1,157 research outputs found
Stochastic modelling of nonlinear dynamical systems
We develop a general theory dealing with stochastic models for dynamical
systems that are governed by various nonlinear, ordinary or partial
differential, equations. In particular, we address the problem how flows in the
random medium (related to driving velocity fields which are generically bound
to obey suitable local conservation laws) can be reconciled with the notion of
dispersion due to a Markovian diffusion process.Comment: in D. S. Broomhead, E. A. Luchinskaya, P. V. E. McClintock and T.
Mullin, ed., "Stochaos: Stochastic and Chaotic Dynamics in the Lakes",
American Institute of Physics, Woodbury, Ny, in pres
Diffusion Process in a Flow
We establish circumstances under which the dispersion of passive contaminants
in a forced, deterministic or random, flow can be consistently interpreted as a
Markovian diffusion process. In case of conservative forcing the repulsive case
only, with bounded from below, is
unquestionably admitted by the compatibility conditions. A class of diffusion
processes is exemplified, such that the attractive forcing is allowed as well,
due to an appropriate compensation coming from the "pressure" term. The
compressible Euler flows form their subclass, when regarded as stochastic
processes. We establish circumstances under which the dispersion of passive
contaminants in a forced, deterministic or random, flow can be consistently
interpreted as a Markovian diffusion process. In case of conservative forcing
the repulsive case only, with bounded
from below, is unquestionably admitted by the compatibility conditions. A class
of diffusion processes is exemplified, such that the attractive forcing is
allowed as well, due to an appropriate compensation coming from the "pressure"
term. The compressible Euler flows form their subclass, when regarded as
stochastic processes.Comment: 10 pages, Late
Quantum dynamics in strong fluctuating fields
A large number of multifaceted quantum transport processes in molecular
systems and physical nanosystems can be treated in terms of quantum relaxation
processes which couple to one or several fluctuating environments. A thermal
equilibrium environment can conveniently be modelled by a thermal bath of
harmonic oscillators. An archetype situation provides a two-state dissipative
quantum dynamics, commonly known under the label of a spin-boson dynamics. An
interesting and nontrivial physical situation emerges, however, when the
quantum dynamics evolves far away from thermal equilibrium. This occurs, for
example, when a charge transferring medium possesses nonequilibrium degrees of
freedom, or when a strong time-dependent control field is applied externally.
Accordingly, certain parameters of underlying quantum subsystem acquire
stochastic character. Herein, we review the general theoretical framework which
is based on the method of projector operators, yielding the quantum master
equations for systems that are exposed to strong external fields. This allows
one to investigate on a common basis the influence of nonequilibrium
fluctuations and periodic electrical fields on quantum transport processes.
Most importantly, such strong fluctuating fields induce a whole variety of
nonlinear and nonequilibrium phenomena. A characteristic feature of such
dynamics is the absence of thermal (quantum) detailed balance.Comment: review article, Advances in Physics (2005), in pres
- âŠ