an:01392796
Zbl 0939.35201
Garbaczewski, Piotr; Kondrat, Grzegorz; Olkiewicz, Robert
Schr??dinger's interpolating dynamics and Burgers' flows
EN
Chaos Solitons Fractals 9, No. 1-2, 29-41 (1998).
00054108
1998
j
35R60 35Q53 37L55 81Q50
forced Burgers equation; probabilistic solutions; Schr??dinger interpolation problem; probability density data; chaos
Summary: We discuss a connection (and a proper place in this framework) of the unforced and deterministically forced Burgers equation for local velocity fields of certain flows, with probabilistic solutions of the so-called Schr??dinger interpolation problem. The latter allows us to reconstruct the microscopic dynamics of the system from the available probability density data, or the input-output statistics in the phenomenological situations. An issue of deducing the most likely dynamics (and matter transport) scenario from the given initial and terminal probability density data, appropriate e.g., for studying chaos in terms of density, is here exemplified in conjunction with Born's statistical interpretation postulate in quantum theory, that yields stochastic processes which are compatible with the Schr??dinger picture of free quantum evolution.