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 TMF, 1999, Volume 121, Number 1, Pages 110–116 (Mi tmf800)

Dynamics of a heavy particle surrounded by a finite number of light particles

Ya. G. Sinaiab

a L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences
b Princeton University, Department of Mathematics

Abstract: We consider a dynamic system consisting of a heavy particle of mass $M$ and surrounding light particles moving independently with elastic reflections in the segment $[0,1]$. At a given total energy value independent of $M$, we find the dynamics of the heavy particle with respect to the slow time $t/\sqrt M$.

DOI: https://doi.org/10.4213/tmf800

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English version:
Theoretical and Mathematical Physics, 1999, 121:1, 1351–1357

Bibliographic databases:

Citation: Ya. G. Sinai, “Dynamics of a heavy particle surrounded by a finite number of light particles”, TMF, 121:1 (1999), 110–116; Theoret. and Math. Phys., 121:1 (1999), 1351–1357

Citation in format AMSBIB
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This publication is cited in the following articles:
1. Lebowitz, J, “Dynamics of an adiabatic piston”, Doklady Mathematics, 62:3 (2000), 398
2. Piasecki, J, “A model of Brownian motion in an inhomogeneous environment”, Journal of Physics-Condensed Matter, 14:40 (2002), 9265
3. Barre, J, “Out-of-equilibrium states as statistical equilibria of an effective dynamics in a system with long-range interactions”, Physical Review Letters, 89:11 (2002), 110601
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6. Neishtadt, AI, “Adiabatic piston as a dynamical system”, Journal of Statistical Physics, 116:1–4 (2004), 815
7. Mansour, MM, “Hydrodynamic relaxation of the adiabatic piston”, Europhysics Letters, 69:4 (2005), 510
8. Wright, P, “A simple piston problem in one dimension”, Nonlinearity, 19:10 (2006), 2365
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10. Mansour, MM, “Hydrodynamic description of the adiabatic piston”, Physical Review E, 73:1 (2006), 016121
11. Hurtado, PI, “Simplest piston problem. I. Elastic collisions”, Physical Review E, 73:1 (2006), 016136
12. Hurtado, PI, “Simplest piston problem. II. Inelastic collisions”, Physical Review E, 73:1 (2006), 016137
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14. Wright, P, “The periodic oscillation of an adiabatic piston in two or three dimensions”, Communications in Mathematical Physics, 275:2 (2007), 553
15. Balint, P, “On the zero mass limit of tagged particle diffusion in the 1-d Rayleigh-gas”, Journal of Statistical Physics, 127:4 (2007), 657
16. Caglioti, E, “Long time behavior of particle systems in the mean field limit”, Communications in Mathematical Sciences, 5 (2007), 11
17. Uranagase, M, “Piston dynamics from a microcanonical ensemble”, Physical Review E, 75:1 (2007), 011110
18. A. V. Kargovsky, L. S. Bulushova, O. A. Chichigina, “Theorem on energy distribution over degrees of freedom for a quasistable symmetric anharmonic oscillator”, Theoret. and Math. Phys., 167:2 (2011), 636–644
19. Gorelyshev I., “On the dynamics in the one-dimensional piston problem”, Nonlinearity, 24:8 (2011), 2119–2142
20. Ee J.-H., Lee J., “Magic Mass Ratios of Complete Energy-Momentum Transfer in One-Dimensional Elastic Three-Body Collisions”, Am. J. Phys., 83:2 (2015), 110–120
21. Gay-Balmaz F., Yoshimura H., “Dirac Structures in Nonequilibrium Thermodynamics”, J. Math. Phys., 59:1 (2018), 012701
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