348 research outputs found
Quantum transport on small-world networks: A continuous-time quantum walk approach
We consider the quantum mechanical transport of (coherent) excitons on
small-world networks (SWN). The SWN are build from a one-dimensional ring of N
nodes by randomly introducing B additional bonds between them. The exciton
dynamics is modeled by continuous-time quantum walks and we evaluate
numerically the ensemble averaged transition probability to reach any node of
the network from the initially excited one. For sufficiently large B we find
that the quantum mechanical transport through the SWN is, first, very fast,
given that the limiting value of the transition probability is reached very
quickly; second, that the transport does not lead to equipartition, given that
on average the exciton is most likely to be found at the initial node.Comment: 8 pages, 8 figures (high quality figures available upon request
Kinetic Regimes and Cross-Over Times in Many-Particle Reacting Systems
We study kinetics of single species reactions ("A+A -> 0") for general local
reactivity Q and dynamical exponent z (rms displacement x_t ~ t^{1/z}.) For
small molecules z=2, whilst z=4,8 for certain polymer systems. For dimensions d
above the critical value d_c=z, kinetics are always mean field (MF). Below d_c,
the density n_t initially follows MF decay, n_0 - n_t ~ n_0^2 Q t. A 2-body
diffusion-controlled regime follows for strongly reactive systems (Q>Qstar ~
n_0^{(z-d)/d}) with n_0 - n_t ~ n_0^2 x_t^d. For Q<Qstar, MF kinetics persist,
with n_t ~ 1/Qt. In all cases n_t ~ 1/x_t^d at the longest times. Our analysis
avoids decoupling approximations by instead postulating weak physically
motivated bounds on correlation functions.Comment: 10 pages, 1 figure, uses bulk2.sty, minor changes, submitted to
Europhysics Letter
An Iterative Method Based on Fractional Derivatives for Solving Nonlinear Equations
The theory of fractional order derivatives are almost as old as the integer-order [5]. There are many applications, for example in physics [1], [2], [6], finance [8], [9] or
biology [3]. Our aim is not to use fractional order operators to modeling such things, we only will use them as a device to prove a theoretical mathematical statement.
In this work our goal is to find a solution numerically for the equation A(u) = f . If we assume that u is time-dependent, then one can do this by finding a stationary
solution of the equation ¶tu(t)
Efficiency of quantum and classical transport on graphs
We propose a measure to quantify the efficiency of classical and quantum
mechanical transport processes on graphs. The measure only depends on the
density of states (DOS), which contains all the necessary information about the
graph. For some given (continuous) DOS, the measure shows a power law behavior,
where the exponent for the quantum transport is twice the exponent of its
classical counterpart. For small-world networks, however, the measure shows
rather a stretched exponential law but still the quantum transport outperforms
the classical one. Some finite tree-graphs have a few highly degenerate
eigenvalues, such that, on the other hand, on them the classical transport may
be more efficient than the quantum one.Comment: 5 pages, 3 figure
Kinetics of stochastically-gated diffusion-limited reactions and geometry of random walk trajectories
In this paper we study the kinetics of diffusion-limited, pseudo-first-order
A + B -> B reactions in situations in which the particles' intrinsic
reactivities vary randomly in time. That is, we suppose that the particles are
bearing "gates" which interchange randomly and independently of each other
between two states - an active state, when the reaction may take place, and a
blocked state, when the reaction is completly inhibited. We consider four
different models, such that the A particle can be either mobile or immobile,
gated or ungated, as well as ungated or gated B particles can be fixed at
random positions or move randomly. All models are formulated on a
-dimensional regular lattice and we suppose that the mobile species perform
independent, homogeneous, discrete-time lattice random walks. The model
involving a single, immobile, ungated target A and a concentration of mobile,
gated B particles is solved exactly. For the remaining three models we
determine exactly, in form of rigorous lower and upper bounds, the large-N
asymptotical behavior of the A particle survival probability. We also realize
that for all four models studied here such a probalibity can be interpreted as
the moment generating function of some functionals of random walk trajectories,
such as, e.g., the number of self-intersections, the number of sites visited
exactly a given number of times, "residence time" on a random array of lattice
sites and etc. Our results thus apply to the asymptotical behavior of the
corresponding generating functions which has not been known as yet.Comment: Latex, 45 pages, 5 ps-figures, submitted to PR
Assessing phytoplankton nutritional status and potential impact of wet deposition in seasonally oligotrophic waters of the Mid‐Atlantic Bight
Author Posting. © American Geophysical Union, 2018. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Geophysical Research Letters 45 (2018): 3203-3211, doi:10.1002/2017GL075361.To assess phytoplankton nutritional status in seasonally oligotrophic waters of the southern Mid‐Atlantic Bight, and the potential for rain to stimulate primary production in this region during summer, shipboard bioassay experiments were performed using natural seawater and phytoplankton collected north and south of the Gulf Stream. Bioassay treatments comprised iron, nitrate, iron + nitrate, iron + nitrate + phosphate, and rainwater. Phytoplankton growth was inferred from changes in chlorophyll a, inorganic nitrogen, and carbon‐13 uptake, relative to unamended control treatments. Results indicated the greatest growth stimulation by iron + nitrate + phosphate, intermediate growth stimulation by rainwater, modest growth stimulation by nitrate and iron + nitrate, and no growth stimulation by iron. Based on these data and analysis of seawater and atmospheric samples, nitrogen was the proximate limiting nutrient, with a secondary limitation imposed by phosphorus. Our results imply that summer rain events increase new production in these waters by contributing nitrogen and phosphorus, with the availability of the latter setting the upper limit on rain‐stimulated new production.US National Science Foundation Grant Numbers: OCE‐1260454, OCE‐1260454, OCE‐12605742018-09-1
Simulations for trapping reactions with subdiffusive traps and subdiffusive particles
While there are many well-known and extensively tested results involving
diffusion-limited binary reactions, reactions involving subdiffusive reactant
species are far less understood. Subdiffusive motion is characterized by a mean
square displacement with . Recently we
calculated the asymptotic survival probability of a (sub)diffusive
particle () surrounded by (sub)diffusive traps () in one
dimension. These are among the few known results for reactions involving
species characterized by different anomalous exponents. Our results were
obtained by bounding, above and below, the exact survival probability by two
other probabilities that are asymptotically identical (except when
and ). Using this approach, we were not able to
estimate the time of validity of the asymptotic result, nor the way in which
the survival probability approaches this regime. Toward this goal, here we
present a detailed comparison of the asymptotic results with numerical
simulations. In some parameter ranges the asymptotic theory describes the
simulation results very well even for relatively short times. However, in other
regimes more time is required for the simulation results to approach asymptotic
behavior, and we arrive at situations where we are not able to reach asymptotia
within our computational means. This is regrettably the case for
and , where we are therefore not able to prove
or disprove even conjectures about the asymptotic survival probability of the
particle.Comment: 15 pages, 10 figures, submitted to Journal of Physics: Condensed
Matter; special issue on Chemical Kinetics Beyond the Textbook: Fluctuations,
Many-Particle Effects and Anomalous Dynamics, eds. K.Lindenberg, G.Oshanin
and M.Tachiy
Levy flights in quenched random force fields
Levy flights, characterized by the microscopic step index f, are for f<2 (the
case of rare events) considered in short range and long range quenched random
force fields with arbitrary vector character to first loop order in an
expansion about the critical dimension 2f-2 in the short range case and the
critical fall-off exponent 2f-2 in the long range case. By means of a dynamic
renormalization group analysis based on the momentum shell integration method,
we determine flows, fixed point, and the associated scaling properties for the
probability distribution and the frequency and wave number dependent diffusion
coefficient. Unlike the case of ordinary Brownian motion in a quenched force
field characterized by a single critical dimension or fall-off exponent d=2,
two critical dimensions appear in the Levy case. A critical dimension (or
fall-off exponent) d=f below which the diffusion coefficient exhibits anomalous
scaling behavior, i.e, algebraic spatial behavior and long time tails, and a
critical dimension (or fall-off exponent) d=2f-2 below which the force
correlations characterized by a non trivial fixed point become relevant. As a
general result we find in all cases that the dynamic exponent z, characterizing
the mean square displacement, locks onto the Levy index f, independent of
dimension and independent of the presence of weak quenched disorder.Comment: 27 pages, Revtex file, 17 figures in ps format attached, submitted to
Phys. Rev.
Exact asymptotics for non-radiative migration-accelerated energy transfer in one-dimensional systems
We study direct energy transfer by multipolar or exchange interactions
between diffusive excited donor and diffusive unexcited acceptors. Extending
over the case of long-range transfer of an excitation energy a non-perturbative
approach by Bray and Blythe [Phys. Rev. Lett. 89, 150601 (2002)], originally
developed for contact diffusion-controlled reactions, we determine exactly
long-time asymptotics of the donor decay function in one-dimensional systems.Comment: 16 page
Order statistics of the trapping problem
When a large number N of independent diffusing particles are placed upon a
site of a d-dimensional Euclidean lattice randomly occupied by a concentration
c of traps, what is the m-th moment of the time t_{j,N} elapsed
until the first j are trapped? An exact answer is given in terms of the
probability Phi_M(t) that no particle of an initial set of M=N, N-1,..., N-j
particles is trapped by time t. The Rosenstock approximation is used to
evaluate Phi_M(t), and it is found that for a large range of trap
concentracions the m-th moment of t_{j,N} goes as x^{-m} and its variance as
x^{-2}, x being ln^{2/d} (1-c) ln N. A rigorous asymptotic expression (dominant
and two corrective terms) is given for for the one-dimensional
lattice.Comment: 11 pages, 7 figures, to be published in Phys. Rev.
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