A quantum group version of quantum gauge theories in two dimensions

For the special case of the quantum group $SL_q (2,{\bf C})\ (q= \exp \pi i/r,\ r\ge 3)$ we present an alternative approach to quantum gauge theories in two dimensions. We exhibit the similarities to Witten's combinatorial approach which is based on ideas of Migdal. The main ingredient is the Turaev-Viro combinatorial construction of topological invariants of closed, compact 3-manifolds and its extension to arbitrary compact 3-manifolds as given by the authors in collaboration with W. Mueller.Comment: 6 pages (plain TeX

Quantum analogues of Hardy's nonlocality paradox

Hardy's nonlocality is a "nonlocality proof without inequalities": it exemplifies that quantum correlations can be qualitatively stronger than classical correlations. This paper introduces variants of Hardy's nonlocality in the CHSH scenario which are realized by the PR-box, but not by quantum correlations. Hence this new kind of Hardy-type nonlocality is a proof without inequalities showing that superquantum correlations can be qualitatively stronger than quantum correlations.Comment: minor fixe

Decidability of quantified propositional intuitionistic logic and S4 on trees

Quantified propositional intuitionistic logic is obtained from propositional intuitionistic logic by adding quantifiers \forall p, \exists p over propositions. In the context of Kripke semantics, a proposition is a subset of the worlds in a model structure which is upward closed. Kremer (1997) has shown that the quantified propositional intuitionistic logic H\pi+ based on the class of all partial orders is recursively isomorphic to full second-order logic. He raised the question of whether the logic resulting from restriction to trees is axiomatizable. It is shown that it is, in fact, decidable. The methods used can also be used to establish the decidability of modal S4 with propositional quantification on similar types of Kripke structures.Comment: v2, 9 pages, corrections and additions; v1 8 page

Numerical Simulation of Vortex Crystals and Merging in N-Point Vortex Systems with Circular Boundary

In two-dimensional (2D) inviscid incompressible flow, low background vorticity distribution accelerates intense vortices (clumps) to merge each other and to array in the symmetric pattern which is called ``vortex crystals''; they are observed in the experiments on pure electron plasma and the simulations of Euler fluid. Vortex merger is thought to be a result of negative ``temperature'' introduced by L. Onsager. Slight difference in the initial distribution from this leads to ``vortex crystals''. We study these phenomena by examining N-point vortex systems governed by the Hamilton equations of motion. First, we study a three-point vortex system without background distribution. It is known that a N-point vortex system with boundary exhibits chaotic behavior for N\geq 3. In order to investigate the properties of the phase space structure of this three-point vortex system with circular boundary, we examine the Poincar\'e plot of this system. Then we show that topology of the Poincar\'e plot of this system drastically changes when the parameters, which are concerned with the sign of ``temperature'', are varied. Next, we introduce a formula for energy spectrum of a N-point vortex system with circular boundary. Further, carrying out numerical computation, we reproduce a vortex crystal and a vortex merger in a few hundred point vortices system. We confirm that the energy of vortices is transferred from the clumps to the background in the course of vortex crystallization. In the vortex merging process, we numerically calculate the energy spectrum introduced above and confirm that it behaves as k^{-\alpha},(\alpha\approx 2.2-2.8) at the region 10^0<k<10^1 after the merging.Comment: 30 pages, 11 figures. to be published in Journal of Physical Society of Japan Vol.74 No.

A note on bound entanglement and local realism

We show using a numerical approach that gives necessary and sufficient conditions for the existence of local realism, that the bound entangled state presented in Bennett et. al. Phys. Rev. Lett. 82, 5385 (1999) admits a local and realistic description. We also find the lowest possible amount of some appropriate entangled state that must be ad-mixed to the bound entangled state so that the resulting density operator has no local and realistic description and as such can be useful in quantum communication and quantum computation.Comment: 5 page

The Bell Theorem as a Special Case of a Theorem of Bass

The theorem of Bell states that certain results of quantum mechanics violate inequalities that are valid for objective local random variables. We show that the inequalities of Bell are special cases of theorems found ten years earlier by Bass and stated in full generality by Vorob'ev. This fact implies precise necessary and sufficient mathematical conditions for the validity of the Bell inequalities. We show that these precise conditions differ significantly from the definition of objective local variable spaces and as an application that the Bell inequalities may be violated even for objective local random variables.Comment: 15 pages, 2 figure