ASD (Abstract Stone Duality) is a re-axiomatisation of general topology in which the topology on a space is treated, not as an infinitary lattice, but as an exponential object of the same category as the original space, with an associated lambda-calculus. In this paper, this is shown to be equivalent to a notion of computable basis for locally compact sober spaces or locales, involving a family...

Lattice gadgets and the associated algorithms are essential building blocks of lattice-based cryptography. In past decade, they have been applied to build versatile powerful cryptosystems. However, practical optimizations designs gadget-based schemes generally lag their theoretical constructions. For example, signatures elegant design capability extending more advanced primitives, but far less ...

Abstract In lattice compact gauge theories, we must impose the admissibility condition to have well-defined topological sectors. The condition, however, usually forbids presence of magnetic operators, and it is not so trivial if one can study physics objects that depends on term, such as Witten effect, lattice. this paper, address question in case 2D scalars would be simplest examples having an...

A new method based on the Monte-Carlo calculation on the lattice is proposed to study the Casimir effect in the compact lattice U(1) theory with Wilson action. We have studied the standard Casimir problem with two parallel plane surfaces (mirrors) and oblique boundary conditions on those as a test of our method. Physically, this boundary conditions may appear in the problem of modelling of the ...

We investigate a model of a U(1)–Higgs theory on the lattice with compact gauge fields but completely suppressed (elementary) monopoles. We study the model at two values of the quartic Higgs self–coupling, a strong coupling, λ = 3.0, and a weak coupling, λ = 0.01. We map out the phase diagrams and find that the monopole suppression eliminated the confined phase of the standard lattice model at ...