363 research outputs found
A superconductor-insulator transition in a one-dimensional array of Josephson junctions
We consider a one-dimensional Josephson junction array, in the regime where
the junction charging energy is much greater than the charging energy of the
superconducting islands. In this regime we critically reexamine the continuum
limit description and establish the relationship between parameters of the
array and the ones of the resulting sine-Gordon model. The later model is
formulated in terms of quasi-charge. We argue that despite arguments to the
contrary in the literature, such quasi-charge sine-Gordon description remains
valid in the vicinity of the phase transition between the insulating and the
superconducting phases. We also discuss the effects of random background
charges, which are always present in experimental realizations of such arrays
Integer Quantum Hall Transition and Random SU(N) Rotation
We reduce the problem of integer quantum Hall transition to a random rotation
of an N-dimensional vector by an su(N) algebra, where only N specially selected
generators of the algebra are nonzero. The group-theoretical structure revealed
in this way allows us to obtain a new series of conservation laws for the
equation describing the electron density evolution in the lowest Landau level.
The resulting formalism is particularly well suited to numerical simulations,
allowing us to obtain the critical exponent \nu numerically in a very simple
way. We also suggest that if the number of nonzero generators is much less than
N, the same model, in a certain intermediate time interval, describes
percolating properties of a random incompressible steady two-dimensional flow.
In other words, quantum Hall transition in a very smooth random potential
inherits certain properties of percolation.Comment: 4 pages, 1 figur
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