195 research outputs found
Fractional vortices in the XY model with bonds
We define a new set of excitations in the XY model which we call ``fractional
vortices''. In the frustrated XY model containing bonds, we make the
ansatz that the ground state configurations can be characterized by pairs of
oppositely charged fractional vortices. For a chain of bonds, the ground
state energy and the phase configurations calculated on the basis of this
ansatz agree well with the results from direct numerical simulations. Finally,
we discuss the possible connection of these results to some recent experiments
by Kirtley {\it et al} [Phys. Rev. B {\bf 51}, R12057 (1995)] on high-T
superconductors where fractional flux trapping was observed along certain grain
boundaries.Comment: 13 pages, 14 figures included (.eps). No essential differences to
previous version, however more compact forma
Theory of Two-Dimensional Josephson Arrays in a Resonant Cavity
We consider the dynamics of a two-dimensional array of underdamped Josephson
junctions placed in a single-mode resonant cavity. Starting from a well-defined
model Hamiltonian, which includes the effects of driving current and
dissipative coupling to a heat bath, we write down the Heisenberg equations of
motion for the variables of the Josephson junction and the cavity mode,
extending our previous one-dimensional model. In the limit of large numbers of
photons, these equations can be expressed as coupled differential equations and
can be solved numerically. The numerical results show many features similar to
experiment. These include (i) self-induced resonant steps (SIRS's) at voltages
V = (n hbar Omega)/(2e), where Omega is the cavity frequency, and n is
generally an integer; (ii) a threshold number N_c of active rows of junctions
above which the array is coherent; and (iii) a time-averaged cavity energy
which is quadratic in the number of active junctions, when the array is above
threshold. Some differences between the observed and calculated threshold
behavior are also observed in the simulations and discussed. In two dimensions,
we find a conspicuous polarization effect: if the cavity mode is polarized
perpendicular to the direction of current injection in a square array, it does
not couple to the array and there is no power radiated into the cavity. We
speculate that the perpendicular polarization would couple to the array, in the
presence of magnetic-field-induced frustration. Finally, when the array is
biased on a SIRS, then, for given junction parameters, the power radiated into
the array is found to vary as the square of the number of active junctions,
consistent with expectations for a coherent radiation.Comment: 11 pages, 8 eps figures, submitted to Phys. Rev
Several small Josephson junctions in a Resonant Cavity: Deviation from the Dicke Model
We have studied quantum-mechanically a system of several small identical
Josephson junctions in a lossless single-mode cavity for different initial
states, under conditions such that the system is at resonance. This system is
analogous to a collection of identical atoms in a cavity, which is described
under appropriate conditions by the Dicke model. We find that our system can be
well approximated by a reduced Hamiltonian consisting of two levels per
junction. The reduced Hamiltonian is similar to the Dicke Hamiltonian, but
contains an additional term resembling a dipole-dipole interaction between the
junctions. This extra term arises when states outside the degenerate group are
included via degenerate second-order (L\"{o}wdin) perturbation theory. As in
the Dicke model, we find that, when N junctions are present in the cavity, the
oscillation frequency due to the junction-cavity interaction is enhanced by
. The corresponding decrease in the Rabi oscillation period may cause
it to be smaller than the decoherence time due to dissipation, making these
oscillations observable. Finally, we find that the frequency enhancement
survives even if the junctions differ slightly from one another, as expected in
a realistic system.Comment: 11 pages. To be published in Phys. Rev.
Emergence of weight-topology correlations in complex scale-free networks
Different weighted scale-free networks show weights-topology correlations
indicated by the non linear scaling of the node strength with node
connectivity. In this paper we show that networks with and without
weight-topology correlations can emerge from the same simple growth dynamics of
the node connectivities and of the link weights. A weighted fitness network is
introduced in which both nodes and links are assigned intrinsic fitness. This
model can show a local dependence of the weight-topology correlations and can
undergo a phase transition to a state in which the network is dominated by few
links which acquire a finite fraction of the total weight of the network.Comment: (4 pages,3 figures
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