5,915 research outputs found
Assume-guarantee verification for probabilistic systems
We present a compositional verification technique for systems that exhibit both probabilistic and nondeterministic behaviour. We adopt an assume- guarantee approach to verification, where both the assumptions made about system components and the guarantees that they provide are regular safety properties, represented by finite automata. Unlike previous proposals for assume-guarantee reasoning about probabilistic systems, our approach does not require that components interact in a fully synchronous fashion. In addition, the compositional verification method is efficient and fully automated, based on a reduction to the problem of multi-objective probabilistic model checking. We present asymmetric and circular assume-guarantee rules, and show how they can be adapted to form quantitative queries, yielding lower and upper bounds on the actual probabilities that a property is satisfied. Our techniques have been implemented and applied to several large case studies, including instances where conventional probabilistic verification is infeasible
Protected nodes and the collapse of the Fermi arcs in high Tc cuprates
Angle resolved photoemission on underdoped Bi2Sr2CaCu2O8 reveals that the
magnitude and d-wave anisotropy of the superconducting state energy gap are
independent of temperature all the way up to Tc. This lack of T variation of
the entire k-dependent gap is in marked contrast to mean field theory. At Tc
the point nodes of the d-wave gap abruptly expand into finite length ``Fermi
arcs''. This change occurs within the width of the resistive transition, and
thus the Fermi arcs are not simply thermally broadened nodes but rather a
unique signature of the pseudogap phase.Comment: Accepted by Phys. Rev. Let
Evidence for pairing above Tc from the dispersion in the pseudogap phase of cuprates
In the underdoped high temperature superconductors, instead of a complete
Fermi surface above Tc, only disconnected Fermi arcs appear, separated by
regions that still exhibit an energy gap. We show that in this pseudogap phase,
the energy-momentum relation of electronic excitations near E_F behaves like
the dispersion of a normal metal on the Fermi arcs, but like that of a
superconductor in the gapped regions. We argue that this dichotomy in the
dispersion is hard to reconcile with a competing order parameter, but is
consistent with pairing without condensation
Momentum anisotropy of the scattering rate in cuprate superconductors
We examine the momentum and energy dependence of the scattering rate of the
high temperature cuprate superconductors using angle resolved photoemission
spectroscopy. The scattering rate is of the form a + b*w. The inelastic
coefficient b is found to be isotropic. The elastic term, a, however, is found
to be highly anisotropic in the pseudogap phase of optimal doped samples, with
an anisotropy which correlates with that of the pseudogap. This can be
contrasted with heavily overdoped samples, which show an isotropic scattering
rate in the normal state
Modeling the Fermi arc in underdoped cuprates
Angle resolved photoemission data in the pseudogap phase of underdoped cuprates have revealed the presence of a truncated Fermi surface consisting of Fermi arcs. We compare a number of proposed models for the arcs and find that the one that best models the data is a d-wave energy gap with a lifetime broadening whose temperature dependence is suggestive of fluctuating pairs
Gap Anisotropy and de Haas-van Alphen Effect in Type-II Superconductors
We present a theoretical study on the de Haas-van Alphen (dHvA) oscillation
in the vortex state of type-II superconductors, with a special focus on the
connection between the gap anisotropy and the oscillation damping. Numerical
calculations for three different gap structures clearly indicate that the
average gap along extremal orbits is relevant for the magnitude of the extra
damping, thereby providing a support for experimental efforts to probe gap
anisotropy through the dHvA signal. We also derive an analytic formula for the
extra damping which gives a good fit to the numerical results.Comment: 5 pages, 1 figure, changes in Introductio
Interacting holographic tachyon model of dark energy
We propose a holographic tachyon model of dark energy with interaction
between the components of the dark sector. The correspondence between the
tachyon field and the holographic dark energy densities allows the
reconstruction of the potential and the dynamics of the tachyon scalar field in
a flat Friedmann-Robertson-Walker universe. We show that this model can
describe the observed accelerated expansion of our universe with a parameter
space given by the most recent observational results.Comment: 7 pages, 8 figures, accepted for publication in IJMP
Where is the pi particle?
We discuss the interplay of particle-particle and particle-hole spin-triplet
channels in high-T_c superconductors using a quasiparticle dispersion motivated
by angle-resolved photoemission. Within a generalized RPA, we find a well
defined antibound state of two holes, the pi resonance of Demler and Zhang, as
well as a bound state of a particle and a hole, the spin exciton. We show that
the energy of the pi resonance always exceeds 2 Delta, twice the maximum d-wave
gap, therefore the neutron resonance observed in the cuprates around energy
Delta is most likely a spin exciton. At the same time, we speculate that the pi
particle can exist at higher energies and might be observed in neutron
scattering around 100 meV.Comment: RevTeX, 5 pages, 4 eps figure
- …