21,873 research outputs found
Two-loop Improved Truncation of the Ghost-Gluon Dyson-Schwinger Equations: Multiplicatively Renormalizable Propagators and Nonperturbative Running Coupling
The coupled Dyson-Schwinger equations for the gluon and ghost propagators are
investigated in the Landau gauge using a two-loop improved truncation that
preserves the multiplicative renormalizability of the propagators. In this
truncation all diagrams contribute to the leading order infrared analysis. The
infrared contributions of the nonperturbative two-loop diagrams to the gluon
vacuum polarization are computed analytically, and this reveals that infrared
power behaved propagator solutions only exist when the squint diagram
contribution is taken into account. For small momenta the gluon and ghost
dressing functions behave respectively like (p^2)^{2\kappa} and
(p^2)^{-\kappa}, and the running coupling exhibits a fixed point. The values of
the infrared exponent and fixed point depend on the precise details of the
truncation. The coupled ghost-gluon system is solved numerically for all
momenta, and the solutions have infrared behaviors consistent with the
predictions of the infrared analysis. For truncation parameters chosen such
that \kappa=0.5, the two-loop improved truncation is able to produce solutions
for the propagators and running coupling which are in very good agreement with
recent lattice simulations.Comment: 41 pages, LateX; minor corrections; accepted for publication in
Few-Body System
Comment on "Nucleon form factors and a nonpointlike diquark"
Authors of Phys. Rev. C 60, 062201 (1999) presented a calculation of the
electromagnetic form factors of the nucleon using a diquark ansatz in the
relativistic three-quark Faddeev equations. In this Comment it is pointed out
that the calculations of these form factors stem from a three-quark bound state
current that contains overcounted contributions. The corrected expression for
the three-quark bound state current is derived.Comment: 6 pages, 1 figure, revtex, eps
Finite Controllability of Infinite-Dimensional Quantum Systems
Quantum phenomena of interest in connection with applications to computation
and communication almost always involve generating specific transfers between
eigenstates, and their linear superpositions. For some quantum systems, such as
spin systems, the quantum evolution equation (the Schr\"{o}dinger equation) is
finite-dimensional and old results on controllability of systems defined on on
Lie groups and quotient spaces provide most of what is needed insofar as
controllability of non-dissipative systems is concerned. However, in an
infinite-dimensional setting, controlling the evolution of quantum systems
often presents difficulties, both conceptual and technical. In this paper we
present a systematic approach to a class of such problems for which it is
possible to avoid some of the technical issues. In particular, we analyze
controllability for infinite-dimensional bilinear systems under assumptions
that make controllability possible using trajectories lying in a nested family
of pre-defined subspaces. This result, which we call the Finite Controllability
Theorem, provides a set of sufficient conditions for controllability in an
infinite-dimensional setting. We consider specific physical systems that are of
interest for quantum computing, and provide insights into the types of quantum
operations (gates) that may be developed.Comment: This is a much improved version of the paper first submitted to the
arxiv in 2006 that has been under review since 2005. A shortened version of
this paper has been conditionally accepted for publication in IEEE
Transactions in Automatic Control (2009
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