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Duality in two capacitively coupled layered arrays of ultrasmall Josephson junctions
We consider the problem of two capacitively coupled Josephson junction arrays
made of ultrasmall junctions. Each one of the arrays can be in the
semiclassical or quantum regimes, depending on their physical parameter values.
The former case is dominated by a Cooper-pair superfluid while the quantum one
is dominated by dynamic vortices leading to an insulating behavior. We first
consider the limit when both arrays are in the semiclassical limit, and next
the case when one array is quantum and the other semiclassical. We present WKB
and Mean Field theory results for the critical temperature of each array when
both are in the semiclassical limit. When one array is in the semiclassical
regime and the other one in the quantum fluctuations dominated regimes, we
derive a duality transformation between the charged and vortex dominated arrays
that involve a gauge vector field, which is proportional to the site coupling
capacitance between the arrays. The system considered here has been fabricated
and we make some predictions as to possible experimentally measurable
quantities that could be compared with theory.Comment: 25 pages in Revtex, To appear in J. Stat. Physics In the November
1998 issu
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