EXPONENTIALLY LONG EQUILIBRIUM TIMES IN A ONE-DIMENSIONAL COLLISIONAL MODEL OF CLASSICAL GAS
作者： Giancarlo Benettin , Poul Hjorth , Paolo Sempio
关键词: Heat capacity 、 Metastability 、 Degrees of freedom (physics and chemistry) 、 Equipartition theorem 、 Adiabatic invariant 、 Kinetic theory of gases 、 Scale (ratio) 、 Physics 、 Classical mechanics 、 Diatomic molecule
摘要: Around 1900, J. H. Jeans suggested that the “abnormal” specific heats observed in diatomic gases, specifically lack of contribution to heat capacity from internal vibrational degrees freedom, apparent violation equipartition theorem, might be caused by large separation between time scale for vibration and associated with a typical binary collision gas. We consider here simple 1D model show how, when these scales are well separated, collisional dynamics is constrained many- particle adiabatic invariant. The effect energy exchanges betgween translational freedom slowed down an exponential factor (as conjectured). A metastable situation thus occurs, which fast effectively do not contribute heat. Hence, “freezing out” could principle explained terms classical mechanics. discuss phenomenon analytically, on basis approximation introduced Landau Teller (1936) related phenomenon, estimate evolution statistical equilibrium. theoretical analysis supported numerical examples.
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sci-hub.se 参考文章(11)
節夫 一丸, H. M. Van Horn, Strongly coupled plasma physics University of Rochester Press. ,(1993)
James Jeans, The dynamical theory of gases ,(1904)
Ludwig Boltzmann, Vorlesungen über Gastheorie ,(2009)
Giancarlo Benettin, Francesco Fassò, From Hamiltonian perturbation theory to symplectic integrators and back Applied Numerical Mathematics. ,vol. 29, pp. 73- 87 ,(1999) , 10.1016/S0168-9274(98)00074-9
Giancarlo Benettin, Andrea Carati, Paolo Sempio, On the Landau-Teller approximation for energy exchanges with fast degrees of freedom Journal of Statistical Physics. ,vol. 73, pp. 175- 192 ,(1993) , 10.1007/BF01052756
T. M. O’Neil, P. G. Hjorth, Collisional dynamics of a strongly magnetized pure electron plasma Physics of Fluids. ,vol. 28, pp. 3241- 3252 ,(1985) , 10.1063/1.865322
Giancarlo Benettin, A Carati, Francesco Fassò, On the conservation of adiabatic invariants for a system of coupled rotators Physica D: Nonlinear Phenomena. ,vol. 104, pp. 253- 268 ,(1997) , 10.1016/S0167-2789(97)00295-9
Giancarlo Benettin, Antonio Giorgilli, On the Hamiltonian Interpolation of Near-to-the-Identity Symplectic Mappings with Application to Symplectic Integration Algorithms Journal of Statistical Physics. ,vol. 74, pp. 1117- 1143 ,(1994) , 10.1007/BF02188219
LUDWIG BOLTZMANN, On Certain Questions of the Theory of Gases Nature. ,vol. 51, pp. 413- 415 ,(1895) , 10.1038/051413B0
G. Gallavotti, G. Benettin, A. Carati, A rigorous implementation of the Jeans - Landau - Teller approximation for adiabatic invariants Nonlinearity. ,vol. 10, pp. 479- 505 ,(1997) , 10.1088/0951-7715/10/2/011