Electronic dynamics in chains with Ornstein–Uhlenbeck correlated disorder

2020 ◽  
Vol 31 (12) ◽  
pp. 2050176
Author(s):  
J. L. S. Soares ◽  
R. D. dos Santos ◽  
F. J. S. Sousa ◽  
M. O. Sales ◽  
F. A. B. F. Moura
Keyword(s):  
Differential Equation ◽  
Evolution Operator ◽  
Mean Square Displacement ◽  
Time Dependent ◽  
Mean Square ◽  
Strong Correlations ◽  
Uhlenbeck Process ◽  
Electronic Dynamics ◽  
Ornstein Uhlenbeck Process ◽  
The Mean

In this paper, we present a detailed study of the electronic dynamics in systems with correlated disorder generated from the Ornstein–Uhlenbeck process (OU). In short, we used numeric methods for solving the time-dependent Schrödinger equation. We apply a Taylor’s expansion of the evolution operator in order to solve the differential equation. We calculate some typical tools, such as the participation function [Formula: see text], the mean square displacement [Formula: see text] and the probability of return [Formula: see text]. In our analysis, we show that for low correlations the system behaves as in the standard Anderson model (i.e. all eigenstates are localized). For strong correlations, our results suggest the existence of a quasi-ballistic dynamics.

scholarly journals Reconstruction of Diffusion Coefficients and Power Exponents from Single Lagrangian Trajectories

Fluids ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 111
Author(s):  
Leonid M. Ivanov ◽  
Collins A. Collins ◽  
Tetyana Margolina
Keyword(s):  
Black Sea ◽  
Diffusion Coefficients ◽  
Current System ◽  
Mean Square Displacement ◽  
California Current ◽  
The Black Sea ◽  
Mean Square ◽  
California Current System ◽  
The Mean ◽  
Non Gaussian

Using discrete wavelets, a novel technique is developed to estimate turbulent diffusion coefficients and power exponents from single Lagrangian particle trajectories. The technique differs from the classical approach (Davis (1991)’s technique) because averaging over a statistical ensemble of the mean square displacement (<X2>) is replaced by averaging along a single Lagrangian trajectory X(t) = {X(t), Y(t)}. Metzler et al. (2014) have demonstrated that for an ergodic (for example, normal diffusion) flow, the mean square displacement is <X2> = limT→∞τX2(T,s), where τX2 (T, s) = 1/(T − s) ∫0T−s(X(t+Δt) − X(t))2 dt, T and s are observational and lag times but for weak non-ergodic (such as super-diffusion and sub-diffusion) flows <X2> = limT→∞≪τX2(T,s)≫, where ≪…≫ is some additional averaging. Numerical calculations for surface drifters in the Black Sea and isobaric RAFOS floats deployed at mid depths in the California Current system demonstrated that the reconstructed diffusion coefficients were smaller than those calculated by Davis (1991)’s technique. This difference is caused by the choice of the Lagrangian mean. The technique proposed here is applied to the analysis of Lagrangian motions in the Black Sea (horizontal diffusion coefficients varied from 105 to 106 cm2/s) and for the sub-diffusion of two RAFOS floats in the California Current system where power exponents varied from 0.65 to 0.72. RAFOS float motions were found to be strongly non-ergodic and non-Gaussian.

Molecular Dynamics Study of Microscopic Mechanism of Diffusion in Li2SiO3 System

1991 ◽  
Vol 46 (7) ◽  
pp. 616-620 ◽  
Author(s):  
Junko Habasaki
Keyword(s):  
Molecular Dynamics ◽  
Coordination Number ◽  
Md Simulation ◽  
Mean Square Displacement ◽  
Mean Square ◽  
Lithium Ions ◽  
Microscopic Mechanism ◽  
Trapping Model ◽  
The Mean

MD simulation has been performed to learn the microscopic mechanism of diffusion of ions in the Li2SiO3 system. The motion of lithium ions can be explained by the trapping model, where lithium is trapped in the polyhedron and moves with fluctuation of the coordination number. The mean square displacement of lithium was found to correlate well with the net changes in coordination number.

THE EFFECT OF PREMELTING: STUDY FOR SEMI-INFINITE CRYSTALS AND NANO-SYSTEMS

1994 ◽  
Vol 08 (24) ◽  
pp. 3411-3422 ◽  
Author(s):  
W. SCHOMMERS
Keyword(s):  
Pair Correlation ◽  
Mean Square Displacement ◽  
Phonon Density ◽  
Mean Square ◽  
Phonon Density Of States ◽  
Molecular Dynamics Calculations ◽  
Theory Of Melting ◽  
The Mean ◽  
Dynamical Properties ◽  
Reliable Interaction

The effect of premelting is of particular interest in connection with the theory of melting. In this paper, we discuss the structural and dynamical properties of the surfaces of semi-infinite crystals as well as of nano-clusters, which show the effect of premelting. The investigations are based on molecular-dynamics calculations: different models are used for the systematic study of the effect of premelting. In particular, the behaviour of the following functions have been studied: pair correlation function, generalized phonon density of states, and the mean-square displacement as a function of time. The calculations have been done for krypton since for this substance a reliable interaction potential is available.

scholarly journals Hierarchical correction of p-values via an ultrametric tree running Ornstein-Uhlenbeck process

2021 ◽  
Author(s):  
Antoine Bichat ◽  
Christophe Ambroise ◽  
Mahendra Mariadassou
Keyword(s):  
Multiple Testing ◽  
R Package ◽  
Statistical Testing ◽  
Uhlenbeck Process ◽  
Explanatory Variables ◽  
New Associations ◽  
Penalized Estimation ◽  
Ultrametric Tree ◽  
Ornstein Uhlenbeck Process ◽  
The Mean

AbstractStatistical testing is classically used as an exploratory tool to search for association between a phenotype and many possible explanatory variables. This approach often leads to multiple testing under dependence. We assume a hierarchical structure between tests via an Ornstein-Uhlenbeck process on a tree. The process correlation structure is used for smoothing the p-values. We design a penalized estimation of the mean of the Ornstein-Uhlenbeck process for p-value computation. The performances of the algorithm are assessed via simulations. Its ability to discover new associations is demonstrated on a metagenomic dataset. The corresponding R package is available from https://github.com/abichat/zazou.

Non-Markovian effect of the fractional damping environment and Newton’s second law of motion

2018 ◽  
Vol 32 (19) ◽  
pp. 1850210
Author(s):  
Chun-Yang Wang ◽  
Zhao-Peng Sun ◽  
Ming Qin ◽  
Yu-Qing Xu ◽  
Shu-Qin Lv ◽  
...  
Keyword(s):  
Diffusion Process ◽  
Mean Square Displacement ◽  
Dynamical Analysis ◽  
Second Law ◽  
Mean Square ◽  
Fractional Damping ◽  
Dynamical Mechanism ◽  
Brownian Particles ◽  
The Mean ◽  
Dissipative Environments

We report, in this paper, a recent study on the dynamical mechanism of Brownian particles diffusing in the fractional damping environment, where several important quantities such as the mean square displacement (MSD) and mean square velocity are calculated for dynamical analysis. A particular type of backward motion is found in the diffusion process. The reason of it is analyzed intrinsically by comparing with the diffusion in various dissipative environments. Results show that the diffusion in the fractional damping environment obeys the Langevin dynamics which is quite different form what is expected.

Transient Response of a Shear Beam to Correlated Random Boundary Excitation

1977 ◽  
Vol 44 (3) ◽  
pp. 487-491 ◽  
Author(s):  
S. F. Masri ◽  
F. Udwadia
Keyword(s):  
Time Delays ◽  
Spectral Characteristics ◽  
Mean Square Displacement ◽  
Dimensionless Time ◽  
Mean Square ◽  
Random Boundary ◽  
Mean Square Response ◽  
Shear Beam ◽  
The Mean ◽  
Support Motion

The transient mean-square displacement, slope, and relative motion of a viscously damped shear beam subjected to correlated random boundary excitation is presented. The effects of various system parameters including the spectral characteristics of the excitation, the delay time between the beam support motion, and the beam damping have been investigated. Marked amplifications in the mean-square response are shown to occur for certain dimensionless time delays.

scholarly journals Planning of experiments for a nonautonomous ornstein-uhlenbeck process

2012 ◽  
Vol 51 (1) ◽  
pp. 101-113 ◽  
Author(s):  
Vladimír Lacko
Keyword(s):  
Sampling Design ◽  
Information Matrix ◽  
Mean Reversion ◽  
Time Dependent ◽  
Optimal Designs ◽  
Optimal Sampling ◽  
Uhlenbeck Process ◽  
Optimal Sampling Design ◽  
Ornstein Uhlenbeck Process ◽  
Planning Of Experiments

ABSTRACT We study exact optimal designs for processes governed by mean- -reversion stochastic differential equations with a time dependent volatility and known mean-reversion speed. It turns out that any mean-reversion It¯o process has a product covariance structure.We prove the existence of a nondegenerate optimal sampling design for the parameter estimation and derive the information matrix corresponding to the observation of the full path. The results are demonstrated on a process with exponential volatility.

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