2,414 research outputs found
Ergodic properties of quasi-Markovian generalized Langevin equations with configuration dependent noise and non-conservative force
We discuss the ergodic properties of quasi-Markovian stochastic differential
equations, providing general conditions that ensure existence and uniqueness of
a smooth invariant distribution and exponential convergence of the evolution
operator in suitably weighted spaces, which implies the validity
of central limit theorem for the respective solution processes. The main new
result is an ergodicity condition for the generalized Langevin equation with
configuration-dependent noise and (non-)conservative force
Nonequilibrium polarity-induced mechanism for chemotaxis: emergent Galilean symmetry and exact scaling exponents
A generically observed mechanism that drives the self-organization of living
systems is interaction via chemical signals among the individual elements --
which may represent cells, bacteria, or even enzymes. Here we propose a novel
mechanism for such interactions, in the context of chemotaxis, which originates
from the polarity of the particles and which generalizes the well-known
Keller--Segel interaction term. We study the resulting large-scale dynamical
properties of a system of such chemotactic particles using the exact stochastic
formulation of Dean and Kawasaki along with dynamical renormalization group
analysis of the critical state of the system. At this critical point, an
emergent "Galilean" symmetry is identified, which allows us to obtain the
dynamical scaling exponents exactly; these exponents reveal superdiffusive
density fluctuations and non-Poissonian number fluctuations. We expect our
results to shed light on how molecular regulation of chemotactic circuits can
determine large-scale behavior of cell colonies and tissues.Comment: The first three authors contributed equall
Stochastic interpretation of Kadanoff-Baym equations and their relation to Langevin processes
In this more pedagogical study we want to elucidate on stochastic aspects
inherent to the (non-)equilibrium real time Green's function description (or
`closed time path Green's function' -- CTPGF) of transport equations, the so
called `Kadanoff-Baym equations'. As a toy model we couple a free scalar boson
quantum field to an exemplaric heat bath with some given temperature T. It will
be shown in detail that the emerging transport equations have to be understood
as the ensemble average over stochastic equations of Langevin type. This
corresponds to the equivalence of the influence functional approach by Feynman
and Vernon and the CTP technique. The former, however, gives a more intuitive
physical picture. In particular the physical role of (quantum) noise and the
connection of its correlation kernel to the Kadanoff-Baym equations will be
discussed. The inherent presence of noise and dissipation related by the
fluctuation-dissipation theorem guarantees that the modes or particles become
thermally populated on average in the long-time limit. For long wavelength
modes with momenta much less than the temperature the emerging wave equation do
behave nearly as classical. On the other hand, a kinetic transport description
can be obtained in the semi-classical particle regime. Including fluctuations,
its form resembles that of a phenomenological Boltzmann-Langevin description.
However, we will point out some severe discrepancies in comparison to the
Boltzmann- Langevin scheme. As a further byproduct we also note how the
occurrence of so called pinch singularities is circumvented by a clear physical
necessity of damping within the one-particle propagator.Comment: 57 pages, Revtex, 2 figure
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