KINETIC EQUATION FOR A GAS WITH LONG-RANGE ATTRACTION

1967 ◽  
Vol 45 (11) ◽  
pp. 3555-3567 ◽  
Author(s):  
R. A. Elliott ◽  
Luis de Sobrino
Keyword(s):  
Kinetic Equation ◽  
Long Range ◽  
Short Range ◽  
Kinetic Equations ◽  
Perturbation Expansion ◽  
Interparticle Distance ◽  
Range Interaction ◽  
Short Range Repulsion ◽  
Self Consistent Field ◽  
Range Force

A classical gas whose particles interact through a weak long-range attraction and a strong short-range repulsion is studied. The Liouville equation is solved as an infinite-order perturbation expansion. The terms in this series are classified by Prigogine-type diagrams according to their order in the ratio of the range of the interaction to the average interparticle distance. It is shown that, provided the range of the short-range force is much less than the average interparticle distance which, in turn, is much less than the range of the long-range force, the terms can be grouped into two classes. The one class, represented by chain diagrams, constitutes the significant contributions of the short-range interaction; the other, represented by ring diagrams, makes up, apart from a self-consistent field term, the significant contributions from the long-range force. These contributions are summed to yield a kinetic equation. The orders of magnitude of the terms in this equation are compared for various ranges of the parameters of the system. Retaining only the dominant terms then produces a set of eight kinetic equations, each of which is valid for a definite range of the parameters of the system.

scholarly journals LEVEL REARRANGEMENT IN EXOTIC ATOMS AND QUANTUM DOTS

2007 ◽  
Vol 21 (22) ◽  
pp. 3765-3781 ◽  
Author(s):  
MONIQUE COMBESCURE ◽  
AVINASH KHARE ◽  
ASHOK K. RAINA ◽  
JEAN-MARC RICHARD ◽  
CAROLE WEYDERT
Keyword(s):  
Quantum Dots ◽  
Long Range ◽  
Short Range ◽  
Condensed Matter ◽  
Attractive Potential ◽  
Condensed Matter Physics ◽  
Exotic Atoms ◽  
Short Range Interaction ◽  
Range Interaction ◽  
Harmonic Confinement

A presentation and a generalization are given of the phenomenon of level rearrangement. This occurs when an attractive long-range potential is perturbed by a short-range attractive potential as its strength is increased. This phenomenon was first discovered in condensed matter physics and has also been studied in the physics of exotic atoms. A similar phenomenon occurs in a model that we propose, inspired by quantum dots, where a short-range interaction is added to a harmonic confinement.

Long-range dispersion-corrected density functional for noncovalent interactions

2019 ◽  
Vol 33 (26) ◽  
pp. 1950300 ◽  
Author(s):  
Hong Tang ◽  
Jianmin Tao
Keyword(s):  
Long Range ◽  
Short Range ◽  
Density Functional ◽  
Intramolecular Interaction ◽  
Noncovalent Interactions ◽  
Molecular Complexes ◽  
Generalized Gradient ◽  
Range Interaction ◽  
Large Size ◽  
Vdw Interaction

Noncovalent interactions are important in determining structures and properties of molecular complexes and biological molecules, and for understanding adsorption processes in chemistry and biological science, and are still challenging to conventional density functional theories. In this work, the recently developed Tao-Mo (TM) meta-GGA (generalized gradient approximation) functional is combined with the D3 scheme of long-range van der Waals (vdW) interaction correction and the parameters of damping function are optimized with the S66[Formula: see text]×[Formula: see text]8 set. The resulting TM-D3 method is applied to the medium-sized molecular set S22 and large size molecular complexes set L7 to calculate intramolecular interaction energies. The TM-D3 method produces the best accuracy for the S22 set with a MAE of 0.2 kcal/mol, improving upon the PBE-D3 (MAE[Formula: see text]=[Formula: see text]0.5 kcal/mol), PBE0-D3 (MAE[Formula: see text]=[Formula: see text]0.5 kcal/mol), TPSS-D3 (MAE[Formula: see text]=[Formula: see text]0.4 kcal/mol), M06L (MAE[Formula: see text]=[Formula: see text]0.8 kcal/mol), and SCAN-D3 (MAE[Formula: see text]=[Formula: see text]0.4 kcal/mol) methods. For the large size set L7, the TM-D3 (MAE[Formula: see text]=[Formula: see text]2.1 kcal/mol) also performs better than the PBE-D3 (MAE[Formula: see text]=[Formula: see text]2.6 kcal/mol), SCAN-D3 (2.5 kcal/mol) and M06L (3.0 kcal/mol), but not accurate than the PBE0-D3 (MAE[Formula: see text]=[Formula: see text]0.8 kcal/mol) and TPSS-D3 (MAE[Formula: see text]=[Formula: see text]1.1 kcal/mol). However, overall, the TM-D3 method performs very well with an error of 2.7% of mean binding of the S22 set and an error of 12.6% of the mean binding of the L7 set for the two typical and important medium and large size molecular complex sets. The success of the dispersion-corrected TM functional benefits from the ability of the plain TM functional to capture the short-range vdW interaction or extend the short-range interaction to the middle range, and the right coupling between the TM and the long-range vdW correction D3 scheme, leading to the improved description of noncovalent interactions.

On Fluids of Particles with Short‐Range Repulsion and Weak Long‐Range Attractive Interaction

1969 ◽  
Vol 10 (8) ◽  
pp. 1442-1454 ◽  
Author(s):  
John B. Jalickee ◽  
Arnold J. F. Siegert ◽  
David J. Vezzetti
Keyword(s):  
Long Range ◽  
Short Range ◽  
Attractive Interaction ◽  
Short Range Repulsion

scholarly journals Longitudinal and transverse coupling in infrared gold nanoantenna arrays: long range versus short range interaction regimes

2011 ◽  
Vol 19 (16) ◽  
pp. 15047 ◽  
Author(s):  
Daniel Weber ◽  
Pablo Albella ◽  
Pablo Alonso-González ◽  
Frank Neubrech ◽  
Han Gui ◽  
...  
Keyword(s):  
Long Range ◽  
Short Range ◽  
Short Range Interaction ◽  
Range Interaction ◽  
Nanoantenna Arrays

scholarly journals Critical Behaviour in Systems in which Long-Range and Short-Range Forces Compete

2019 ◽  
pp. 37-47 ◽  
Author(s):  
S.V. Belim
Keyword(s):  
Critical Exponent ◽  
Long Range ◽  
Critical Exponents ◽  
Short Range ◽  
Asymptotic Series ◽  
Critical Behaviour ◽  
Interaction Parameters ◽  
Theory Approach ◽  
Range Interaction ◽  
Long Range Interaction

Critical behaviour of a range of ferromagnetic materials deviates from the predictions of the Ising, XY and Heisenberg models. Additional long-range forces competing with regular exchange interaction may explain this deviation. These competing interactions lead to new universality classes of critical behaviour. The paper uses the field theory approach to investigate critical behaviour in those systems in which long-range and short-range forces compete. We consider the case when a power function of distance r-D-σ, when 1.5 < σ < 2.0, can describe the long-range forces. There exists a distinctive critical behaviour mode for these values. We derived vertex functions using a two-loop approximation directly in three-dimensional space (D = 3) and, for all values, obtained a linear approximation of asymptotic series in terms of long-range interaction parameters. We applied the Pade --- Borel summation technique to these asymptotic series. We computed stable fixed points and critical exponents as functions of long-range interaction parameters for low relativeefficiency of the long-range interaction. We investigated how critical exponents depend on the factor in the power law and relative long-range interaction intensity. We compared our results to the critical exponent values found experimentally for manganites. We used the experimental critical exponent γ values to compute long-range interaction parameters and then used the long-range interaction parameters to derive the ß exponent values, which we then compared to the experimental values. We show good agreement between our theoretical results and experimental data.

scholarly journals Long-range vector models at large N

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Noam Chai ◽  
Mikhail Goykhman ◽  
Ritam Sinha
Keyword(s):  
Long Range ◽  
Short Range ◽  
Conformal Symmetry ◽  
Vector Model ◽  
Entire Region ◽  
Crossover Point ◽  
Range Interaction ◽  
Large N ◽  
Long Range Interaction ◽  
Range Vector

Abstract We calculate various CFT data for the O(N) vector model with the long-range interaction, working at the next-to-leading order in the 1/N expansion. Our results provide additional evidence for the existence of conformal symmetry at the long-range fixed point, as well as the continuity of the CFT data at the long-range to short-range crossover point s* of the exponent parameter s. We also develop the N > 1 generalization of the recently proposed IR duality between the long-range and the deformed short-range models, providing further evidence for its non-perturbative validity in the entire region d/2 < s < s*.

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