Theory of relativistic Brownian motion: The (1 + 1)-dimensional case

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 71, Issue 1, 2005, Pages

  Dunkel, Jörn ^a   Hänggi, Peter ^b  

^a HUMBOLDT UNIVERSITY   (Germany)

^b UNIVERSITY OF AUGSBURG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BROWNIAN PARTICLES; DIFFUSION THEORY; VISCOUS MEDIUM;

DYNAMICS; EQUATIONS OF MOTION; MARKOV PROCESSES; MAXWELL EQUATIONS; NEWTONIAN FLOW; VELOCITY MEASUREMENT; VISCOSITY; WHITE NOISE;

BROWNIAN MOVEMENT;

EID: 41349106368     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.71.016124     Document Type: Article

References (47)

1. A. Einstein, Ann. Phys. (Leipzig) 17, 891 (1905).
2. A. Einstein, Ann. Phys. (Leipzig) 18, 639 (1905).
3. G. Schay, Ph.D. thesis, Princeton University (1961), available through University Microfilms, Ann Arbor, Michigan, https://wwwlib.umi.com
4. R. M. Dudley, Arkiv Feur Matematik 6, 241 (1965).
5. R. Hakim, J. Math. Phys. 6, 1482 (1965).
6. U. Ben-Ya'acov, Phys. Rev. D 23, 1441 (1981).
7. O. Oron and L. P. Horwitz (2003), e-print math-ph/0312003.
8. T. H. Boyer, Phys. Rev. D 19, 1112 (1979).
9. T. H. Boyer, Phys. Rev. D 19, 3635 (1979).
10. F. Guerra and P. Ruggiero, Lett. Nuovo Cimento Soc. Ital. Fis. 23, 529 (1978).
11. L. M. Morato and L. Viola, J. Math. Phys. 36, 4691 (1995); 37, 4769(E) (1996).
12. L. M. Morato and L. Viola, J. Math. Phys. 36, 4691 (1995); 37, 4769(E) (1996).
13. A. Posilicano, Lett. Math. Phys. 42, 85 (1997).
14. J. Franchi and Y. Le Jan (2004), e-print math.PR/0403499.
15. A. Einstein, Ann. Phys. (Leipzig) 17, 549 (1905).
16. A. Einstein and M. von Smoluchowski, Untersuchungen über die Theorie der Brownschen Bewegung/Abhandlungen über die Brownsche Bewegung und verwandte Erscheinungen, 3rd ed. (Harri Deutsch, Frankfurt, 1999), Vol. 199.
17. M. C. Wang and G. E. Uhlenbeck, Rev. Mod. Phys. 17, 323 (1945).
18. G. E. Uhlenbeck and L. S. Ornstein, Phys. Rev. 36, 823 (1930).
19. S. Chandrasekhar, Rev. Mod. Phys. 15, 1 (1943).
20. P. Hänggi and H. Thomas, Phys. Rep. 88, 207 (1982).
21. N. G. Van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 2003).
22. N. Wiener, J. Math. Phys. 58, 131 (1923).
23. M. Grigoriu, Stochastic Calculus: Applications in Science and Engineering (Birkhäuser, Boston, 2002).
24. I. Karatzas and S. E. Shreve, Brownian Motion and Stochastic Calculus, 2nd ed. Graduate Texts in Mathematics Vol. 113 (Springer-Verlag, New York, 1991).
25. F. Jüttner, Ann. Phys. (Leipzig) 34, 856 (1911).
26. S. Weinberg, Gravitation and Cosmology (Wiley, 1972).
27. R. W. Lindquist, Ann. Phys. (N.Y.) 37, 487 (1966).
28. J. M. Stewart, Non-Equilibrium Relativistic Kinetic Theory, Lecture Notes in Physics Vol. 10 (Springer-Verlag, Berlin, 1971).
29. R. L. Liboff, Kinetic Theory (Prentice Hall, Englewood Cliffs, NJ, 1990).
30. S. R. de Groot, W. van Leeuwen, and C. O. van Weert, Relativistic Kinetic Theory: Principles and Applications (North-Holland, Amsterdam, 1980).
31. S. A. Trigger, Phys. Rev. E 67, 046403 (2003).
32. Y. L. Klimontovich, Phys. Usp. 37, 737 (1994).
33. U. Erdmann, W. Ebeling, L. Schimansky-Geier, and F. Schweitzer, Eur. Phys. J. B 15, 105 (2000).
34. K. Ito, Proc. Imp. Acad. Tokyo 20, 519 (1944).
35. K. Ito, Mem. Am. Math. Soc. 4, 51 (1951).
36. F. Schwabl, Statistische Mechanik (Springer, Berlin, 2000).
37. R. L. Stratonovich, Vestn. Mosk. Univ., Ser. 1: Mat., Mekh. 1, 3 (1964).
38. R. L. Stratonovich, SIAM J. Control Optim. 4, 362 (1966).
39. D. Fisk, Ph.D. thesis, Michigan State University, Dept. of Statistics (1963).
40. D. Fisk, Trans. Am. Math. Soc. 120, 369 (1965).
41. P. Hänggi, Helv. Phys. Acta 51, 183 (1978).
42. P. Hänggi, Helv. Phys. Acta 53, 491 (1980).
43. P. Hänggi and H. Thomas, Phys. Rep. 88, 207 (1982), see pp. 292-294.
44. J. L. Synge, The Relativislic Gas (North-Holland, Amsterdam, 1957).
45. P. Hänggi and P. Jung, Adv. Chem. Phys. 89, 239 (1995).
46. F. Debbasch, K. Mallick, and J. P. Rivet, J. Stat. Phys. 88, 945 (1997).
47. F. Debbasch, J. Math. Phys. 45, 2744 (2004).