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The European Physical Journal B

Mean-field theories for the quantum phase transition in Josephson junction arrays

J. G. Kissner, Ulrich Eckern

Published Jun 1, 1993• 15 citations
Publisher
DOI
10.1007/bf01315230

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In this paper, by employing Bogliubov backreaction method, we investigate quantum correction effects on dynamical phase transition in a single species bosonic Josephson junction induced by increasing nonlinear interaction. Compared with mean field theory results, we find that the transition point is shifted. The dynamical phase transition is accompanied by a change of the entanglement entropy, which is found to reach a maximum at the transition point of the mean field theory.

Communications in Theoretical Physics•Aug 1, 2013•2 citations
We describe a simple Hamiltonian for an underdamped Josephson array coupled to a single photon mode in a resonant cavity. Using a Hartree-like mean-field theory, we show that, for any given strength of coupling between the photon field and the Josephson junctions, there is a transition from incoherence to coherence as a function of N, the number of Josephson junctions in the array. Above that value of N, the energy in the photon field is proportional to N2,{N}^{2},N2, suggestive of coherent emission. These features remain even when the junction parameters have some random variation from junction to junction, as expected in a real array. Both of these features agree with recent experiments by Barbara and co-workers.
I present here some results on the mean field theory approach to the statistical mechanics of a D-dimensional array of Josephson junctions in the presence of a magnetic field. The mean field theory equations are obtained by computing the thermodynamical properties. In the high temperature region in the limit D→∞, where the problem is simplified, this limit defines the mean field approximation. Close to the transition point the system behaves very similar to a particular form of spin glasses, i.e., to gauge glasses. We have noticed that in this limit the evaluation of the coefficients of the high temperature expansion may be mapped onto the computation of some matrix elements for the q-deformed harmonic oscillator. The same arguments can be used to predict the thermodynamical properties in the mean field limit. These results can be extended to the low temperature phase using a conjecture on the equivalence of some system without disorder with appropriate random systems.