arXiv subjects

G. Kondrat

Publications and source records attributed to G. Kondrat.

5 recordsLinked to original sources

arXiv1998

Burgers velocity fields and dynamical transport processes

We explore a connection of the forced Burgers equation with the Schrödinger (diffusive) interpolating dynamics in the presence of deterministic external forces. This entails an exploration of the consistency conditions that allow to interpret dispersion of passive contaminants in the Burgers flow as a Markovian diffusion process. In general, the usage of a continuity equation $\partial_tρ=-\nabla (\vec{v}ρ)$, where $\vec{v}=\vec{v}(\vec{x},t)$ stands for the Burgers field and $ρ$ is the density of transported matter, is at variance with the explicit diffusion scenario. Under these circumstances, we give a complete characterisation of the diffusive matter transport that is governed by Burgers velocity fields. The result extends both to the approximate description of the transport driven by an incompressible fluid and to motions in an infinitely compressible medium.

cond-mat↗

arXiv1998

Burgers' Flows as Markovian Diffusion Processes

We analyze the unforced and deterministically forced Burgers equation in the framework of the (diffusive) interpolating dynamics that solves the so-called Schrödinger boundary data problem for the random matter transport. This entails an exploration of the consistency conditions that allow to interpret dispersion of passive contaminants in the Burgers flow as a Markovian diffusion process. In general, the usage of a continuity equation $\partial_tρ=-\nabla (\vec{v}ρ)$, where $\vec{v}=\vec{v}(\vec{x},t)$ stands for the Burgers field and $ρ$ is the density of transported matter, is at variance with the explicit diffusion scenario. Under these circumstances, we give a complete characterisation of the diffusive transport that is governed by Burgers velocity fields. The result extends both to the approximate description of the transport driven by an incompressible fluid and to motions in an infinitely compressible medium. Also, in conjunction with the Born statistical postulate in quantum theory, it pertains to the probabilistic (diffusive) counterpart of the Schrödinger picture quantum dynamics.

cond-mat↗

arXiv1997

Schroedinger's Interpolating Dynamics and Burgers' Flows

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 Schrödinger interpolation problem. The latter allows 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 densities, is here exemplified in conjunction with Born's statistical interpretation postulate in quantum theory, that yields stochastic processes which are compatible with the Schrödinger picture free quantum evolution.

quant-ph↗

arXiv1996

Burgers Velocity Fields and the Electromagnetic Forcing in Schroedinger's Interpolating Dynamics

We explore a connection of the deterministically forced Burgers equation for local velocity fields with probabilistic solutions of the Schrödinger boundary data problem. An issue of deducing the most likely interpolating dynamics from the given initial and terminal probability density data is here investigated to give account of the perturbation by external electromagnetic fields. A suitable extension of the Hopf-Cole logarithmic transformation allows to deal with nonconservative drift fields and implies the validity of appropriately generalised heat equations, which completely determine the dynamics.

chao-dyn↗

arXiv1995

On Uniqueness of the Jump Process in Quantum Measurement Theory

We prove that, contrary to the standard quantum theory of continuous observation, in the formalism of Event Enhanced Quantum Theory the stochastic process generating individual sample histories of pairs (observed quantum system, observing classical apparatus) is unique. This result gives a rigorous basis to the previous heuristic argument of Blanchard and Jadczyk. Possible implications of this result are discussed.

quant-ph↗