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.

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

2021 ◽  
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 of 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.

scholarly journals Strong-coupling ansatz for the one-dimensional Fermi gas in a harmonic potential

2015 ◽  
Vol 1 (6) ◽  
pp. e1500197 ◽  
Author(s):  
Jesper Levinsen ◽  
Pietro Massignan ◽  
Georg M. Bruun ◽  
Meera M. Parish
Keyword(s):  
Fermi Gas ◽  
Harmonic Potential ◽  
Chain Model ◽  
Many Body ◽  
Exact Methods ◽  
One Dimensional ◽  
Heisenberg Spin Chain ◽  
Precise Knowledge ◽  
Short Range Repulsion ◽  
The One

A major challenge in modern physics is to accurately describe strongly interacting quantum many-body systems. One-dimensional systems provide fundamental insights because they are often amenable to exact methods. However, no exact solution is known for the experimentally relevant case of external confinement. We propose a powerful ansatz for the one-dimensional Fermi gas in a harmonic potential near the limit of infinite short-range repulsion. For the case of a single impurity in a Fermi sea, we show that our ansatz is indistinguishable from numerically exact results in both the few- and many-body limits. We furthermore derive an effective Heisenberg spin-chain model corresponding to our ansatz, valid for any spin-mixture, within which we obtain the impurity eigenstates analytically. In particular, the classical Pascal’s triangle emerges in the expression for the ground-state wave function. As well as providing an important benchmark for strongly correlated physics, our results are relevant for emerging quantum technologies, where a precise knowledge of one-dimensional quantum states is paramount.

scholarly journals Nonequilibrium Time Reversibility with Maps and Walks

Entropy ◽  
2022 ◽  
Vol 24 (1) ◽  
pp. 78
Author(s):  
William Graham Hoover ◽  
Carol Griswold Hoover ◽  
Edward Ronald Smith
Keyword(s):  
Piecewise Linear ◽  
Second Law Of Thermodynamics ◽  
Model Systems ◽  
Computational Time ◽  
Nonequilibrium Systems ◽  
Time Reversibility ◽  
One Dimensional ◽  
Fractal Properties ◽  
Dynamical Simulations ◽  
The One

Time-reversible dynamical simulations of nonequilibrium systems exemplify both Loschmidt’s and Zermélo’s paradoxes. That is, computational time-reversible simulations invariably produce solutions consistent with the irreversible Second Law of Thermodynamics (Loschmidt’s) as well as periodic in the time (Zermélo’s, illustrating Poincaré recurrence). Understanding these paradoxical aspects of time-reversible systems is enhanced here by studying the simplest pair of such model systems. The first is time-reversible, but nevertheless dissipative and periodic, the piecewise-linear compressible Baker Map. The fractal properties of that two-dimensional map are mirrored by an even simpler example, the one-dimensional random walk, confined to the unit interval. As a further puzzle the two models yield ambiguities in determining the fractals’ information dimensions. These puzzles, including the classical paradoxes, are reviewed and explored here.

ESR Study of Electrochemically Doped Chalcogenide Nanotubes

2003 ◽  
Vol 775 ◽  
Author(s):  
Denis Arcon ◽  
Andrej Zorko ◽  
Pavel Cevc ◽  
Ales Mrzel ◽  
Maja Remskar ◽  
...  
Keyword(s):  
Room Temperature ◽  
Electrochemical Activity ◽  
Chain Model ◽  
Heisenberg Chain ◽  
One Dimensional ◽  
Narrow Component ◽  
Broad Component ◽  
X Band ◽  
Heavily Doped ◽  
The One

AbstractElectrochemical activity of differently pretreated single-wall subnanometer-diameter molybdenum disulfide tubes (nMoS2) was tested and compared with layered MoS2 material. In as prepared and de-iodized nMoS2 samples a significant increase in the charge capacity has been found compared to the one measured in dispersed nMoS2 or layered MoS2. Enhanced electrochemical activity has been attributed to a particular one-dimensional topology of nanotubes bundles. Electrochemically doped samples were then studied with X-band ESR. While undoped nMoS2 show no X-band ESR signal between room temperature and 4 K we found in heavily doped nMoS2 samples two distinct ESR components: a narrow component with a linewidth of few Guass and a broad component with a linewidth of more than 800 G. The broad ESR component is characteristic of Mo d-orbital-derived band. The temperature dependence of the ESR spin susceptibility and the linewidth of the broad ESR component can be discussed either in terms of conducting electrons coupled to defects or in terms of random-exchange Mo Heisenberg chain model.

Electronic Structure of One-Dimensional Biradical Molecular Chain

2014 ◽  
Vol 1605 ◽  
Author(s):  
H. Koike ◽  
K. Ogawa ◽  
T. Kubo ◽  
K. Uchida ◽  
M. Chikamatsu ◽  
...  
Keyword(s):  
Electronic Structure ◽  
Band Structure ◽  
Photoelectron Spectroscopy ◽  
Organic Molecules ◽  
Molecular Chain ◽  
Ultraviolet Photoelectron Spectroscopy ◽  
Deposition Method ◽  
One Dimensional ◽  
The One

ABSTRACTWe investigated electronic structure of one-dimensional biradical molecular chain which is constructed by exploiting the covalency between organic molecules of a diphenyl derivative of s-indacenodiphenalene (Ph2-IDPL). To control the crystallinity, we used gas deposition method. Ultraviolet photoelectron spectroscopy (UPS) revealed developed band structure with wide dispersion of the one-dimensional biradical molecular chain.

scholarly journals A New Diffusion Scheme for Numerical Models Based on Full Irreversibility

2009 ◽  
Vol 24 (2) ◽  
pp. 595-600 ◽  
Author(s):  
C. Liu ◽  
Y. Liu ◽  
H. Xu
Keyword(s):  
Numerical Models ◽  
Weather Prediction ◽  
Forecast Accuracy ◽  
Second Law Of Thermodynamics ◽  
New Physics ◽  
Numerical Weather Prediction Model ◽  
One Dimensional ◽  
Diffusion Scheme ◽  
The One ◽  
Mean Square Errors

Abstract In this work, the forecast accuracy of a numerical weather prediction model is improved by emulating physical dissipation as suggested by the second law of thermodynamics, which controls the irreversible evolutionary direction of a many-body system like the atmosphere. The ability of the new physics-based scheme to improve model accuracy is demonstrated via the case of the one-dimensional viscous Burgers equation and the one-dimensional diffusion equation, as well as a series of numerical simulations of the well-known 1998 successive torrential rains along the Yangtze River valley and 365 continuous 24-h simulations during 2005–06 with decreased root-mean-square errors and improved forecasts in all of the simulations.

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