7 research outputs found
Vortex ordering in fully-frustrated superconducting systems with dice lattice
The structure and the degenracy of the ground state of a fully-frustrated
XY-model are investigated for the case of a dice lattice geometry.
The results are applicable for the description of Josephson junction arrays
and thin superconducting wire networks in the external magnetic field providing
half-integer number of flux quanta per plaquette. The mechanisms of disordering
of vortex pattern in such systems are briefly discussed.Comment: 10 pages, 3 figure
Strongly correlated hopping and many-body bound states
We study a system in which the quantum dynamics of electrons depend on the
particle density in their neighborhood. For any on-site repulsive interaction,
we show that the exact two-body and three-body ground states are bound states.
We also discuss the finite density case in a mean-field framework and we show
that the system can undergo an unusual transition from an effective attractive
interaction to a repulsive one, when varying the electron density.Comment: 6 pages, 6 EPS figures, minor modifications and references adde
Cantor and band spectra for periodic quantum graphs with magnetic fields
We provide an exhaustive spectral analysis of the two-dimensional periodic
square graph lattice with a magnetic field. We show that the spectrum consists
of the Dirichlet eigenvalues of the edges and of the preimage of the spectrum
of a certain discrete operator under the discriminant (Lyapunov function) of a
suitable Kronig-Penney Hamiltonian. In particular, between any two Dirichlet
eigenvalues the spectrum is a Cantor set for an irrational flux, and is
absolutely continuous and has a band structure for a rational flux. The
Dirichlet eigenvalues can be isolated or embedded, subject to the choice of
parameters. Conditions for both possibilities are given. We show that
generically there are infinitely many gaps in the spectrum, and the
Bethe-Sommerfeld conjecture fails in this case.Comment: Misprints correcte
Quantum Interference in Superconducting Wire Networks and Josephson Junction Arrays: Analytical Approach based on Multiple-Loop Aharonov-Bohm Feynman Path-Integrals
We investigate analytically and numerically the mean-field
superconducting-normal phase boundaries of two-dimensional superconducting wire
networks and Josephson junction arrays immersed in a transverse magnetic field.
The geometries we consider include square, honeycomb, triangular, and kagome'
lattices. Our approach is based on an analytical study of multiple-loop
Aharonov-Bohm effects: the quantum interference between different electron
closed paths where each one of them encloses a net magnetic flux. Specifically,
we compute exactly the sums of magnetic phase factors, i.e., the lattice path
integrals, on all closed lattice paths of different lengths. A very large
number, e.g., up to for the square lattice, exact lattice path
integrals are obtained. Analytic results of these lattice path integrals then
enable us to obtain the resistive transition temperature as a continuous
function of the field. In particular, we can analyze measurable effects on the
superconducting transition temperature, , as a function of the magnetic
filed , originating from electron trajectories over loops of various
lengths. In addition to systematically deriving previously observed features,
and understanding the physical origin of the dips in as a result of
multiple-loop quantum interference effects, we also find novel results. In
particular, we explicitly derive the self-similarity in the phase diagram of
square networks. Our approach allows us to analyze the complex structure
present in the phase boundaries from the viewpoint of quantum interference
effects due to the electron motion on the underlying lattices.Comment: 18 PRB-type pages, plus 8 large figure
A hybrid heuristic for the diameter constrained minimum spanning tree problem
Spanning trees, Diameter constrained spanning trees, Heuristics, GRASP, Iterated local search,