A Paraconsistent Higher Order Logic

Classical logic predicts that everything (thus nothing useful at all) follows from inconsistency. A paraconsistent logic is a logic where an inconsistency does not lead to such an explosion, and since in practice consistency is difficult to achieve there are many potential applications of paraconsistent logics in knowledge-based systems, logical semantics of natural language, etc. Higher order logics have the advantages of being expressive and with several automated theorem provers available. Also the type system can be helpful. We present a concise description of a paraconsistent higher order logic with countable infinite indeterminacy, where each basic formula can get its own indeterminate truth value (or as we prefer: truth code). The meaning of the logical operators is new and rather different from traditional many-valued logics as well as from logics based on bilattices. The adequacy of the logic is examined by a case study in the domain of medicine. Thus we try to build a bridge between the HOL and MVL communities. A sequent calculus is proposed based on recent work by Muskens.Comment: Originally in the proceedings of PCL 2002, editors Hendrik Decker, Joergen Villadsen, Toshiharu Waragai (http://floc02.diku.dk/PCL/). Correcte

Superfluid Spin-down, with Random Unpinning of the Vortices

The so-called ``creeping'' motion of the pinned vortices in a rotating superfluid involves ``random unpinning'' and ``vortex motion'' as two physically separate processes. We argue that such a creeping motion of the vortices need not be (biased) in the direction of an existing radial Magnus force, nor should a constant microscopic radial velocity be assigned to the vortex motion, in contradiction with the basic assumptions of the ``vortex creep'' model. We point out internal inconsistencies in the predictions of this model which arise due to this unjustified foundation that ignores the role of the actual torque on the superfluid. The proper spin-down rate of a pinned superfluid is then calculated and turns out to be much less than that suggested in the vortex creep model, hence being of even less observational significance for its possible application in explaining the post-glitch relaxations of the radio pulsars.Comment: To be published in J. Low Temp. Phys., Vol. 139, May 2005 [Eqs 11, 15-17 here, have been revised and, may be substituted for the corresponding ones in that paper

Maximum solutions of normalized Ricci flows on 4-manifolds

We consider maximum solution $g(t)$, $t\in [0, +\infty)$, to the normalized Ricci flow. Among other things, we prove that, if $(M, \omega)$ is a smooth compact symplectic 4-manifold such that $b_2^+(M)>1$ and let $g(t),t\in[0,\infty)$, be a solution to (1.3) on $M$ whose Ricci curvature satisfies that $|\text{Ric}(g(t))|\leq 3$ and additionally $\chi(M)=3 \tau (M)>0$, then there exists an $m\in \mathbb{N}$, and a sequence of points $\{x_{j,k}\in M\}$, $j=1, ..., m$, satisfying that, by passing to a subsequence, $$(M, g(t_{k}+t), x_{1,k},..., x_{m,k}) \stackrel{d_{GH}}\longrightarrow (\coprod_{j=1}^m N_j, g_{\infty}, x_{1,\infty}, ...,, x_{m,\infty}),$$ $t\in [0, \infty)$, in the $m$-pointed Gromov-Hausdorff sense for any sequence $t_{k}\longrightarrow \infty$, where $(N_{j}, g_{\infty})$, $j=1,..., m$, are complete complex hyperbolic orbifolds of complex dimension 2 with at most finitely many isolated orbifold points. Moreover, the convergence is $C^{\infty}$ in the non-singular part of $\coprod_1^m N_{j}$ and $\text{Vol}_{g_{0}}(M)=\sum_{j=1}^{m}\text{Vol}_{g_{\infty}}(N_{j})$, where $\chi(M)$ (resp. $\tau(M)$) is the Euler characteristic (resp. signature) of $M$.Comment: 23 page

Condensate fluctuations of a trapped, ideal Bose gas

For a non-self-interacting Bose gas with a fixed, large number of particles confined to a trap, as the ground state occupation becomes macroscopic, the condensate number fluctuations remain micrscopic. However, this is the only significant aspect in which the grand canonical description differs from canonical or microcanonical in the thermodynamic limit. General arguments and estimates including some vanishingly small quantities are compared to explicit, fixed-number calculations for 10^2 to 10^6 particles.Comment: 16 pages (REVTeX) plus 4 figures (ps), revision includes brief comparison of repulsive-interaction vs. fixed-N fluctuation damping. To be published in Phys. Rev.

Quantum backreaction of massive fields and self-consistent semiclassical extreme black holes and acceleration horizons

We consider the effect of backreaction of quantized massive fields on the metric of extreme black holes (EBH). We find the analytical approximate expression for the stress-energy tensor for a scalar (with an arbitrary coupling), spinor and vector fields near an event horizon. We show that, independent of a concrete type of EBH, the energy measured by a freely falling observer is finite on the horizon, so that quantum backreaction is consistent with the existence of EBH. For the Reissner-Nordstrom EBH with a total mass M_{tot} and charge Q we show that for all cases of physical interest M_{tot}< Q. We also discuss different types of quantum-corrected Bertotti-Robinson spacetimes, find for them exact self-consistent solutions and consider situations in which tiny quantum corrections lead to the qualitative change of the classical geometry and topology. In all cases one should start not from a classical background with further adding quantum corrections but from the quantum-corrected self-consistent geometries from the very beginning.Comment: Minor corrections. To appear in Phys. Rev.

Mean field approach to antiferromagnetic domains in the doped Hubbard model

We present a restricted path integral approach to the 2D and 3D repulsive Hubbard model. In this approach the partition function is approximated by restricting the summation over all states to a (small) subclass which is chosen such as to well represent the important states. This procedure generalizes mean field theory and can be systematically improved by including more states or fluctuations. We analyze in detail the simplest of these approximations which corresponds to summing over states with local antiferromagnetic (AF) order. If in the states considered the AF order changes sufficiently little in space and time, the path integral becomes a finite dimensional integral for which the saddle point evaluation is exact. This leads to generalized mean field equations allowing for the possibility of more than one relevant saddle points. In a big parameter regime (both in temperature and filling), we find that this integral has {\em two} relevant saddle points, one corresponding to finite AF order and the other without. These degenerate saddle points describe a phase of AF ordered fermions coexisting with free, metallic fermions. We argue that this mixed phase is a simple mean field description of a variety of possible inhomogeneous states, appropriate on length scales where these states appear homogeneous. We sketch systematic refinements of this approximation which can give more detailed descriptions of the system.Comment: 14 pages RevTex, 6 postscript figures included using eps

Thermal Hall conductivity of marginal Fermi liquids subject to out-of plane impurities in high-TcT_c cuprates

The effect of out-of-plane impurities on the thermal Hall conductivity $\kappa_{xy}$ of in-plane marginal-Fermi-liquid (MFL) quasiparticles in high-$T_c$ cuprates is examined by following the work on electrical Hall conductivity $\sigma_{xy}$ by Varma and Abraham [Phys. Rev. Lett. 86, 4652 (2001)]. It is shown that the effective Lorentz force exerted by these impurities is a weak function of energies of the MFL quasiparticles, resulting in nearly the same temperature dependence of $\kappa_{xy}/T$ and $\sigma_{xy}$, indicative of obedience of the Wiedemann-Franz law. The inconsistency of the theoretical result with the experimental one is speculated to be the consequence of the different amounts of out-of-plane impurities in the two YBaCuO samples used for the $\kappa_{xy}$ and $\sigma_{xy}$ measurements.Comment: 5 pages, 2 eps figures; final versio

Resistivity of a Metal between the Boltzmann Transport Regime and the Anderson Transition

We study the transport properties of a finite three dimensional disordered conductor, for both weak and strong scattering on impurities, employing the real-space Green function technique and related Landauer-type formula. The dirty metal is described by a nearest neighbor tight-binding Hamiltonian with a single s-orbital per site and random on-site potential (Anderson model). We compute exactly the zero-temperature conductance of a finite size sample placed between two semi-infinite disorder-free leads. The resistivity is found from the coefficient of linear scaling of the disorder averaged resistance with sample length. This ``quantum'' resistivity is compared to the semiclassical Boltzmann expression computed in both Born approximation and multiple scattering approximation.Comment: 5 pages, 3 embedded EPS figure

Analytical approximation of the stress-energy tensor of a quantized scalar field in static spherically symmetric spacetimes

Analytical approximations for ${}$ and ${}$ of a quantized scalar field in static spherically symmetric spacetimes are obtained. The field is assumed to be both massive and massless, with an arbitrary coupling $\xi$ to the scalar curvature, and in a zero temperature vacuum state. The expressions for ${}$ and ${}$ are divided into low- and high-frequency parts. The contributions of the high-frequency modes to these quantities are calculated for an arbitrary quantum state. As an example, the low-frequency contributions to ${}$ and ${}$ are calculated in asymptotically flat spacetimes in a quantum state corresponding to the Minkowski vacuum (Boulware quantum state). The limits of the applicability of these approximations are discussed.Comment: revtex4, 17 pages; v2: three references adde

Anderson-Yuval approach to the multichannel Kondo problem

We analyze the structure of the perturbation expansion of the general multichannel Kondo model with channel anisotropic exchange couplings and in the presence of an external magnetic field, generalizing to this case the Anderson-Yuval technique. For two channels, we are able to map the Kondo model onto a generalized resonant level model. Limiting cases in which the equivalent resonant level model is solvable are identified. The solution correctly captures the properties of the two channel Kondo model, and also allows an analytic description of the cross-over from the non Fermi liquid to the Fermi liquid behavior caused by the channel anisotropy.Comment: 23 pages, ReVTeX, 4 figures av. on reques