Anomalous diffusion of a quantum Brownian particle in a one-dimensional molecular chain

2020 ◽  
Vol 102 (3) ◽  
Author(s):  
Sho Nakade ◽  
Kazuki Kanki ◽  
Satoshi Tanaka ◽  
Tomio Petrosky
Keyword(s):  
Anomalous Diffusion ◽  
Brownian Particle ◽  
Molecular Chain ◽  
One Dimensional

scholarly journals Anomalous Diffusion with an Apparently Negative Diffusion Coefficient in a One-Dimensional Quantum Molecular Chain Model

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 506
Author(s):  
Sho Nakade ◽  
Kazuki Kanki ◽  
Satoshi Tanaka ◽  
Tomio Petrosky
Keyword(s):  
Diffusion Coefficient ◽  
Diffusion Constant ◽  
Mean Square Displacement ◽  
Second Law Of Thermodynamics ◽  
Molecular Chain ◽  
Chain Model ◽  
Phase Mixing ◽  
One Dimensional ◽  
The One ◽  
Negative Diffusion

An interesting anomaly in the diffusion process with an apparently negative diffusion coefficient defined through the mean-square displacement in a one-dimensional quantum molecular chain model is shown. Nevertheless, the system satisfies the H-theorem so that the second law of thermodynamics is satisfied. The reason why the “diffusion constant” becomes negative is due to the effect of the phase mixing process, which is a characteristic result of the one-dimensionality of the system. We illustrate the situation where this negative “diffusion constant” appears.

Time-dependent barrier passage of one-dimensional fractional damping reactive system

2018 ◽  
Vol 32 (26) ◽  
pp. 1850285
Author(s):  
Chun-Yang Wang ◽  
Zhao-Peng Sun ◽  
Ming Qing ◽  
Yu-Qing Xu
Keyword(s):  
Transmission Coefficient ◽  
Brownian Particle ◽  
Time Dependent ◽  
Reactive System ◽  
Damping Properties ◽  
Flux Method ◽  
Fractional Damping ◽  
One Dimensional ◽  
Reactive Process ◽  
Insight Into

The time-dependent barrier passage of a Brownian particle diffusing in the fractional damping environment is studied by using the reactive flux method. Characteristic quantities such as the rate constant and stationary transmission coefficient are computed for a thimbleful of insight into the barrier escaping dynamics. Results show that the barrier recrossing of the fractional damping reactive system is obviously weakened. And the nonmonotonic varying of the stationary transmission coefficient reveals a close dependence of the escaping process on the fractional damping properties. The time-dependent barrier passage of one-dimensional fractional damping reactive process is found very similar to the two-dimensional non-Ohmic case.

scholarly journals Typical structure of the program for dynamics of one-dimensional DNA molecular chain simulation and its hardware implementation

2018 ◽  
pp. 1-16
Author(s):  
Sergey Sergeevich Andreev ◽  
Svetlana Alekseevna Dbar ◽  
Aleksey Ottovich Lacis ◽  
Ilya Vyacheslavovich Likhachev ◽  
Elena Aronovna Plotkina ◽  
...  
Keyword(s):  
Hardware Implementation ◽  
Molecular Chain ◽  
Typical Structure ◽  
One Dimensional

scholarly journals Unique continuation principle for the one-dimensional time-fractional diffusion equation

2019 ◽  
Vol 22 (3) ◽  
pp. 644-657 ◽  
Author(s):  
Zhiyuan Li ◽  
Masahiro Yamamoto
Keyword(s):  
Diffusion Equation ◽  
Anomalous Diffusion ◽  
Function Method ◽  
Unique Continuation ◽  
Fractional Diffusion ◽  
Uniqueness Of Solutions ◽  
One Dimensional ◽  
Continuation Principle ◽  
Time Fractional Diffusion Equation ◽  
The One

Abstract This paper deals with the unique continuation of solutions for a one-dimensional anomalous diffusion equation with Caputo derivative of order α ∈ (0, 1). Firstly, the uniqueness of solutions to a lateral Cauchy problem for the anomalous diffusion equation is given via the Theta function method, from which we further verify the unique continuation principle.

scholarly journals Entropic Characterisation of Diffusion

1994 ◽  
Vol 49 (12) ◽  
pp. 1215-1218 ◽  
Author(s):  
R. Stoop ◽  
W.-H. Steeb
Keyword(s):  
Anomalous Diffusion ◽  
Thermodynamic Approach ◽  
One Dimensional ◽  
Unit Cells ◽  
One Dimensional Maps ◽  
Entropy Functions ◽  
Critical Lines

Abstract The thermodynamic approach is applied for the description of normal and anomalous diffusion of one-dimensional maps on a grid of unit cells. The characteristic entropy functions are calculated. For the anomalous cases, the locations of the critical lines are determined.

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