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 $l^{*}$ and $l_{c}$, 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 $L_c(T)$ becoming exponentially sensitive to temperature. Using a functional renormalization group (FRG) approach we find $L_c(T) \propto \exp[(32/\pi)(T/T_{\rm dp})^3]$, with $T_{\rm dp}$ the depinning temperature. A slow decay of disorder correlations as it appears in the problem of flux line pinning in superconductors modifies this result, $\ln L_c(T)\propto T^{3/2}$.Comment: 4 pages, RevTeX, 1 figure inserte