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 $w_{nm}$ that form a symmetric matrix. The long time evolution of the system is characterized by a diffusion coefficient $D$. In one dimension it is well known that $D$ can display an abrupt percolation-like transition from diffusion ($D>0$) to sub-diffusion (D=0). A question arises whether such a transition happens in higher dimensions. Numerically $D$ 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 $D$ 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 $\tau_c$ which can greatly exceed mean residence time in any trap, $\tau_c\gg$, and even not being related to it. Asymptotically, on a macroscale transport becomes normal for $t\gg\tau_c$. 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

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