From nesting to dressing

In integrable field theories the S-matrix is usually a product of a relatively simple matrix and a complicated scalar factor. We make an observation that in many relativistic integrable field theories the scalar factor can be expressed as a convolution of simple kernels appearing in the nested levels of the nested Bethe ansatz. We formulate a proposal, up to some discrete ambiguities, how to reconstruct the scalar factor from the nested Bethe equations and check it for several relativistic integrable field theories. We then apply this proposal to the AdS asymptotic Bethe ansatz and recover the dressing factor in the integral representation of Dorey, Hofman and Maldacena.Comment: 23 pages, no figures; v2: small improvements, references adde

Satisfiability in multi-valued circuits

Satisfiability of Boolean circuits is among the most known and important problems in theoretical computer science. This problem is NP-complete in general but becomes polynomial time when restricted either to monotone gates or linear gates. We go outside Boolean realm and consider circuits built of any fixed set of gates on an arbitrary large finite domain. From the complexity point of view this is strictly connected with the problems of solving equations (or systems of equations) over finite algebras. The research reported in this work was motivated by a desire to know for which finite algebras $\mathbf A$ there is a polynomial time algorithm that decides if an equation over $\mathbf A$ has a solution. We are also looking for polynomial time algorithms that decide if two circuits over a finite algebra compute the same function. Although we have not managed to solve these problems in the most general setting we have obtained such a characterization for a very broad class of algebras from congruence modular varieties. This class includes most known and well-studied algebras such as groups, rings, modules (and their generalizations like quasigroups, loops, near-rings, nonassociative rings, Lie algebras), lattices (and their extensions like Boolean algebras, Heyting algebras or other algebras connected with multi-valued logics including MV-algebras). This paper seems to be the first systematic study of the computational complexity of satisfiability of non-Boolean circuits and solving equations over finite algebras. The characterization results provided by the paper is given in terms of nice structural properties of algebras for which the problems are solvable in polynomial time.Comment: 50 page

How far is it to a sudden future singularity of pressure?

We discuss the constraints coming from current observations of type Ia supernovae on cosmological models which allow sudden future singularities of pressure (with the scale factor and the energy density regular). We show that such a sudden singularity may happen in the very near future (e.g. within ten million years) and its prediction at the present moment of cosmic evolution cannot be distinguished, with current observational data, from the prediction given by the standard quintessence scenario of future evolution. Fortunately, sudden future singularities are characterized by a momentary peak of infinite tidal forces only; there is no geodesic incompletness which means that the evolution of the universe may eventually be continued throughout until another ``more serious'' singularity such as Big-Crunch or Big-Rip.Comment: REVTEX4, 4 pages, 2 figures, references change

Quantum Telescopes: feasibility and constrains

Quantum Telescope is a recent idea aimed at beating the diffraction limit of spaceborne telescopes and possibly also other distant target imaging systems. There is no agreement yet on the best setup of such devices, but some configurations have been already proposed. In this Letter we characterize the predicted performance of Quantum Telescopes and their possible limitations. Our extensive simulations confirm that the presented model of such instruments is feasible and the device can provide considerable gains in the angular resolution of imaging in the UV, optical and infrared bands. We argue that it is generally possible to construct and manufacture such instruments using the latest or soon to be available technology. We refer to the latest literature to discuss the feasibility of the proposed QT system design.Comment: Optics Letters - published after major revisio

Phase diagram of the non-uniform chiral condensate in different regularization schemes at T=0

We show that the qualitative picture of the phase diagram which includes the non-uniform chiral phase and 2SC superconducting phase is independent of the considered regularization schemes. We also demonstrate that the quantitative results agree with each other reasonably for the set of so called "relativistic" regularization schemes. On the other hand the "non-relativistic" momentum cut-off is clearly differ from the others