65,267 research outputs found
Fine Tuning Classical and Quantum Molecular Dynamics using a Generalized Langevin Equation
Generalized Langevin Equation (GLE) thermostats have been used very
effectively as a tool to manipulate and optimize the sampling of thermodynamic
ensembles and the associated static properties. Here we show that a similar,
exquisite level of control can be achieved for the dynamical properties
computed from thermostatted trajectories. By developing quantitative measures
of the disturbance induced by the GLE to the Hamiltonian dynamics of a harmonic
oscillator, we show that these analytical results accurately predict the
behavior of strongly anharmonic systems. We also show that it is possible to
correct, to a significant extent, the effects of the GLE term onto the
corresponding microcanonical dynamics, which puts on more solid grounds the use
of non-equilibrium Langevin dynamics to approximate quantum nuclear effects and
could help improve the prediction of dynamical quantities from techniques that
use a Langevin term to stabilize dynamics. Finally we address the use of
thermostats in the context of approximate path-integral-based models of quantum
nuclear dynamics. We demonstrate that a custom-tailored GLE can alleviate some
of the artifacts associated with these techniques, improving the quality of
results for the modelling of vibrational dynamics of molecules, liquids and
solids
Concepts of quantum non-Markovianity: a hierarchy
Markovian approximation is a widely-employed idea in descriptions of the
dynamics of open quantum systems (OQSs). Although it is usually claimed to be a
concept inspired by classical Markovianity, the term quantum Markovianity is
used inconsistently and often unrigorously in the literature. In this report we
compare the descriptions of classical stochastic processes and quantum
stochastic processes (as arising in OQSs), and show that there are inherent
differences that lead to the non-trivial problem of characterizing quantum
non-Markovianity. Rather than proposing a single definition of quantum
Markovianity, we study a host of Markov-related concepts in the quantum regime.
Some of these concepts have long been used in quantum theory, such as quantum
white noise, factorization approximation, divisibility, Lindblad master
equation, etc.. Others are first proposed in this report, including those we
call past-future independence, no (quantum) information backflow, and
composability. All of these concepts are defined under a unified framework,
which allows us to rigorously build hierarchy relations among them. With
various examples, we argue that the current most often used definitions of
quantum Markovianity in the literature do not fully capture the memoryless
property of OQSs. In fact, quantum non-Markovianity is highly
context-dependent. The results in this report, summarized as a hierarchy
figure, bring clarity to the nature of quantum non-Markovianity.Comment: Clarifications and references added; discussion of the related
classical hierarchy significantly improved. To appear in Physics Report
Stability measures in metastable states with Gaussian colored noise
We present a study of the escape time from a metastable state of an
overdamped Brownian particle, in the presence of colored noise generated by
Ornstein-Uhlenbeck process. We analyze the role of the correlation time on the
enhancement of the mean first passage time through a potential barrier and on
the behavior of the mean growth rate coefficient as a function of the noise
intensity. We observe the noise enhanced stability effect for all the initial
unstable states used, and for all values of the correlation time
investigated. We can distinguish two dynamical regimes characterized by weak
and strong correlated noise respectively, depending on the value of
with respect to the relaxation time of the system.Comment: 6 pages, 7 figure
Simulations of Noise in Disordered Systems
We use particle dynamics simulations to probe the correlations between noise
and dynamics in a variety of disordered systems, including superconducting
vortices, 2D electron liquid crystals, colloids, domain walls, and granular
media. The noise measurements offer an experimentally accessible link to the
microscopic dynamics, such as plastic versus elastic flow during transport, and
can provide a signature of dynamical reordering transitions in the system. We
consider broad and narrow band noise in transport systems, as well as the
fluctuations of dislocation density in a system near the melting transition.Comment: 12 pages, 9 postscript figures, requires spie.cls. SPIE Conference on
Fluctuations and Noise 2003, invited contributio
Transient Resetting: A Novel Mechanism for Synchrony and Its Biological Examples
The study of synchronization in biological systems is essential for the
understanding of the rhythmic phenomena of living organisms at both molecular
and cellular levels. In this paper, by using simple dynamical systems theory,
we present a novel mechanism, named transient resetting, for the
synchronization of uncoupled biological oscillators with stimuli. This
mechanism not only can unify and extend many existing results on (deterministic
and stochastic) stimulus-induced synchrony, but also may actually play an
important role in biological rhythms. We argue that transient resetting is a
possible mechanism for the synchronization in many biological organisms, which
might also be further used in medical therapy of rhythmic disorders. Examples
on the synchronization of neural and circadian oscillators are presented to
verify our hypothesis.Comment: 17 pages, 7 figure
- …