276 research outputs found
Temporal Justification Logic
Justification logics are modal-like logics with the additional capability of recording the reason, or justification, for modalities in syntactic structures, called justification terms. Justification logics can be seen as explicit counterparts to modal logics. The behavior and interaction of agents in distributed system is often modeled using logics of knowledge and time. In this paper, we sketch some preliminary ideas on how the modal knowledge part of such logics of knowledge and time could be replaced with an appropriate justification logic
Optical excitation of phase modes in strongly disordered superconductors
According to the Goldstone theorem the breaking of a continuous U(1) symmetry
comes along with the existence of low-energy collective modes. In the context
of superconductivity these excitations are related to the phase of the
superconducting (SC) order parameter and for clean systems are optically
inactive. Here we show that for strongly disordered superconductors phase modes
acquire a dipole moment and appear as a subgap spectral feature in the optical
conductivity. This finding is obtained with both a gauge-invariant random-phase
approximation scheme based on a fermionic Bogoliubov-de Gennes state as well as
with a prototypical bosonic model for disordered superconductors. In the
strongly disordered regime, where the system displays an effective granularity
of the SC properties, the optically active dipoles are linked to the isolated
SC islands, offering a new perspective for realizing microwave optical devices
Singularities of the renormalization group flow for random elastic manifolds
We consider the singularities of the zero temperature renormalization group
flow for random elastic manifolds. When starting from small scales, this flow
goes through two particular points and , where the average value
of the random squared potential turnes negative ($l^{*}$) and where
the fourth derivative of the potential correlator becomes infinite at the
origin ($l_{c}$). The latter point sets the scale where simple perturbation
theory breaks down as a consequence of the competition between many metastable
states. We show that under physically well defined circumstances $l_{c} to negative values does not
take place.Comment: RevTeX, 3 page
Explicit Evidence Systems with Common Knowledge
Justification logics are epistemic logics that explicitly include
justifications for the agents' knowledge. We develop a multi-agent
justification logic with evidence terms for individual agents as well as for
common knowledge. We define a Kripke-style semantics that is similar to
Fitting's semantics for the Logic of Proofs LP. We show the soundness,
completeness, and finite model property of our multi-agent justification logic
with respect to this Kripke-style semantics. We demonstrate that our logic is a
conservative extension of Yavorskaya's minimal bimodal explicit evidence logic,
which is a two-agent version of LP. We discuss the relationship of our logic to
the multi-agent modal logic S4 with common knowledge. Finally, we give a brief
analysis of the coordinated attack problem in the newly developed language of
our logic
Impact of long-range interactions on the disordered vortex lattice
The interaction between the vortex lines in a type-II superconductor is
mediated by currents. In the absence of transverse screening this interaction
is long-ranged, stiffening up the vortex lattice as expressed by the dispersive
elastic moduli. The effect of disorder is strongly reduced, resulting in a
mean-squared displacement correlator =
characterized by a mere logarithmic growth with distance. Finite screening cuts
the interaction on the scale of the London penetration depth \lambda and limits
the above behavior to distances R<\lambda. Using a functional renormalization
group (RG) approach, we derive the flow equation for the disorder correlation
function and calculate the disorder-averaged mean-squared relative displacement
\propto ln^{2\sigma} (R/a_0). The logarithmic growth (2\sigma=1) in
the perturbative regime at small distances [A.I. Larkin and Yu.N. Ovchinnikov,
J. Low Temp. Phys. 34, 409 (1979)] crosses over to a sub-logarithmic growth
with 2\sigma=0.348 at large distances.Comment: 9 pages, no figure
Marginal Pinning of Quenched Random Polymers
An elastic string embedded in 3D space and subject to a short-range
correlated random potential exhibits marginal pinning at high temperatures,
with the pinning length becoming exponentially sensitive to
temperature. Using a functional renormalization group (FRG) approach we find
, with the
depinning temperature. A slow decay of disorder correlations as it appears in
the problem of flux line pinning in superconductors modifies this result, .Comment: 4 pages, RevTeX, 1 figure inserte
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