Debye screening in spatially inhomogeneous systems of charged particles. II. Proof of convergence of cluster expansions
A decisive factor in the convergence proof for cluster expansions in the case of a spatially homogeneous system is the exponential decrease of the covariance of the Gaussian measure, which is essentially also the potential of the screened interactions. However, more accurate estimates of tree type graphs makes it possible to obtain an additional factor 1/Nexclamation and, thus, dispense with the condition of exponential decrease. In the investigation of systems of charged particles near difference surfaces it has been found that the potential of the screened interactions decreases exponentially only in directions perpendicular to the interface of two media, while in directions parallel to the interface it decreases as 1/r/sup 3/. The authors use this fact to prove the convergence. Since the system we consider has the property of neutrality near the surface Omega/sub 0/ and interacts with the surface theta Omega/sub 0/ through a hard-core potential, the cluster expansions can be constructed and their convergence proved.
- OSTI ID:
- 5617061
- Journal Information:
- Theor. Math. Phys.; (United States), Vol. 70:2; Other Information: Translated from Teor. Mat. Fiz.; 70: No. 2, 278-288(Feb 1987)
- Country of Publication:
- United States
- Language:
- English
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CHARGED PARTICLES
DEBYE LENGTH
PARTICLE MODELS
CONVERGENCE
HARD-CORE POTENTIAL
SERIES EXPANSION
BOUNDARY CONDITIONS
GAUSS FUNCTION
INHOMOGENEOUS PLASMA
INTERFACES
INVARIANCE PRINCIPLES
PARTICLE INTERACTIONS
PLASMA SIMULATION
SCREENING
SURFACES
DIMENSIONS
FUNCTIONS
INTERACTIONS
LENGTH
MATHEMATICAL MODELS
NUCLEAR POTENTIAL
PLASMA
POTENTIALS
SIMULATION
645300* - High Energy Physics- Particle Invariance Principles & Symmetries