Non-Gaussian statistics, classical field theory, and realizable Langevin models
The direct-interaction approximation (DIA) to the fourth-order statistic Z {approximately}{l_angle}{lambda}{psi}{sup 2}){sup 2}{r_angle}, where {lambda} is a specified operator and {psi} is a random field, is discussed from several points of view distinct from that of Chen et al. [Phys. Fluids A 1, 1844 (1989)]. It is shown that the formula for Z{sub DIA} already appeared in the seminal work of Martin, Siggia, and Rose (Phys. Rev. A 8, 423 (1973)] on the functional approach to classical statistical dynamics. It does not follow from the original generalized Langevin equation (GLE) of Leith [J. Atmos. Sd. 28, 145 (1971)] and Kraichnan [J. Fluid Mech. 41, 189 (1970)] (frequently described as an amplitude representation for the DIA), in which the random forcing is realized by a particular superposition of products of random variables. The relationship of that GLE to renormalized field theories with non-Gaussian corrections (``spurious vertices``) is described. It is shown how to derive an improved representation, that realizes cumulants through O({psi}{sup 4}), by adding to the GLE a particular non-Gaussian correction. A Markovian approximation Z{sub DIA}{sup M} to Z{sub DIA} is derived. Both Z{sub DIA} and Z{sub DIA}{sup M} incorrectly predict a Gaussian kurtosis for the steady state of a solvable three-mode example.
- Research Organization:
- Princeton Univ., NJ (United States). Plasma Physics Lab.
- Sponsoring Organization:
- USDOE, Washington, DC (United States)
- DOE Contract Number:
- AC02-76CH03073
- OSTI ID:
- 211662
- Report Number(s):
- PPPL--3153; ON: DE96007495
- Country of Publication:
- United States
- Language:
- English
Similar Records
Non-Gaussian statistics, classical field theory, and realizable Langevin models
Virtualities of quarks and gluons in a QCD vacuum and nonlocal condensates within the single instanton approximation
Spin correlation functions in random-exchange {ital s}=1/2 {ital XXZ} chains
Journal Article
·
Wed May 01 00:00:00 EDT 1996
· Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
·
OSTI ID:283825
Virtualities of quarks and gluons in a QCD vacuum and nonlocal condensates within the single instanton approximation
Journal Article
·
Wed Oct 01 00:00:00 EDT 1997
· Physical Review, D
·
OSTI ID:542757
Spin correlation functions in random-exchange {ital s}=1/2 {ital XXZ} chains
Journal Article
·
Sun Mar 31 23:00:00 EST 1996
· Journal of Applied Physics
·
OSTI ID:280003