170 research outputs found
Classical open systems with nonlinear nonlocal dissipation and state-dependent diffusion: Dynamical responses and the Jarzynski equality
We have studied dynamical responses and the Jarzynski equality (JE) of
classical open systems described by the generalized Caldeira-Leggett model with
the nonlocal system-bath coupling. In the derived non-Markovian Langevin
equation, the nonlinear nonlocal dissipative term and state-dependent diffusion
term yielding multiplicative colored noise satisfy the fluctuation-dissipation
relation. Simulation results for harmonic oscillator systems have shown the
following: (a) averaged responses of the system to applied sinusoidal
and step forces significantly depend on model parameters of magnitudes of
additive and multiplicative noises and the relaxation time of colored noise,
although stationary marginal probability distribution functions are independent
of them, (b) a combined effect of nonlinear dissipation and multiplicative
colored noise induces enhanced fluctuations for an applied
sinusoidal force, and (c) the JE holds for an applied ramp force independently
of the model parameters with a work distribution function which is (symmetric)
Gaussian and asymmetric non-Gaussian for additive and multiplicative noises,
respectively. It has been shown that the non-Markovian Langevin equation in the
local and over-damped limits is quite different from the widely adopted
phenomenological Markovian Langevin equation subjected to multiplicative noise.Comment: 25 pages, 12 figures, the final version accepted in Phys. Rev.
Brownian Molecules Formed by Delayed Harmonic Interactions
A time-delayed response of individual living organisms to information
exchanged within flocks or swarms leads to the emergence of complex collective
behaviors. A recent experimental setup by (Khadka et al 2018 Nat. Commun. 9
3864), employing synthetic microswimmers, allows to emulate and study such
behavior in a controlled way, in the lab. Motivated by these experiments, we
study a system of N Brownian particles interacting via a retarded harmonic
interaction. For , we characterize its collective behavior
analytically, by solving the pertinent stochastic delay-differential equations,
and for by Brownian dynamics simulations. The particles form
molecule-like non-equilibrium structures which become unstable with increasing
number of particles, delay time, and interaction strength. We evaluate the
entropy and information fluxes maintaining these structures and, to
quantitatively characterize their stability, develop an approximate
time-dependent transition-state theory to characterize transitions between
different isomers of the molecules. For completeness, we include a
comprehensive discussion of the analytical solution procedure for systems of
linear stochastic delay differential equations in finite dimension, and new
results for covariance and time-correlation matrices.Comment: 36 pages, 26 figures, current version: further improvements and one
correctio
Langevin analysis for time-nonlocal Brownian motion with algebraic memories and delay interactions
Starting from a Langevin equation with memory describing the attraction of a particle to
a center, we investigate its transport and response properties corresponding to two
special forms of the memory: one is algebraic, i.e., power-law, and the other involves a
delay. We examine the properties of the Green function of the Langevin equation and
encounter Mittag-Leffler and Lambert W-functions well-known in the literature. In the
presence of white noise, we study two experimental situations, one involving the motional
narrowing of spectral lines and the other the steady-state size of the particle under
consideration. By comparing the results to counterparts for a simple exponential memory,
we uncover instructive similarities and differences. Perhaps surprisingly, we find that
the Balescu-Swenson theorem that states that non-Markoffian equations do not add anything
new to the description of steady-state or equilibrium
observables is violated for our system in that the saturation size of the
particle in the steady-state depends on the memory function utilized. A natural
generalization of the Smoluchowski equation for the time-local case is examined and found
to satisfy the Balescu-Swenson theorem and describe accurately the first moment but not
the second and higher moments. We also calculate two-time correlation functions for all
three cases of the memory, and show how they differ from (tend to) their Markoffian
counterparts at small (large) values of the difference between the two times
Langevin analysis for time-nonlocal Brownian motion with algebraic memories and delay interactions
Starting from a Langevin equation with memory describing the attraction of a particle to
a center, we investigate its transport and response properties corresponding to two
special forms of the memory: one is algebraic, i.e., power-law, and the other involves a
delay. We examine the properties of the Green function of the Langevin equation and
encounter Mittag-Leffler and Lambert W-functions well-known in the literature. In the
presence of white noise, we study two experimental situations, one involving the motional
narrowing of spectral lines and the other the steady-state size of the particle under
consideration. By comparing the results to counterparts for a simple exponential memory,
we uncover instructive similarities and differences. Perhaps surprisingly, we find that
the Balescu-Swenson theorem that states that non-Markoffian equations do not add anything
new to the description of steady-state or equilibrium
observables is violated for our system in that the saturation size of the
particle in the steady-state depends on the memory function utilized. A natural
generalization of the Smoluchowski equation for the time-local case is examined and found
to satisfy the Balescu-Swenson theorem and describe accurately the first moment but not
the second and higher moments. We also calculate two-time correlation functions for all
three cases of the memory, and show how they differ from (tend to) their Markoffian
counterparts at small (large) values of the difference between the two times
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