1,018 research outputs found
Quantum quenches and driven dynamics in a single-molecule device
The nonequilibrium dynamics of molecular devices is studied in the framework
of a generic model for single-molecule transistors: a resonant level coupled by
displacement to a single vibrational mode. In the limit of a broad level and in
the vicinity of the resonance, the model can be controllably reduced to a form
quadratic in bosonic operators, which in turn is exactly solvable. The response
of the system to a broad class of sudden quenches and ac drives is thus
computed in a nonperturbative manner, providing an asymptotically exact
solution in the limit of weak electron-phonon coupling. From the analytic
solution we are able to (1) explicitly show that the system thermalizes
following a local quantum quench, (2) analyze in detail the time scales
involved, (3) show that the relaxation time in response to a quantum quench
depends on the observable in question, and (4) reveal how the amplitude of
long-time oscillations evolves as the frequency of an ac drive is tuned across
the resonance frequency. Explicit analytical expressions are given for all
physical quantities and all nonequilibrium scenarios under study.Comment: 23 pages, 13 figure
Diffusion in sparse networks: linear to semi-linear crossover
We consider random networks whose dynamics is described by a rate equation,
with transition rates that form a symmetric matrix. The long time
evolution of the system is characterized by a diffusion coefficient . In one
dimension it is well known that can display an abrupt percolation-like
transition from diffusion () to sub-diffusion (D=0). A question arises
whether such a transition happens in higher dimensions. Numerically can be
evaluated using a resistor network calculation, or optionally it can be deduced
from the spectral properties of the system. Contrary to a recent expectation
that is based on a renormalization-group analysis, we deduce that is
finite; suggest an "effective-range-hopping" procedure to evaluate it; and
contrast the results with the linear estimate. The same approach is useful for
the analysis of networks that are described by quasi-one-dimensional sparse
banded matrices.Comment: 13 pages, 4 figures, proofed as publishe
Fractional time random walk subdiffusion and anomalous transport with finite mean residence times: faster, not slower
Continuous time random walk (CTRW) subdiffusion along with the associated
fractional Fokker-Planck equation (FFPE) is traditionally based on the premise
of random clock with divergent mean period. This work considers an alternative
CTRW and FFPE description which is featured by finite mean residence times
(MRTs) in any spatial domain of finite size. Transient subdiffusive transport
can occur on a very large time scale which can greatly exceed mean
residence time in any trap, , and even not being related to
it. Asymptotically, on a macroscale transport becomes normal for .
However, mesoscopic transport is anomalous. Differently from viscoelastic
subdiffusion no long-range anti-correlations among position increments are
required. Moreover, our study makes it obvious that the transient subdiffusion
and transport are faster than one expects from their normal asymptotic limit on
a macroscale. This observation has profound implications for anomalous
mesoscopic transport processes in biological cells because of macroscopic
viscosity of cytoplasm is finite
Non-Markovian Random Walks and Non-Linear Reactions: Subdiffusion and Propagating Fronts
We propose a reaction-transport model for CTRW with non-linear reactions and
non-exponential waiting time distributions. We derive non-linear evolution
equation for mesoscopic density of particles. We apply this equation to the
problem of fronts propagation into unstable state of reaction-transport systems
with anomalous diffusion. We have found an explicit expression for the speed of
propagating front in the case of subdiffusion transport.Comment: 7 page
Recommended from our members
Securing Provenance
Provenance describes how an object came to be in its present state. Intelligence dossiers, medical records and corporate financial reports capture provenance information. Many of these applications call for security, but existing security models are not up to the task. Provenance is a causality graph with annotations. The causality graph connects the various participating objects describing the process that produced an object’s present state. Each node represents an object and each edge represents a relationship between two objects. This graph is an immutable directed acyclic graph (DAG). Existing security models do not apply to DAGs nor do they easily extend to DAGs. Any model to control access to the structure of the graph must integrate with existing security models for the objects. We need to develop an access control model tailored to provenance and study how it interacts with existing access control models. This paper frames the problem and identifies issues requiring further research.Engineering and Applied Science
A Method of Intervals for the Study of Diffusion-Limited Annihilation, A + A --> 0
We introduce a method of intervals for the analysis of diffusion-limited
annihilation, A+A -> 0, on the line. The method leads to manageable diffusion
equations whose interpretation is intuitively clear. As an example, we treat
the following cases: (a) annihilation in the infinite line and in infinite
(discrete) chains; (b) annihilation with input of single particles, adjacent
particle pairs, and particle pairs separated by a given distance; (c)
annihilation, A+A -> 0, along with the birth reaction A -> 3A, on finite rings,
with and without diffusion.Comment: RevTeX, 13 pages, 4 figures, 1 table. References Added, and some
other minor changes, to conform with final for
Anomalous biased diffusion in a randomly layered medium
We present analytical results for the biased diffusion of particles moving
under a constant force in a randomly layered medium. The influence of this
medium on the particle dynamics is modeled by a piecewise constant random
force. The long-time behavior of the particle position is studied in the frame
of a continuous-time random walk on a semi-infinite one-dimensional lattice. We
formulate the conditions for anomalous diffusion, derive the diffusion laws and
analyze their dependence on the particle mass and the distribution of the
random force.Comment: 19 pages, 1 figur
Unified description of correlations in double quantum dots
The two-level model for a double quantum dot coupled to two leads, which is
ubiquitously used to describe charge oscillations, transmission-phase lapses
and correlation-induced resonances, is considered in its general form. The
model features arbitrary tunnelling matrix elements among the two levels and
the leads and between the levels themselves (including the effect of
Aharonov-Bohm fluxes), as well as inter-level repulsive interactions. We show
that this model is exactly mapped onto a generalized Anderson model of a single
impurity, where the electrons acquire a pseudo-spin degree of freedom, which is
conserved by the tunnelling but not within the dot. Focusing on the
local-moment regime where the dot is singly occupied, we show that the
effective low-energy Hamiltonian is that of the anisotropic Kondo model in the
presence of a tilted magnetic field. For moderate values of the (renormalized)
field, the Bethe ansatz solution of the isotropic Kondo model allows us to
derive accurate expressions for the dot occupation numbers, and henceforth its
zero-temperature transmission. Our results are in excellent agreement with
those obtained from the Bethe ansatz for the isotropic Anderson model, and with
the functional and numerical renormalization-group calculations of Meden and
Marquardt [Phys. Rev. Lett. 96, 146801 (2006)], which are valid for the general
anisotropic case. In addition we present highly accurate estimates for the
validity of the Schrieffer-Wolff transformation (which maps the Anderson
Hamiltonian onto the low-energy Kondo model) at both the high- and low-magnetic
field limits. Perhaps most importantly, we provide a single coherent picture
for the host of phenomena to which this model has been applied.Comment: 23 pages, 7 figure
Diffusion-limited reactions on a two-dimensional lattice with binary disorder
Reaction-diffusion systems where transition rates exhibit quenched disorder
are common in physical and chemical systems. We study pair reactions on a
periodic two-dimensional lattice, including continuous deposition and
spontaneous desorption of particles. Hopping and desorption are taken to be
thermally activated processes. The activation energies are drawn from a binary
distribution of well depths, corresponding to `shallow' and `deep' sites. This
is the simplest non-trivial distribution, which we use to examine and explain
fundamental features of the system. We simulate the system using kinetic Monte
Carlo methods and provide a thorough understanding of our findings. We show
that the combination of shallow and deep sites broadens the temperature window
in which the reaction is efficient, compared to either homogeneous system. We
also examine the role of spatial correlations, including systems where one type
of site is arranged in a cluster or a sublattice. Finally, we show that a
simple rate equation model reproduces simulation results with very good
accuracy.Comment: 9 pages, 5 figure
- …