29 research outputs found
Bogoliubov - de Gennes versus Quasiclassical Description of Josephson Structures
The applicability of the quasiclassical theory of superconductivity in
Josephson multi-layer structures is analyzed. The quasiclassical approach is
compared with the exact theory based on the Bogoliubov - de Gennes equation.
The angle and energy resolved (coarse-grain) currents are calculated using both
techniques. It is shown that the two approaches agree in geometries
after the coarse-grain averaging. A quantitative discrepancy, which exceeds the
quasiclassical accuracy, is observed when three or more interfaces are present.
The invalidity of the quasiclassical theory is attributed to the presence of
closed trajectories formed by sequential reflections on the interfaces.Comment: revtex4,12 pages, 12 figure
Nonlocal Andreev reflection at high transmissions
We analyze non-local effects in electron transport across three-terminal
normal-superconducting-normal (NSN) structures. Subgap electrons entering
S-electrode from one N-metal may form Cooper pairs with their counterparts
penetrating from another N-metal. This phenomenon of crossed Andreev reflection
-- combined with normal scattering at SN interfaces -- yields two different
contributions to non-local conductance which we evaluate non-perturbatively at
arbitrary interface transmissions. Both these contributions reach their maximum
values at fully transmitting interfaces and demonstrate interesting features
which can be tested in future experiments.Comment: 4 pages, 4 figure
Percolation and epidemics in a two-dimensional small world
Percolation on two-dimensional small-world networks has been proposed as a
model for the spread of plant diseases. In this paper we give an analytic
solution of this model using a combination of generating function methods and
high-order series expansion. Our solution gives accurate predictions for
quantities such as the position of the percolation threshold and the typical
size of disease outbreaks as a function of the density of "shortcuts" in the
small-world network. Our results agree with scaling hypotheses and numerical
simulations for the same model.Comment: 7 pages, 3 figures, 2 table
Layered ferromagnet-superconductor structures: the state and proximity effects
We investigate clean mutilayered structures of the SFS and SFSFS type, (where
the S layer is intrinsically superconducting and the F layer is ferromagnetic)
through numerical solution of the self-consistent Bogoliubov-de Gennes
equations for these systems. We obtain results for the pair amplitude, the
local density of states, and the local magnetic moment. We find that as a
function of the thickness of the magnetic layers separating adjacent
superconductors, the ground state energy varies periodically between two stable
states. The first state is an ordinary "0-state", in which the order parameter
has a phase difference of zero between consecutive S layers, and the second is
a "-state", where the sign alternates, corresponding to a phase difference
of between adjacent S layers. This behavior can be understood from simple
arguments. The density of states and the local magnetic moment reflect also
this periodicity.Comment: 12 pages, 10 Figure
XY model in small-world networks
The phase transition in the XY model on one-dimensional small-world networks
is investigated by means of Monte-Carlo simulations. It is found that
long-range order is present at finite temperatures, even for very small values
of the rewiring probability, suggesting a finite-temperature transition for any
nonzero rewiring probability. Nature of the phase transition is discussed in
comparison with the globally-coupled XY model.Comment: 5 pages, accepted in PR
Charged hydrogenic problem in a magnetic field: Non-commutative translations, unitary transformations, and coherent states
An operator formalism is developed for a description of charged electron-hole
complexes in magnetic fields. A novel unitary transformation of the Hamiltonian
that allows one to partially separate the center-of-mass and internal motions
is proposed. We study the operator algebra that leads to the appearance of new
effective particles, electrons and holes with modified interparticle
interactions, and their coherent states in magnetic fields. The developed
formalism is used for studying a two-dimensional negatively charged
magnetoexciton . It is shown that Fano-resonances are present in the
spectra of internal transitions, indicating the existence of
three-particle quasi-bound states embedded in the continuum of higher Landau
levels.Comment: 9 pages + 2 figures, accepted in PRB, a couple of typos correcte
Quasiclassical theory of superconductivity: a multiple interface geometry
The purpose of the paper is to suggest a new method which allows one to study
multiple coherent reflection/transmissions by partially transparent interfaces
(e.g. in multi-layer mesoscopic structures or grain boundaries in high-Tc's) in
the framework of the quasiclassical theory of superconductivity. It is argued
that typically the trajectory of the particle is a simply connected tree (no
loops) with knots, i.e. the points where interface scattering events occur and
ballistic pieces of the trajectory are mixed. A linear boundary condition for
the 2-component trajectory "wave function" which factorizes matrix (retarded)
Green's function, is formulated for an arbitrary interface, specular or
diffusive. To show the usage of the method, the current response to the vector
potential (the total superfluid density rho_s) of a SS' sandwich with the
different signs of the order parameter in S and S', is calculated. In this
model, a few percent of reflection by the SS' interface transforms the
paramagnetic response (rho_s < 0) created by the zero-energy Andreev bound
states near an ideal interface (see Fauchere et al. PRL, 82, 3336 (1999),
cond-mat/9901112), into the usual diamagnetic one (rho_s >0).Comment: Extended abstract submitted to "Electron Transport in Mesoscopic
Systems", Satellite conference to LT22, Goteborg, 12-15 August, 1999. 2 pages
Minor changes + the text height problem fixe
Edge overload breakdown in evolving networks
We investigate growing networks based on Barabasi and Albert's algorithm for
generating scale-free networks, but with edges sensitive to overload breakdown.
the load is defined through edge betweenness centrality. We focus on the
situation where the average number of connections per vertex is, as the number
of vertices, linearly increasing in time. After an initial stage of growth, the
network undergoes avalanching breakdowns to a fragmented state from which it
never recovers. This breakdown is much less violent if the growth is by random
rather than preferential attachment (as defines the Barabasi and Albert model).
We briefly discuss the case where the average number of connections per vertex
is constant. In this case no breakdown avalanches occur. Implications to the
growth of real-world communication networks are discussed.Comment: To appear in Phys. Rev.
Vertex overload breakdown in evolving networks
We study evolving networks based on the Barabasi-Albert scale-free network
model with vertices sensitive to overload breakdown. The load of a vertex is
defined as the betweenness centrality of the vertex. Two cases of load
limitation are considered, corresponding to that the average number of
connections per vertex is increasing with the network's size ("extrinsic
communication activity"), or that it is constant ("intrinsic communication
activity"). Avalanche-like breakdowns for both load limitations are observed.
In order to avoid such avalanches we argue that the capacity of the vertices
has to grow with the size of the system. An interesting irregular dynamics of
the formation of the giant component (for the intrinsic communication activity
case is also studied). Implications on the growth of the Internet is discussed.Comment: To appear in Phys. Rev.