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Long-time tails in continuous-time random walks
Physical Review A, 1990We analyze the long-time behavior of ${\mathit{P}}_{0}$(t), the probability that a random walker is found at the origin at time t after its start. For continuous-time random walks with algebraic waiting-time distributions \ensuremath{\psi}(t)\ensuremath{\sim}${\mathit{t}}^{\mathrm{\ensuremath{-}}1\mathrm{\ensuremath{-}}\ensuremath{\gamma}}$ we find in ...
, Schnörer, , Blumen
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Dynamical continuous time random walk
The European Physical Journal B, 2015We consider a continuous time random walk model in which each jump is considered to be dynamical process. Dissipative launch velocity and hopping time in each jump is the key factor in this model. Within the model, normal diffusion and anomalous diffusion is realized theoretically and numerically in the force free potential. Besides, external potential
Liu, Jian, Yang, B., Chen, X., Bao, J.
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Composite continuous time random walks
The European Physical Journal B, 2017Random walks in composite continuous time are introduced. Composite time flow is the product of translational time flow and fractional time flow [see Chem. Phys. 84, 399 (2002)]. The continuum limit of composite continuous time random walks gives a diffusion equation where the infinitesimal generator of time flow is the sum of a first order and a ...
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Continuous-time random walk under time-dependent resetting
Physical Review E, 2017Continuous-time random walks of a particle that is randomly reset to an initial position are considered. The distribution of the waiting time between the reset events is represented as a sum of an arbitrary number of exponentials. The governing equation of this stochastic process is established.
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1995
Abstract In Chapter 4, we obtained the governing equations of continuous-time random processes by taking a suitable joint limit Δ -→0 and τ -→0 of a lattice random walk, where Δ is the lattice spacing and τ the constant time between successive steps.
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Abstract In Chapter 4, we obtained the governing equations of continuous-time random processes by taking a suitable joint limit Δ -→0 and τ -→0 of a lattice random walk, where Δ is the lattice spacing and τ the constant time between successive steps.
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From Continuous-Time Random Walks to Continuous-Time Quantum Walks: Disordered Networks
2013Recent years have seen a growing interest in dynamical quantum processes; thus it was found that the electronic energy transfer through photosynthetic antennae displays quantum features, aspects also known from the dynamics of charge carriers along polymer backbones.
Mülken, Oliver, Blumen, Alexander
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Continuous-time random walks on random media
Journal of Physics A: Mathematical and General, 1993A continuous-time random-walk method is introduced for applications to transport processes in random media. The method is efficient and is easily parallelizable. It can be used to calculate the diffusivity of homogeneous mixtures of many components, with applications to effective permeability and conductivity measurements.
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Continuous Time Branching Random Walk
1999What is in this chapter? Branching random walks are among the simplest continuous time spatial processes. Consider a system of particles that undergo branching and random motion on a countable graph (such as Z d or a homogeneous tree) according to the two following rules.
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