2,792 research outputs found
The evolution problem associated with eigenvalues of the Hessian
In this paper we study the evolution problem where is a bounded
domain in (that verifies a suitable geometric condition on its
boundary) and stands for the st eigenvalue of the
Hessian matrix . We assume that and are continuous functions
with the compatibility condition , .
We show that the (unique) solution to this problem exists in the viscosity
sense and can be approximated by the value function of a two-player zero-sum
game as the parameter measuring the size of the step that we move in each round
of the game goes to zero.
In addition, when the boundary datum is independent of time, ,
we show that viscosity solutions to this evolution problem stabilize and
converge exponentially fast to the unique stationary solution as .
For the limit profile is just the convex envelope inside of the
boundary datum , while for it is the concave envelope. We obtain this
result with two different techniques: with PDE tools and and with game
theoretical arguments. Moreover, in some special cases (for affine boundary
data) we can show that solutions coincide with the stationary solution in
finite time (that depends only on and not on the initial condition
)
Magnetic-field-dependent quasiparticle energy relaxation in mesoscopic wires
In order to find out if magnetic impurities can mediate interactions between
quasiparticles in metals, we have measured the effect of a magnetic field B on
the energy distribution function f(E) of quasiparticles in two silver wires
driven out-of-equilibrium by a bias voltage U. In a sample showing sharp
distributions at B=0, no magnetic field effect is found, whereas in the other
sample, rounded distributions at low magnetic field get sharper as B is
increased, with a characteristic field proportional to U. Comparison is made
with recent calculations of the effect of magnetic-impurities-mediated
interactions taking into account Kondo physics.Comment: 4 pages, 3 figures, to be published in Physical Review Letter
Influence of Magnetic Field on Effective Electron-Electron Interactions in a Copper Wire
We have measured in a copper wire the energy exchange rate between
quasiparticles as a function of the applied magnetic field. We find that the
effective electron-electron interaction is strongly modified by the magnetic
field, suggesting that magnetic impurities play a role on the interaction
processes.Comment: latex anthore.tex, 8 files, 6 figures, 7 pages in: Proceedings of the
XXXVIth Rencontres de Moriond `Electronic Correlations: From Meso- to
Nano-physics' Les Arcs, France January 20-27, 2001 [SPEC-S01/027
Supercurrent Spectroscopy of Andreev States
We measure the excitation spectrum of a superconducting atomic contact. In
addition to the usual continuum above the superconducting gap, the single
particle excitation spectrum contains discrete, spin-degenerate Andreev levels
inside the gap. Quasiparticle excitations are induced by a broadband on-chip
microwave source and detected by measuring changes in the supercurrent flowing
through the atomic contact. Since microwave photons excite quasiparticles in
pairs, two types of transitions are observed: Andreev transitions, which
consists of putting two quasiparticles in an Andreev level, and transitions to
odd states with a single quasiparticle in an Andreev level and the other one in
the continuum. In contrast to absorption spectroscopy, supercurrent
spectroscopy allows detection of long-lived odd states.Comment: typos correcte
Exciting Andreev pairs in a superconducting atomic contact
The Josephson effect describes the flow of supercurrent in a weak link, such
as a tunnel junction, nanowire, or molecule, between two superconductors. It is
the basis for a variety of circuits and devices, with applications ranging from
medicine to quantum information. Currently, experiments using Josephson
circuits that behave like artificial atoms are revolutionizing the way we probe
and exploit the laws of quantum physics. Microscopically, the supercurrent is
carried by Andreev pair states, which are localized at the weak link. These
states come in doublets and have energies inside the superconducting gap.
Existing Josephson circuits are based on properties of just the ground state of
each doublet and so far the excited states have not been directly detected.
Here we establish their existence through spectroscopic measurements of
superconducting atomic contacts. The spectra, which depend on the atomic
configuration and on the phase difference between the superconductors, are in
complete agreement with theory. Andreev doublets could be exploited to encode
information in novel types of superconducting qubits.Comment: Submitted to Natur
Phase controlled superconducting proximity effect probed by tunneling spectroscopy
Using a dual-mode STM-AFM microscope operating below 50mK we measured the
Local Density of States (LDoS) along small normal wires connected at both ends
to superconductors with different phases. We observe that a uniform minigap can
develop in the whole normal wire and in the superconductors near the
interfaces. The minigap depends periodically on the phase difference. The
quasiclassical theory of superconductivity applied to a simplified 1D model
geometry accounts well for the data.Comment: Accepted for publication in Physical Review Letter
High-gain weakly nonlinear flux-modulated Josephson parametric amplifier using a SQUID-array
We have developed and measured a high-gain quantum-limited microwave
parametric amplifier based on a superconducting lumped LC resonator with the
inductor L including an array of 8 superconducting quantum interference devices
(SQUIDs). This amplifier is parametrically pumped by modulating the flux
threading the SQUIDs at twice the resonator frequency. Around 5 GHz, a maximum
gain of 31 dB, a product amplitude-gain x bandwidth above 60 MHz, and a 1 dB
compression point of -123 dBm at 20 dB gain are obtained in the non-degenerate
mode of operation. Phase sensitive amplification-deamplification is also
measured in the degenerate mode and yields a maximum gain of 37 dB. The
compression point obtained is 18 dB above what would be obtained with a single
SQUID of the same inductance, due to the smaller nonlinearity of the SQUID
array.Comment: 7 pages, 4 figures, 23 reference
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