2,277 research outputs found
Time series irreversibility: a visibility graph approach
We propose a method to measure real-valued time series irreversibility which
combines two differ- ent tools: the horizontal visibility algorithm and the
Kullback-Leibler divergence. This method maps a time series to a directed
network according to a geometric criterion. The degree of irreversibility of
the series is then estimated by the Kullback-Leibler divergence (i.e. the
distinguishability) between the in and out degree distributions of the
associated graph. The method is computationally effi- cient, does not require
any ad hoc symbolization process, and naturally takes into account multiple
scales. We find that the method correctly distinguishes between reversible and
irreversible station- ary time series, including analytical and numerical
studies of its performance for: (i) reversible stochastic processes
(uncorrelated and Gaussian linearly correlated), (ii) irreversible stochastic
pro- cesses (a discrete flashing ratchet in an asymmetric potential), (iii)
reversible (conservative) and irreversible (dissipative) chaotic maps, and (iv)
dissipative chaotic maps in the presence of noise. Two alternative graph
functionals, the degree and the degree-degree distributions, can be used as the
Kullback-Leibler divergence argument. The former is simpler and more intuitive
and can be used as a benchmark, but in the case of an irreversible process with
null net current, the degree-degree distribution has to be considered to
identifiy the irreversible nature of the series.Comment: submitted for publicatio
Demagnetization of Quantum Dot Nuclear Spins: Breakdown of the Nuclear Spin Temperature Approach
The physics of interacting nuclear spins arranged in a crystalline lattice is
typically described using a thermodynamic framework: a variety of experimental
studies in bulk solid-state systems have proven the concept of a spin
temperature to be not only correct but also vital for the understanding of
experimental observations. Using demagnetization experiments we demonstrate
that the mesoscopic nuclear spin ensemble of a quantum dot (QD) can in general
not be described by a spin temperature. We associate the observed deviations
from a thermal spin state with the presence of strong quadrupolar interactions
within the QD that cause significant anharmonicity in the spectrum of the
nuclear spins. Strain-induced, inhomogeneous quadrupolar shifts also lead to a
complete suppression of angular momentum exchange between the nuclear spin
ensemble and its environment, resulting in nuclear spin relaxation times
exceeding an hour. Remarkably, the position dependent axes of quadrupolar
interactions render magnetic field sweeps inherently non-adiabatic, thereby
causing an irreversible loss of nuclear spin polarization.Comment: 15 pages, 3 figure
Kinetic Schemes in Open Interacting Systems
We discuss utilization of kinetic schemes for description of open interacting
systems, focusing on vibrational energy relaxation for an oscillator coupled to
a nonequilibirum electronic bath. Standard kinetic equations with constant rate
coefficients are obtained under the assumption of timescale separation between
system and bath, with the bath dynamics much faster than that of the system of
interest. This assumption may break down in certain limits and we show that
ignoring this may lead to qualitatively wrong predictions. Connection with more
general, nonequilibrium Green's function (NEGF) analysis, is demonstrated. Our
considerations are illustrated within generic molecular junction models with
electron-vibration coupling.Comment: 22 pages, 4 figure
Single-molecule stochastic resonance
Stochastic resonance (SR) is a well known phenomenon in dynamical systems. It
consists of the amplification and optimization of the response of a system
assisted by stochastic noise. Here we carry out the first experimental study of
SR in single DNA hairpins which exhibit cooperatively folding/unfolding
transitions under the action of an applied oscillating mechanical force with
optical tweezers. By varying the frequency of the force oscillation, we
investigated the folding/unfolding kinetics of DNA hairpins in a periodically
driven bistable free-energy potential. We measured several SR quantifiers under
varied conditions of the experimental setup such as trap stiffness and length
of the molecular handles used for single-molecule manipulation. We find that
the signal-to-noise ratio (SNR) of the spectral density of measured
fluctuations in molecular extension of the DNA hairpins is a good quantifier of
the SR. The frequency dependence of the SNR exhibits a peak at a frequency
value given by the resonance matching condition. Finally, we carried out
experiments in short hairpins that show how SR might be useful to enhance the
detection of conformational molecular transitions of low SNR.Comment: 11 pages, 7 figures, supplementary material
(http://prx.aps.org/epaps/PRX/v2/i3/e031012/prx-supp.pdf
Master equations for Wigner functions with spontaneous collapse and their relation to thermodynamic irreversibility
Wigner functions, allowing for a reformulation of quantum mechanics in phase
space, are of central importance for the study of the quantum-classical
transition. A full understanding of the quantum-classical transition, however,
also requires an explanation for the absence of macroscopic superpositions to
solve the quantum measurement problem. Stochastic reformulations of quantum
mechanics based on spontaneous collapses of the wavefunction are a popular
approach to this issue. In this article, we derive the dynamic equations for
the four most important spontaneous collapse models - Ghirardi-Rimini-Weber
(GRW) theory, continuous spontaneous localization (CSL) model, Di\'osi-Penrose
model, and dissipative GRW model - in the Wigner framework. The resulting
master equations are approximated by Fokker-Planck equations. Moreover, we use
the phase-space form of GRW theory to test, via molecular dynamics simulations,
David Albert's suggestion that the stochasticity induced by spontaneous
collapses is responsible for the emergence of thermodynamic irreversibility.
The simulations show that, for initial conditions leading to anti-thermodynamic
behavior in the classical case, GRW-type perturbations do not lead to
thermodynamic behavior. Consequently, the GRW-based equilibration mechanism
proposed by Albert is not observed.Comment: 22 pages, 2 figure
Fundamental Aspects of Quantum Brownian Motion
With this work we elaborate on the physics of quantum noise in thermal
equilibrium and in stationary non-equilibrium. Starting out from the celebrated
quantum fluctuation-dissipation theorem we discuss some important consequences
that must hold for open, dissipative quantum systems in thermal equilibrium.
The issue of quantum dissipation is exemplified with the fundamental problem of
a damped harmonic quantum oscillator. The role of quantum fluctuations is
discussed in the context of both, the nonlinear generalized quantum Langevin
equation and the path integral approach. We discuss the consequences of the
time-reversal symmetry for an open dissipative quantum dynamics and,
furthermore, point to a series of subtleties and possible pitfalls. The path
integral methodology is applied to the decay of metastable states assisted by
quantum Brownian noise.Comment: 13 pages, 4 figures, RevTeX, submitted to Chaos special issue "100
Years of Brownian Motion
Work probability distribution and tossing a biased coin
We show that the rare events present in dissipated work that enters Jarzynski
equality, when mapped appropriately to the phenomenon of large deviations found
in a biased coin toss, are enough to yield a quantitative work probability
distribution for Jarzynski equality. This allows us to propose a recipe for
constructing work probability distribution independent of the details of any
relevant system. The underlying framework, developed herein, is expected to be
of use in modelling other physical phenomena where rare events play an
important role.Comment: 6 pages, 4 figures
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