| F. Langouche, D. Roekaerts, and E. Tirapegui, Discretization problems of functional integrals in phase space, Phys. Rev. D 20, 419-432 (1979). |
....long time macroscopic time event #= u 1)# # 0 , in terms of a Stratonovich path integral over mesoscopic Gaussian conditional probabilities [38 40] Here, macroscopic variables are defined as the long time limit of the evolving mesoscopic system. The corresponding Schr odinger type equation is [39,41] P # = P) GG# (g P) G V , k T # k , g k,G# , G=# [ # . 3) This is properly referred to as a Fokker Planck equation when V # 0. Note that although the partial differential Eq. 3) contains equivalent information regarding M as in the ....
F. Langouche, D. Roekaerts, and E. Tirapegui, "Discretization problems of functional integrals in phase space," Phys. Rev. D 20, pp. 419-432, 1979.
....( G = t = t , A5) the evolution of P : is written as P : t [M , t M 0 , t 0 ] f (t, M) g(t, M) P : G . A6) To perform the stochastic average of Eq. A6) the functional integration by parts lemma [29] is used on an arbitrary function Z ( [181], D: Z( 0 . A7) Applied to Z = Z exp( this yields Z : Z : A8) Applying this to F(M : dM P : F(M ) P : F(M) F(M : M dM F(M) g j ) G , A9) where designates functional differentiation. The ....
F. Langouche, D. Roekaerts, and E. Tirapegui, "Discretization problems of functional integrals in phase space," Phys. Rev. D 20, 419-432 (1979).
....macroscopic time event #= u 1)# # 0 ,in terms of a Stratonovich path integral over mesoscopic Gaussian conditional probabilities [29,54 57] Here, macroscopic variables are defined as the long time limit of the evolving mesoscopic system. The corresponding Schr odinger type equation is [55,56] #P ## = P) GG# (g P) G V , 4) k T # k , k,G# , G =#[ #M . This is properly referred to as a Fokker Planck equation when V # 0. Note that although the partial differential Eq. 4) contains equivalent information regarding M as in the ....
F. Langouche, D. Roekaerts, and E. Tirapegui, Discretization problems of functional integrals in phase space, Phys. Rev. D 20, 419-432 (1979).
....macroscopic time event t u 1 = u 1)# t 0 ,in terms of a Stratonovich path integral over mesoscopic Gaussian conditional probabilities [34 38] Here, macroscopic variables are defined as the long time limit of the evolving mesoscopic system. The corresponding Schr odinger type equation is [36,37] #P #t = P) GG# (g P) G V , # k , k,G# , G =#[ #M . 4) This is properly referred to as a Fokker Planck equation when V # 0. Note that although the partial differential Eq. 4) contains information regarding M as in the stochastic ....
F. Langouche, D. Roekaerts, and E. Tirapegui, "Discretization problems of functional integrals in phase space," Phys. Rev. D, vol. 20, pp. 419-432, 1979.
No context found.
F. Langouche, D. Roekaerts, and E. Tirapegui, Discretization problems of functional integrals in phase space, Phys. Rev. D 20, 419-432 (1979).
No context found.
F. Langouche, D. Roekaerts, and E. Tirapegui, Discretization problems of functional integrals in phase space, Phys. Rev. D 20, 419-432 (1979).
No context found.
F. Langouche, D. Roekaerts, and E. Tirapegui, Discretization problems of functional integrals in phase space, Phys. Rev. D 20, 419-432 (1979).
No context found.
F. Langouche, D. Roekaerts, and E. Tirapegui, Discretization problems of functional integrals in phase space, Phys. Rev. D 20, 419-432 (1979).
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