56,778 research outputs found
Combinatorial Hopf algebras from renormalization
In this paper we describe the right-sided combinatorial Hopf structure of
three Hopf algebras appearing in the context of renormalization in quantum
field theory: the non-commutative version of the Fa\`a di Bruno Hopf algebra,
the non-commutative version of the charge renormalization Hopf algebra on
planar binary trees for quantum electrodynamics, and the non-commutative
version of the Pinter renormalization Hopf algebra on any bosonic field. We
also describe two general ways to define the associative product in such Hopf
algebras, the first one by recursion, and the second one by grafting and
shuffling some decorated rooted trees.Comment: 16 page
Subtractive renormalization of the NN scattering amplitude at leading order in chiral effective theory
The leading-order nucleon-nucleon (NN) potential derived from chiral
perturbation theory consists of one-pion exchange plus a short-distance contact
interaction. We show that in the 1S0 and 3S1-3D1 channels renormalization of
the Lippmann-Schwinger equation for this potential can be achieved by
performing one subtraction. This subtraction requires as its only input
knowledge of the NN scattering lengths. This procedure leads to a set of
integral equations for the partial-wave NN t-matrix which give
cutoff-independent results for the corresponding NN phase shifts. This
reformulation of the NN scattering equation offers practical advantages,
because only observable quantities appear in the integral equation. The
scattering equation may then be analytically continued to negative energies,
where information on bound-state energies and wave functions can be extracted.Comment: 16 pages, 11 figure
CP Violation and Arrows of Time Evolution of a Neutral or Meson from an Incoherent to a Coherent State
We study the evolution of a neutral meson prepared as an incoherent equal
mixture of and . Denoting the density matrix by \rho(t) =
{1/2} N(t) [\1 + \vec{\zeta}(t) \cdot \vec{\sigma} ] , the norm of the state
is found to decrease monotonically from one to zero, while the magnitude
of the Stokes vector increases monotonically from zero to
one. This property qualifies these observables as arrows of time. Requiring
monotonic behaviour of for arbitrary values of and
yields a bound on the CP-violating overlap , which is similar to, but weaker than, the known unitarity
bound. A similar requirement on yields a new bound,
which is particularly effective in limiting
the CP-violating overlap in the - system. We obtain the Stokes
parameter which shows how the average strangeness of the beam
evolves from zero to . The evolution of the Stokes vector from
to has a resemblance to an order
parameter of a system undergoing spontaneous symmetry breaking.Comment: 13 pages, 6 figures. Inserted conon "." in title; minor change in
text. To appear in Physical review
Liquid-induced damping of mechanical feedback effects in single electron tunneling through a suspended carbon nanotube
In single electron tunneling through clean, suspended carbon nanotube devices
at low temperature, distinct switching phenomena have regularly been observed.
These can be explained via strong interaction of single electron tunneling and
vibrational motion of the nanotube. We present measurements on a highly stable
nanotube device, subsequently recorded in the vacuum chamber of a dilution
refrigerator and immersed in the 3He/4He mixture of a second dilution
refrigerator. The switching phenomena are absent when the sample is kept in the
viscous liquid, additionally supporting the interpretation of dc-driven
vibration. Transport measurements in liquid helium can thus be used for finite
bias spectroscopy where otherwise the mechanical effects would dominate the
current.Comment: 4 pages, 3 figure
Subtractive renormalization of the NN interaction in chiral effective theory up to next-to-next-to-leading order: S waves
We extend our subtractive-renormalization method in order to evaluate the 1S0
and 3S1-3D1 NN scattering phase shifts up to next-to-next-to-leading order
(NNLO) in chiral effective theory. We show that, if energy-dependent contact
terms are employed in the NN potential, the 1S0 phase shift can be obtained by
carrying out two subtractions on the Lippmann-Schwinger equation. These
subtractions use knowledge of the the scattering length and the 1S0 phase shift
at a specific energy to eliminate the low-energy constants in the contact
interaction from the scattering equation. For the J=1 coupled channel, a
similar renormalization can be achieved by three subtractions that employ
knowledge of the 3S1 scattering length, the 3S1 phase shift at a specific
energy and the 3S1-3D1 generalized scattering length. In both channels a
similar method can be applied to a potential with momentum-dependent contact
terms, except that in that case one of the subtractions must be replaced by a
fit to one piece of experimental data.
This method allows the use of arbitrarily high cutoffs in the
Lippmann-Schwinger equation. We examine the NNLO S-wave phase shifts for
cutoffs as large as 5 GeV and show that the presence of linear energy
dependence in the NN potential creates spurious poles in the scattering
amplitude. In consequence the results are in conflict with empirical data over
appreciable portions of the considered cutoff range. We also identify problems
with the use of cutoffs greater than 1 GeV when momentum-dependent contact
interactions are employed. These problems are ameliorated, but not eliminated,
by the use of spectral-function regularization for the two-pion exchange part
of the NN potentialComment: 40 pages, 21 figure
Optimal competitiveness for the Rectilinear Steiner Arborescence problem
We present optimal online algorithms for two related known problems involving
Steiner Arborescence, improving both the lower and the upper bounds. One of
them is the well studied continuous problem of the {\em Rectilinear Steiner
Arborescence} (). We improve the lower bound and the upper bound on the
competitive ratio for from and to
, where is the number of Steiner
points. This separates the competitive ratios of and the Symetric-,
two problems for which the bounds of Berman and Coulston is STOC 1997 were
identical. The second problem is one of the Multimedia Content Distribution
problems presented by Papadimitriou et al. in several papers and Charikar et
al. SODA 1998. It can be viewed as the discrete counterparts (or a network
counterpart) of . For this second problem we present tight bounds also in
terms of the network size, in addition to presenting tight bounds in terms of
the number of Steiner points (the latter are similar to those we derived for
)
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