4,273 research outputs found
Force in Kappa-Deformed Relativistic Dynamics
We consider the physical implications of various choices of the
three-momentum basis in the kappa-deformed Poincare algebra. In particular, we
find that the energy dependence of the velocity of a kappa-particle leads to
unexpected features in kappa-deformed kinematics. We also discuss the notion of
kappa-deformed dynamics, and as a tool example we investigate the motion of a
kappa-deformed particle under the action of a constant force.Comment: LaTeX, 9 page
Algebraic Bethe Ansatz for a discrete-state BCS pairing model
We show in detail how Richardson's exact solution of a discrete-state BCS
(DBCS) model can be recovered as a special case of an algebraic Bethe Ansatz
solution of the inhomogeneous XXX vertex model with twisted boundary
conditions: by implementing the twist using Sklyanin's K-matrix construction
and taking the quasiclassical limit, one obtains a complete set of conserved
quantities, H_i, from which the DBCS Hamiltonian can be constructed as a second
order polynomial. The eigenvalues and eigenstates of the H_i (which reduce to
the Gaudin Hamiltonians in the limit of infinitely strong coupling) are exactly
known in terms of a set of parameters determined by a set of on-shell Bethe
Ansatz equations, which reproduce Richardson's equations for these parameters.
We thus clarify that the integrability of the DBCS model is a special case of
the integrability of the twisted inhomogeneous XXX vertex model. Furthermore,
by considering the twisted inhomogeneous XXZ model and/or choosing a generic
polynomial of the H_i as Hamiltonian, more general exactly solvable models can
be constructed. -- To make the paper accessible to readers that are not Bethe
Ansatz experts, the introductory sections include a self-contained review of
those of its feature which are needed here.Comment: 17 pages, 5 figures, submitted to Phys. Rev.
Ornstein-Uhlenbeck-Cauchy Process
We combine earlier investigations of linear systems with L\'{e}vy
fluctuations [Physica {\bf 113A}, 203, (1982)] with recent discussions of
L\'{e}vy flights in external force fields [Phys.Rev. {\bf E 59},2736, (1999)].
We give a complete construction of the Ornstein-Uhlenbeck-Cauchy process as a
fully computable model of an anomalous transport and a paradigm example of
Doob's stable noise-supported Ornstein-Uhlenbeck process. Despite the
nonexistence of all moments, we determine local characteristics (forward drift)
of the process, generators of forward and backward dynamics, relevant
(pseudodifferential) evolution equations. Finally we prove that this random
dynamics is not only mixing (hence ergodic) but also exact. The induced
nonstationary spatial process is proved to be Markovian and quite apart from
its inherent discontinuity defines an associated velocity process in a
probabilistic sense.Comment: Latex fil
Lecture Notes on Noncommutative Algebraic Geometry and Noncommutative Tori
The first part of these notes gives an introduction to noncommutative
projective geometry after Artin--Zhang. The second part provides an overview of
the work of Polishchuk that reconciles noncommutative two-tori having real
multiplication with the Artin--Zhang setting.Comment: Final version - exposition improved; a proof of the derived
equivalence added (Prop. 3.8). To appear in the proceedings volume of the
"International Workshop on Noncommutative Geometry", IPM, Tehran 200
Z2SAL: a translation-based model checker for Z
Despite being widely known and accepted in industry, the Z formal specification language has not so far been well supported by automated verification tools, mostly because of the challenges in handling the abstraction of the language. In this paper we discuss a novel approach to building a model-checker for Z, which involves implementing a translation from Z into SAL, the input language for the Symbolic Analysis Laboratory, a toolset which includes a number of model-checkers and a simulator. The Z2SAL translation deals with a number of important issues, including: mapping unbounded, abstract specifications into bounded, finite models amenable to a BDD-based symbolic checker; converting a non-constructive and piecemeal style of functional specification into a deterministic, automaton-based style of specification; and supporting the rich set-based vocabulary of the Z mathematical toolkit. This paper discusses progress made towards implementing as complete and faithful a translation as possible, while highlighting certain assumptions, respecting certain limitations and making use of available optimisations. The translation is illustrated throughout with examples; and a complete working example is presented, together with performance data
D-branes, orbifolds, and Ext groups
In this note we extend previous work on massless Ramond spectra of open
strings connecting D-branes wrapped on complex manifolds, to consider D-branes
wrapped on smooth complex orbifolds. Using standard methods, we calculate the
massless boundary Ramond sector spectra directly in BCFT, and find that the
states in the spectrum are counted by Ext groups on quotient stacks (which
provide a notion of homological algebra relevant for orbifolds). Subtleties
that cropped up in our previous work also appear here. We also use the McKay
correspondence to relate Ext groups on quotient stacks to Ext groups on (large
radius) resolutions of the quotients. As stacks are not commonly used in the
physics community, we include pedagogical discussions of some basic relevant
properties of stacks.Comment: 51 pages, 3 figures; v2: material on Freed-Witten added; v3: more
typos fixe
An Algebraic Spin and Statistics Theorem
A spin-statistics theorem and a PCT theorem are obtained in the context of
the superselection sectors in Quantum Field Theory on a 4-dimensional
space-time. Our main assumption is the requirement that the modular groups of
the von Neumann algebras of local observables associated with wedge regions act
geometrically as pure Lorentz transformations. Such a property, satisfied by
the local algebras generated by Wightman fields because of the
Bisognano-Wichmann theorem, is regarded as a natural primitive assumption.Comment: 15 pages, plain TeX, an error in the statement of a theorem has been
corrected, to appear in Commun. Math. Phy
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