8,861 research outputs found
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 there is a polynomial time algorithm that
decides if an equation over 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
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