Asymptotic and numerical analyses for mechanical models of heat baths

Journal of Statistical Physics

Volumn 106, Issue 5-6, 2002, Pages 1121-1184

  Hald, Ole H ^a   Kupferman, Raz ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b HEBREW UNIVERSITY OF JERUSALEM   (Israel)

Author keywords

Generalized Langevin equation; Heat bath; Order reduction; Stiff oscillatory systems; Symplectic Euler scheme; Volterra equation

Indexed keywords

EID: 0036112005     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1014093921790     Document Type: Article

References (24)

1. G. Ford, M. Kac, and P. Mazur, Statistical mechanics of assemblies of coupled oscillators, J. Math. Phys. 6:504-515 (1965).
2. P. Ullersma, An exactly solvable model for Brownian motion: I. Derivation of the Langevin equation, Physica 32:27-55 (1966).
3. J. Lewis and L. Thomas, How to make a heat bath, in Functional Integration and Its Application, A. Arthurs, ed. (Oxford, 1975), pp. 97-123.
4. D. Dürr, S. Goldstein, and J. Lebowitz, Stochastic processes originating in deterministic microscopic dynamics, J. Stat. Phys. 30:519-526 (1983).
5. P. de Smedt, D. Dürr, J. Lebowitz, and C. Liverani, Quantum system in contact with a thermal environment: Rigorous treatment of a simple model, Comm. Math. Phys. 120: 195-231 (1988).
6. A. Stuart and J. Warren, Analysis and experiments for a computational model of a heat bath, J. Stat. Phys. 97:687-723 (1999).
7. B. Cano, A. Stuart, E. Süli, and J. Warren, Stiff oscillatory systems, delta jumps and white noise, Found. Comp. Math. 1:69-100 (2001).
8. B. Cano and A. Stuart, Under-resolved simulations of heat baths, J. Comp. Phys., in press.
9. A. Stuart, J. Terry, and P. Tupper, Constructing SDEs from ODEs with random data, preprint (2001).
10. A. Kast, Optimal prediction of stiff oscillatory mechanics, Proc. Nat. Acad. Sci. USA 97:6253-6257 (2000).
11. A. Chorin, A. Kast, and R. Kupferman, Optimal prediction of underresolved dynamics, Proc. Nat. Acad. Sci. USA 95:4094-4098 (1998).
12. A. Chorin, O. Hald, and R. Kupferman, Optimal prediction and the Mori-Zwanzig representation of irreversible processes, Proc. Nat. Acad. Sci. USA 97:2968-2973 (2000).
13. G. Ford and M. Kac, On the quantum Langevin equation, J. Stat. Phys. 46:803-810 (1987).
14. H. Mori, Transport, collective motion, and Brownian motion, Prog. Theor. Phys. 33:423-450 (1965).
15. R. Zwanzig, Problems in nonlinear transport theory, in Systems far from equilibrium, L. Garrido, ed. (Springer, New York, 1980), pp. 198-225.
16. E. Hairer, S. Norsett, and G. Wanner, Solving Ordinary Differential Equations: Nonstiff Problems (Springer-Verlag, Berlin, 1993).
17. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, New York, 1971).
18. G. Gripenberg, S.-O. Londen, and O. Staffans, Volterra Integral and Functional Equations (Cambridge University Press, Cambridge, 1990).
19. J. Lamperti, Probability: A survey of the Mathematical Theory (Wiley, New York, 1996), 2nd ed.
20. P. Billingsley, Probability and Measure (Wiley, New York, 1995), 3rd ed.
21. R. Miller, Nonlinear Volterra integral equations (Benjamin, Philippines, 1971).
22. J.-P. Aubin, Approximation of Elliptic Boundary-Value Problems (Wiley-Interscience, New York, 1972).
23. P. Linz, A general theory for the approximate solution of operator equations of the second kind, SIAM J. Num. Anal. 14:543-554 (1977).
24. T. Rivlin, The Chebyshev polynomials (Wiley, New York, 1974).