Alternative axiomatics and complexity of deliberative STIT theories

We propose two alternatives to Xu's axiomatization of the Chellas STIT. The first one also provides an alternative axiomatization of the deliberative STIT. The second one starts from the idea that the historic necessity operator can be defined as an abbreviation of operators of agency, and can thus be eliminated from the logic of the Chellas STIT. The second axiomatization also allows us to establish that the problem of deciding the satisfiability of a STIT formula without temporal operators is NP-complete in the single-agent case, and is NEXPTIME-complete in the multiagent case, both for the deliberative and the Chellas' STIT.Comment: Submitted to the Journal of Philosophical Logic; 13 pages excluding anne

Fixed-parameter tractability of multicut parameterized by the size of the cutset

Given an undirected graph $G$, a collection $\{(s_1,t_1),..., (s_k,t_k)\}$ of pairs of vertices, and an integer $p$, the Edge Multicut problem ask if there is a set $S$ of at most $p$ edges such that the removal of $S$ disconnects every $s_i$ from the corresponding $t_i$. Vertex Multicut is the analogous problem where $S$ is a set of at most $p$ vertices. Our main result is that both problems can be solved in time $2^{O(p^3)}... n^{O(1)}$, i.e., fixed-parameter tractable parameterized by the size $p$ of the cutset in the solution. By contrast, it is unlikely that an algorithm with running time of the form $f(p)... n^{O(1)}$ exists for the directed version of the problem, as we show it to be W[1]-hard parameterized by the size of the cutset

Quantum Fluctuations Driven Orientational Disordering: A Finite-Size Scaling Study

The orientational ordering transition is investigated in the quantum generalization of the anisotropic-planar-rotor model in the low temperature regime. The phase diagram of the model is first analyzed within the mean-field approximation. This predicts at $T=0$ a phase transition from the ordered to the disordered state when the strength of quantum fluctuations, characterized by the rotational constant $\Theta$, exceeds a critical value $\Theta_{\rm c}^{MF}$. As a function of temperature, mean-field theory predicts a range of values of $\Theta$ where the system develops long-range order upon cooling, but enters again into a disordered state at sufficiently low temperatures (reentrance). The model is further studied by means of path integral Monte Carlo simulations in combination with finite-size scaling techniques, concentrating on the region of parameter space where reentrance is predicted to occur. The phase diagram determined from the simulations does not seem to exhibit reentrant behavior; at intermediate temperatures a pronounced increase of short-range order is observed rather than a genuine long-range order.Comment: 27 pages, 8 figures, RevTe

Superconducting NdCeCuO Bicrystal Grain Boundary Josephson Junctions

We have studied the electric transport properties of symmetrical [001] tilt NdCeCuO bicrystal grain boundary Josephson junctions (GBJs) fabricated on SrTiO bicrystal substrates with misorientation angles of 24 and 36.8 degree. The superconducting properties of the NdCeCuO-GBJs are similar to those of GBJs fabricated from the hole doped high temperature superconductors (HTS). The critical current density Jc decreases strongly with increasing misorientation angle. The products of the critical current Ic and the normal resistance Rn (about 0.1 mV at 4.2 K) are small compared to the gap voltage and fit well to the universal scaling law (IcRn is proportional to the square root of Jc) found for GBJs fabricated from the hole doped HTS. This suggests that the symmetry of the order parameter, which most likely is different for the electron and the hole doped HTS has little influence on the characteristic properties of symmetrical [001] tilt GBJs.Comment: 3 pages, 4 figures, to be published in Applied Physics Letter

Andreev Bound States in High Temperature Superconductors

Andreev bound states (ABS) at the surface of superconductors are expected for any pair potential showing a sign change in different k-directions with their spectral weight depending on the relative orientation of the surface and the pair potential. We report on the observation of ABS in HTS employing tunneling spectroscopy on bicrystal grain boundary Josephson junctions (GBJs). The tunneling spectra were studied as a function of temperature and applied magnetic field. The tunneling spectra of GBJ formed by YBCO, BSCCO, and LSCO show a pronounced zero bias conductance peak that can be interpreted in terms of Andreev bound states at zero energy that are expected at the surface of HTS having a d-wave symmetry of the order parameter. In contrast, for the most likely s-wave HTS NCCO no zero bias conductance peak was observed. Applying a magnetic field results in a shift of spectral weight from zero to finite energy. This shift is found to depend nonlinearly on the applied magnetic field. Further consequences of the Andreev bound states are discussed and experimental evidence for anomalous Meissner currents is presented.Comment: 17 pages, 10 figures, to appear in Eur. Phys. J.