Charge Fluctuations in the Two-Dimensional One-Component Plasma |
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Authors: | D Levesque J-J Weis J L Lebowitz |
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Institution: | (1) Laboratoire de Physique Théorique, Université de Paris-Sud, 91405 Orsay Cedex, France;(2) Department of Mathematics and Physics, Rutgers University, New Brunswick, New Jersey 08903 |
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Abstract: | We study, via computer simulations, the fluctuations in the net electric charge in a two-dimensional, one component plasma (OCP) with uniform background charge density –e in a region inside a much larger overall neutral system. Setting e=1, this is the same as the fluctuations in N
, the number of mobile particles of charge e. As expected, the distribution of N
has, for large , a Gaussian form with a variance which grows only as ^ |![part](/content/p945730077530853/xxlarge8706.gif) |, where |![part](/content/p945730077530853/xxlarge8706.gif) | is the length of the perimeter of . The properties of this system depend only on the coupling parameter =kT, which is the same as the reciprocal temperature in our units. Our simulations show that when the coupling parameter increases, ^ ( ) decreases to an asymptotic value ^ ( ) ^ (2)/2 which is equal (or very close) to that obtained for the corresponding variance of particles on a rigid triangular lattice. Thus, for large , the characteristic length
L=2^ / associated with charge fluctuations behaves very differently from that of the Debye length,
D 1/
, which it approaches as ![Gamma](/content/p945730077530853/xxlarge915.gif) 0. The pair correlation function of the OCP is also studied. |
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Keywords: | charge fluctuations one-component plasma two dimensions perimeter law |
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