problems can be correlated with dissipation and with the Second Law of Thermodynamics. Accordingly, these asymmetric stabilities of Hamilton's equations can provide an "Arrow of Time". We illustrate these facts for two small crystallites colliding so as to make a warm liquid. We use a specially-symmetrized form of Levesque and Verlet's bit-reversible Leapfrog integrator. We analyze trajectories over millions of collisions with several equally-spaced time reversals.
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| Date |
2019-06-14T11:03:59Z
2019-06-14T11:03:59Z 2015 |
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| Type |
Article
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| Identifier |
What is liquid? Lyapunov instability reveals symmetry-breaking irreversibilities hidden within Hamilton's many-body equations of motion / Wm.G. Hoover, C.G. Hoover // Condensed Matter Physics. — 2015. — Т. 18, № 1. — С. 13003:1-13. — Бібліогр.: 22 назв. — англ.
1607-324X DOI:10.5488/CMP.18.13003 arXiv:1405.2485 PACS: 05.10.-a, 05.45.-a http://dspace.nbuv.gov.ua/handle/123456789/153582 |
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| Language |
en
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| Relation |
Condensed Matter Physics
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| Publisher |
Інститут фізики конденсованих систем НАН України
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