Probability and quanta: why back to Nelson?

• Autorzy: Piotr Garbaczewski
• Języki publikacji: EN

Abstrakty

EN

We establish circumstances under which the dispersion of passive contaminants in a forced flow can be consistently interpreted as a Markovian diffusion process.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1998
• Tom: 43
• Numer: 1
• Strony: 191-199

Daty

wydano

1998

Twórcy

autor

Piotr Garbaczewski

• Institute of Theoretical Physics, University of Wrocław, pl. M. Borna 9, 50-204 Wrocław, Poland

Bibliografia

• [1] Ph. Blanchard and P. Garbaczewski, Natural boundaries for the Smoluchowski equation and affiliated diffusion processes, Phys. Rev. E 49, (1994), 3815.
• [2] K. L. Chung and Z. Zhao, From Brownian Motion to Schrödinger Equation, Springer-Verlag, Berlin, 1995.
• [3] M. Freidlin, Functional Integration and Partial Differential Equations, Princeton University Press, Princeton, 1985.
• [4] P. Garbaczewski, J. R. Klauder and R. Olkiewicz, Schrödinger problem, Lévy processes, and noise in relativistic quantum mechanics, Phys. Rev. E 51, (1995), 4114.
• [5] P. Garbaczewski and R. Olkiewicz, Feynman-Kac kernels in Markovian representations of the Schrödinger interpolating dynamics, J. Math. Phys. 37, (1996), 730.
• [6] P. Garbaczewski, Schrödinger's interpolation problem through Feynman-Kac kernels, Acta Phys. Polon. B 27, (1996), 617.
• [7] P.Garbaczewski and G. Kondrat, Burgers velocity fields and dynamical transport processes, Phys. Rev. Lett. 77, (1996), 2608.
• [8] P. Garbaczewski, G. Kondrat and R. Olkiewicz, Burgers flows as Markovian diffusion processes, Phys. Rev. E 55, (1997), 1401.
• [9] W. Horsthemke and R. Lefever, Noise-Induced Transitions, Springer-Verlag, Berlin, 1984.
• [10] C. Marchioro and M. Pulvirenti, Vortex methods in Two-Dimensional Fluid Dynamics, Lecture Notes in Physics 203, Springer-Verlag, Berlin, 1984.
• [11] E. Nelson, Dynamical Theories of the Brownian Motion, Princeton University Press, Princeton, 1967.
• [12] H. Spohn, Large Scale Dynamics of Interacting Particles, Springer-Verlag, Berlin, 1992.
• [13] H. Risken, The Fokker-Planck Equation, Springer-Verlag, Berlin, 1989.
• [14] E. Schrödinger, Relativistic electron, Ann. Inst. Henri Poincaré, 2, (1932), 269.
• [15] J. C. Zambrini, Variational processes and stochastic versions of mechanics, J. Math. Phys. 27, (1986), 3207.