Energy exchange, localization, and transfer in nanoscale systems (weak-coupling approximation)

2012 ◽  
Vol 6 (4) ◽  
pp. 563-581 ◽  
Author(s):  
L. I. Manevich
Keyword(s):  
Weak Coupling ◽  
Energy Exchange ◽  
Nanoscale Systems ◽  
Coupling Approximation ◽  
Weak Coupling Approximation

Non-linear Convection at High Rayleigh Number

1970 ◽  
Vol 1 (8) ◽  
pp. 382-383 ◽  
Author(s):  
R. Van Der Borght
Keyword(s):  
Rayleigh Number ◽  
Numerical Solution ◽  
Asymptotic Method ◽  
Weak Coupling ◽  
Coupling Approximation ◽  
Non Linear ◽  
Weak Coupling Approximation ◽  
Basic Equations ◽  
Rayleigh Numbers ◽  
Steady Convection

The numerical solution of the basic equations for non-linear steady convection in the weak-coupling approximation is exceedingly difficult. In astronomical applications the Rayleigh number R will be of the order of1012, and we wish to report here some results obtained in the case of high Rayleigh numbers with the use of an asymptotic method.

Boundary conditions, gauge fixing ambiguities and exact expectation values in U(1) lattice gauge theory

2016 ◽  
Vol 31 (08) ◽  
pp. 1650035
Author(s):  
Carlos Pinto
Keyword(s):  
Gauge Theory ◽  
Boundary Conditions ◽  
Weak Coupling ◽  
Lattice Gauge Theory ◽  
Exact Results ◽  
Feynman Gauge ◽  
Lattice Gauge ◽  
Coupling Approximation ◽  
Gauge Fixing ◽  
Weak Coupling Approximation

We analyze the interplay between gauge fixing and boundary conditions in two-dimensional U(1) lattice gauge theory. We show on the basis of a general argument that periodic boundary conditions result in an ill-defined weak coupling approximation but that the approximation can be made well-defined if the boundaries are fixed to zero. We confirm this result in the particular case of the Feynman gauge. We show that the zero momentum mode divergence in the propagator that appears in the Feynman gauge vanishes when the weak coupling approximation is well-defined. In addition we obtain exact results (for arbitrary coupling), including finite size corrections, for the partition function and for general one-point and two-point functions in the axial gauge under both periodic and zero boundary conditions and confirm these results numerically. The dependence of these objects on both lattice size and coupling constant is investigated using specific examples. These exact results may provide insight into similar gauge fixing issues in more complex models.

Multiple spatial scaling and the weak-coupling approximation. Part 1. General formulation and equilibrium theory

1976 ◽  
Vol 15 (2) ◽  
pp. 223-238 ◽  
Author(s):  
Paul E. Kleinsmith
Keyword(s):  
Correlation Function ◽  
Cluster Expansion ◽  
Weak Coupling ◽  
Formal Solution ◽  
Bbgky Hierarchy ◽  
Distribution Functions ◽  
Spatial Scaling ◽  
Particle Correlation ◽  
Coupling Approximation ◽  
Weak Coupling Approximation

Multiple spatial scaling is incorporated in a modified form of the Bogoliubov plasma cluster expansion; then this proposed reformulation of the plasma weak- coupling approximation is used to derive, from the BBGKY Hierarchy, a decoupled set of equations for the one- and two-particle distribution functions in the limit as the plasma parameter goes to zero. Because the reformulated cluster expansion permits retention of essential two-particle collisional information in the limiting equations, while simultaneously retaining the well-established Debye-scale relative ordering of the correlation functions, decoupling of the Hierarchy is accomplished without introduction of the divergence problems encountered in the Bogoliubov theory, as is indicated by an exact solution of the limiting equations for the equilibrium case. To establish additional links with existing plasma equilibrium theories, the two-particle equilibrium correlation function is used to calculate the interaction energy and the equation of state. The limiting equation for the equilibrium three-particle correlation function is then developed, and a formal solution is obtained.

Multiple spatial scaling and the weak coupling approximation. Part 2. Homogeneous kinetic equation

1977 ◽  
Vol 18 (1) ◽  
pp. 99-111 ◽  
Author(s):  
P. E. Kleinsmith
Keyword(s):  
Kinetic Equation ◽  
Cluster Expansion ◽  
Weak Coupling ◽  
Bbgky Hierarchy ◽  
Spatial Scaling ◽  
Plasma Cluster ◽  
Coupling Approximation ◽  
Weak Coupling Approximation ◽  
Divergence Free

A modified form of the Bogoliubov plasma cluster expansion is applied to the derivation of a divergence-free kinetic equation from the BBGKY hierarchy. Special attention is given to the conditions under which the Landau kinetic equation may be derived from this more general formulation.

Derivation and properties of a Balescu–Lenard like equation for stationary plasma turbulence in the weak-coupling approximation

1975 ◽  
Vol 14 (1) ◽  
pp. 153-167 ◽  
Author(s):  
Guy Pelletier ◽  
Claude Pomot
Keyword(s):  
Kinetic Equation ◽  
Weak Coupling ◽  
Turbulent Plasma ◽  
Particle Model ◽  
Stationary Plasma ◽  
Coupling Approximation ◽  
Weak Coupling Approximation ◽  
Maxwellian Distribution Function ◽  
Velocity Diffusion ◽  
Physical Quantities

In this paper, we derive a kinetic equation and discuss its validity for a stationary turbulent plasma. We use, for this purpose, the Dupree— Weinstock model in the weak-coupling approximation, and take into account ballistic streams. Frictional effects appear, in addition to the velocity diffusion. The diffusion causes a resonance broadening, the friction causes a frequency shift. Our model is a generalization of the dressed test particle model, and leads to a kinetic equation formally similar to Balescu— Lenard' s. A comparison between our model and the Dupree ‘clump’ theory is developed. Physical quantities are conserved, the H theorem is satisfied; but the asymptotic solution is not necessarily a Maxwellian distribution function.

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