Solution of a quantum mechanical eigenvalue problem with long range potentials

1979 ◽  
Vol 20 (9) ◽  
pp. 1891-1895 ◽  
Author(s):  
Frank H. Stillinger
Keyword(s):  
Eigenvalue Problem ◽  
Long Range ◽  
Quantum Mechanical

scholarly journals Deterministic chaos, fractals, and quantumlike mechanics in atmospheric flows

1990 ◽  
Vol 68 (9) ◽  
pp. 831-841 ◽  
Author(s):  
A. Mary Selvam
Keyword(s):  
Long Range ◽  
Deterministic Chaos ◽  
Logarithmic Spiral ◽  
Quantum Mechanical ◽  
Energy Structure ◽  
Penrose Tiling ◽  
Atmospheric Flow ◽  
Closed Set ◽  
Atmospheric Flows ◽  
Temporal Correlations

The complex spatiotemporal patterns of atmospheric flows that result from the cooperative existence of fluctuations ranging in size from millimetres to thousands of kilometres are found to exhibit long-range spatial and temporal correlations. These correlations are manifested as the self-similar fractal geometry of the global cloud cover pattern and the inverse power-law form for the atmospheric eddy energy spectrum. Such long-range spatiotemporal correlations are ubiquitous in extended natural dynamical systems and are signatures of deterministic chaos or self-organized criticality. In this paper, a cell dynamical system model for atmospheric flows is developed by consideration of microscopic domain eddy dynamical processes. This nondeterministic model enables formulation of a simple closed set of governing equations for the prediction and description of observed atmospheric flow structure characteristics as follows. The strange-attractor design of the field of deterministic chaos in atmospheric flows consists of a nested continuum of logarithmic spiral circulations that trace out the quasi-periodic Penrose tiling pattern, identified as the quasi-crystalline structure in condensed matter physics. The atmospheric eddy energy structure follows laws similar to quantum mechanical laws. The apparent waveparticle duality that characterizes quantum mechanical laws is attributed to the bimodal phenomenological form of energy display in the bidirectional energy flow that is intrinsic to eddy circulations, e.g., formation of clouds in updrafts and dissipation of clouds in downdrafts that result in the observed discrete cellular geometry of cloud structure.

scholarly journals Magnetic structure ofCu2CdB2O6exhibiting a quantum-mechanical magnetization plateau and classical antiferromagnetic long-range order

2009 ◽  
Vol 80 (10) ◽  
Author(s):  
Masashi Hase ◽  
Andreas Dönni ◽  
Vladimir Yu. Pomjakushin ◽  
Lukas Keller ◽  
Fabia Gozzo ◽  
...  
Keyword(s):  
Magnetic Structure ◽  
Long Range ◽  
Range Order ◽  
Quantum Mechanical ◽  
Long Range Order ◽  
Magnetization Plateau

scholarly journals Quantifying the Long-Range Coupling of Electronic Properties in Proteins with Ab Initio Molecular Dynamics

2020 ◽  
Author(s):  
Zhongyue Yang ◽  
Natalia Hajlasz ◽  
Adam Steeves ◽  
Heather Kulik
Keyword(s):  
Molecular Dynamics ◽  
Mutual Information ◽  
Ab Initio ◽  
Long Range ◽  
Density Functional ◽  
Ab Initio Molecular Dynamics ◽  
Quantum Mechanical ◽  
Charge Distributions ◽  
Small Proteins ◽  
Charged Residues

A delicate interplay of covalent and noncovalent interactions gives proteins their unique ability to flexibly play numerous roles in cellular processes. This interplay is inherently quantum mechanical and highly dynamic in nature. To directly interrogate the evolving nature of the electronic structure of proteins, we carry out 100-ps-scale <i>ab initio</i> molecular dynamics simulations of three representative small proteins with range-separated hybrid density functional theory. We quantify the nature and length-scale of the coupling of residue-specific charge probability distributions in these proteins. While some nonpolar residues exhibit expectedly narrow charge distributions, most polar and charged residues exhibit broad, multimodal distributions. Even for nonpolar residues, we observe sequence-specific deviations corresponding to charge accumulation or depletion that would be challenging to capture in a fixed charge force field. We quantify the effect of residue–residue interactions on charge distributions first with linear cross-correlations. We then show how additional insight can be gained from evaluating the mutual information of charge distributions. We show that a significant number of residues couple most strongly with residues that are distant in both sequence and space over a range of secondary structures including a-helical, b-sheet, disulfide bridging, and lasso motifs. The mutual information analysis is necessary to capture coupling between some polar and charged residues. These analyses are expected to be broadly useful in understanding the mechanisms of long-range charge transfer in proteins and for determining what interactions require a quantum mechanical description for predictive simulation of enzyme mechanism and protein function.

Second Virial Coefficient of Low-density Lithium-7 (7Li) Gas in the Temperature Range 1 K40000 K and Beyond

2021 ◽  
Vol 14 (3) ◽  
pp. 239-247
Keyword(s):  
Long Range ◽  
Short Range ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Quantum Mechanical ◽  
Low Density ◽  
Temperature Range ◽  
Repulsive Potentials ◽  
Repulsive Forces ◽  
Good Agreement

Abstract: The second virial coefficient B for low-dense 7Lithium (7Li) gas is calculated over a wide temperature range 1 K40000 K. In the ‘high’-T limit (600 K45000 K), the classical coefficient, Bcl, and the contribution of the first quantum-mechanical correction, Bqc, are computed from standard expressions, using a suitable binary potential. The classical coefficient, Bcl, together with the Boyle temperature, TB, are determined and their values are in good agreement with previous results. In addition, the interface between the classical and quantum regimes is systematically investigated. Furthermore, the calculation of the quantum-mechanical second virial coefficient, Bq, is evaluated using the Beth-Uhlenbeck formula in the temperature range 1 K500 K. A positive value of Bq indicates that the net interaction energy is repulsive, implying that the short-range repulsive forces dominate the long-range attractive forces. However, quite the opposite occurs for negative values of Bq, which are indicative of net attractive interaction. The general behavior of Bq is similar to the potential energy itself, such that the long-range attractive and the short-range repulsive potentials can be deduced from the measurements of Bq. Keywords: Second virial coefficient, Low-density Lithium-7 Gas, Short-range repulsive forces, Long-range attractive forces. PACS: 51.30.+i.

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