17,028 research outputs found
Checking Observational Purity of Procedures
Verifying whether a procedure is observationally pure is useful in many
software engineering scenarios. An observationally pure procedure always
returns the same value for the same argument, and thus mimics a mathematical
function. The problem is challenging when procedures use private mutable global
variables, e.g., for memoization of frequently returned answers, and when they
involve recursion.
We present a novel verification approach for this problem. Our approach
involves encoding the procedure's code as a formula that is a disjunction of
path constraints, with the recursive calls being replaced in the formula with
references to a mathematical function symbol. Then, a theorem prover is invoked
to check whether the formula that has been constructed agrees with the function
symbol referred to above in terms of input-output behavior for all arguments.
We evaluate our approach on a set of realistic examples, using the Boogie
intermediate language and theorem prover. Our evaluation shows that the
invariants are easy to construct manually, and that our approach is effective
at verifying observationally pure procedures.Comment: FASE 201
Flavour-conserving oscillations of Dirac-Majorana neutrinos
We analyze both chirality-changing and chirality-preserving transitions of
Dirac-Majorana neutrinos. In vacuum, the first ones are suppressed with respect
to the others due to helicity conservation and the interactions with a
(``normal'') medium practically does not affect the expressions of the
probabilities for these transitions, even if the amplitudes of oscillations
slightly change. For usual situations involving relativistic neutrinos we find
no resonant enhancement for all flavour-conserving transitions. However, for
very light neutrinos propagating in superdense media, the pattern of
oscillations is dramatically altered with respect to the
vacuum case, the transition probability practically vanishing. An application
of this result is envisaged.Comment: 14 pages, latex 2E, no figure
Quantum temporal correlations and entanglement via adiabatic control of vector solitons
It is shown that optical pulses with a mean position accuracy beyond the
standard quantum limit can be produced by adiabatically expanding an optical
vector soliton followed by classical dispersion management. The proposed scheme
is also capable of entangling positions of optical pulses and can potentially
be used for general continuous-variable quantum information processing.Comment: 5 pages, 1 figure, v2: accepted by Physical Review Letters, v3: minor
editing and shortening, v4: included the submitted erratu
Photon production from the vacuum close to the super-radiant transition: When Casimir meets Kibble-Zurek
The dynamical Casimir effect (DCE) predicts the generation of photons from
the vacuum due to the parametric amplification of the quantum fluctuation of an
electromagnetic field\cite{casimir1,casimir2}. The verification of such effect
is still elusive in optical systems due to the very demanding requirements of
its experimental implementation. This typically requires very fast changes of
the boundary conditions of the problem, such as the high-frequency driving of
the positions of the mirrors of a cavity accommodating the field. Here, we show
that an ensemble of two-level atoms collectively coupled to the electromagnetic
field of a cavity (thus embodying the quantum Dicke model\cite{dicke}), driven
at low frequencies and close to a quantum phase transition, stimulates the
production of photons from the vacuum. This paves the way to an effective
simulation of the DCE through a mechanism that has recently found an
outstanding experimental demonstration\cite{esslinger}. The spectral properties
of the emitted radiation reflect the critical nature of the system and allow us
to link the detection of DCE to the Kibble-Zurek mechanism for the production
of defects when crossing a continuous phase transition\cite{KZ1,KZ2}. We
illustrate the features of our proposal by addressing a simple cavity
quantum-electrodynamics (cQED) setting of immediate experimental realisation.Comment: 4+1 pages, major changes in the second part of the paper. To appear
in Physical Review Letter
Are the reactions a challenge for the factorized Pomeron at high energies?
We would like to point to the strong violation of the putative factorized
Pomeron exchange model in the reactions in the
high-energy region where this model works fairly well in all other cases.Comment: 4 pages, LaTex, 1 fig. in postscript, minor typos corrected, to be
published in Phys. Rev. D 60, 117503 (1999
Sampling bias in systems with structural heterogeneity and limited internal diffusion
Complex systems research is becomingly increasingly data-driven, particularly
in the social and biological domains. Many of the systems from which sample
data are collected feature structural heterogeneity at the mesoscopic scale
(i.e. communities) and limited inter-community diffusion. Here we show that the
interplay between these two features can yield a significant bias in the global
characteristics inferred from the data. We present a general framework to
quantify this bias, and derive an explicit corrective factor for a wide class
of systems. Applying our analysis to a recent high-profile survey of conflict
mortality in Iraq suggests a significant overestimate of deaths
Generalized Hermite-Gauss decomposition of the two-photon state produced by spontaneous parametric down-conversion
We provide a general decomposition of the two-photon state produced by
spontaneous parametric down-conversion in Hermite-Gaussian modes, in the case
that the pump beam is described by a Hermite-Gaussian beam of any order. We
show that the spatial correlations depend explicitly on the order of the pump
beam, as well as other experimental parameters. We use the decomposition to
demonstrate a few interesting cases. Our results are applicable to the
engineering of two-photon spatial entanglement, in particular for non-Gaussian
states.Comment: 14 page draft, 5 figure
Total Widths And Slopes From Complex Regge Trajectories
Maximally complex Regge trajectories are introduced for which both Re
and Im grow as ( small and
positive). Our expression reduces to the standard real linear form as the
imaginary part (proportional to ) goes to zero. A scaling formula for
the total widths emerges: constant for large M, in very
good agreement with data for mesons and baryons. The unitarity corrections also
enhance the space-like slopes from their time-like values, thereby resolving an
old problem with the trajectory in charge exchange. Finally, the
unitarily enhanced intercept, , \nolinebreak is in
good accord with the Donnachie-Landshoff total cross section analysis.Comment: 9 pages, 3 Figure
Quantum Field Theory of Meson Mixing
We have developed a quantum field theoretic framework for scalar and
pseudoscalar meson mixing and oscillations in time. The unitary inequivalence
of the Fock space of base (unmixed) eigenstates and the physical mixed
eigenstates is proven and shown to lead to a rich condensate structure. This is
exploited to develop formulas for two flavor boson oscillations in systems of
arbitrary boson occupation number. The mixing and oscillation can be understood
in terms of vacuum condensate which interacts with the bare particles to induce
non-trivial effects. We apply these formulas to analyze the mixing of
with and comment on the system. In addition, we consider the
mixing of boson coherent states, which may have future applications in the
construction of meson lasers.Comment: 12 pages, 3 figures; Eqs.(10-12) corrected, leading to new physical
insights; added paragraph under Eq.(24) explaining physical interpretation of
mixing in terms of vacuum condensation; references added and minor typo
correcte
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