18,128 research outputs found
Improved Estimates for the Parameters of the Heavy Quark Expansion
We give improved estimates for the non-perturbative parameters appearing in
the heavy quark expansion for inclusive decays. While the parameters appearing
in low orders of this expansion can be extracted from data, the number of
parameters in higher orders proliferates strongly, making a determination of
these parameters from data impossible. Thus, one has to rely on theoretical
estimates which may be obtained from an insertion of intermediate states. In
this paper we refine this method and attempt to estimate the uncertainties of
this approach.Comment: 18 pages (v2: Fixed sign error in section 3. conclusions unchanged
Simplification of the Spectral Analysis of the Volume Operator in Loop Quantum Gravity
The Volume Operator plays a crucial role in the definition of the quantum
dynamics of Loop Quantum Gravity (LQG). Efficient calculations for dynamical
problems of LQG can therefore be performed only if one has sufficient control
over the volume spectrum. While closed formulas for the matrix elements are
currently available in the literature, these are complicated polynomials in 6j
symbols which in turn are given in terms of Racah's formula which is too
complicated in order to perform even numerical calculations for the
semiclassically important regime of large spins. Hence, so far not even
numerically the spectrum could be accessed. In this article we demonstrate that
by means of the Elliot -- Biedenharn identity one can get rid of all the 6j
symbols for any valence of the gauge invariant vertex, thus immensely reducing
the computational effort. We use the resulting compact formula to study
numerically the spectrum of the gauge invariant 4 -- vertex. The techniques
derived in this paper could be of use also for the analysis of spin -- spin
interaction Hamiltonians of many -- particle problems in atomic and nuclear
physics.Comment: 56 pages, Latex2e, 15 picture
The Decay of Unstable Noncommutative Solitons
We study the classical decay of unstable scalar solitons in noncommutative
field theory in 2+1 dimensions. This can, but does not have to, be viewed as a
toy model for the decay of D-branes in string theory. In the limit that the
noncommutativity parameter \theta is infinite, the gradient term is absent,
there are no propagating modes and the soliton does not decay at all. If \theta
is large, but finite, the rotationally symmetric decay channel can be described
as a highly excited nonlinear oscillator weakly coupled to a continuum of
linear modes. This system is closely akin to those studied in the context of
discrete breathers. We here diagonalize the linear problem and compute the
decay rate to first order using a version of Fermi's Golden Rule, leaving a
more rigorous treatment for future work.Comment: 36 pages, 7 figures, dedicated to Rudolf Haag. v2: uniform estimate
for Weyl criterion provided, refs adde
Estimating the privacy of quantum-random numbers
We analyze the information an attacker can obtain on the numbers generated by
a user by measurements on a subsystem of a system consisting of two entangled
two-level systems. The attacker and the user make measurements on their
respective subsystems, only. Already the knowledge of the density matrix of the
subsystem of the user completely determines the upper bound on the information
accessible to the attacker. We compare and contrast this information to the
appropriate bounds provided by quantum state discrimination.Comment: 26 pages, 4 figure
Support Sets in Exponential Families and Oriented Matroid Theory
The closure of a discrete exponential family is described by a finite set of
equations corresponding to the circuits of an underlying oriented matroid.
These equations are similar to the equations used in algebraic statistics,
although they need not be polynomial in the general case. This description
allows for a combinatorial study of the possible support sets in the closure of
an exponential family. If two exponential families induce the same oriented
matroid, then their closures have the same support sets. Furthermore, the
positive cocircuits give a parameterization of the closure of the exponential
family.Comment: 27 pages, extended version published in IJA
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