2,862 research outputs found
A Quantum Field Theoretical Representation of Euler-Zagier Sums
We establish a novel representation of arbitrary Euler-Zagier sums in terms
of weighted vacuum graphs. This representation uses a toy quantum field theory
with infinitely many propagators and interaction vertices. The propagators
involve Bernoulli polynomials and Clausen functions to arbitrary orders. The
Feynman integrals of this model can be decomposed in terms of an algebra of
elementary vertex integrals whose structure we investigate. We derive a large
class of relations between multiple zeta values, of arbitrary lengths and
weights, using only a certain set of graphical manipulations on Feynman
diagrams. Further uses and possible generalizations of the model are pointed
out.Comment: Standard latex, 31 pages, 13 figures, final published versio
Comparison of ion sites and diffusion paths in glasses obtained by molecular dynamics simulations and bond valence analysis
Based on molecular dynamics simulations of a lithium metasilicate glass we
study the potential of bond valence sum calculations to identify sites and
diffusion pathways of mobile Li ions in a glassy silicate network. We find that
the bond valence method is not well suitable to locate the sites, but allows
one to estimate the number of sites. Spatial regions of the glass determined as
accessible for the Li ions by the bond valence method can capture up to 90% of
the diffusion path. These regions however entail a significant fraction that
does not belong to the diffusion path. Because of this low specificity, care
must be taken to determine the diffusive motion of particles in amorphous
systems based on the bond valence method. The best identification of the
diffusion path is achieved by using a modified valence mismatch in the BV
analysis that takes into account that a Li ion favors equal partial valences to
the neighboring oxygen ions. Using this modified valence mismatch it is
possible to replace hard geometric constraints formerly applied in the BV
method. Further investigations are necessary to better understand the relation
between the complex structure of the host network and the ionic diffusion
paths.Comment: 16 pages, 10 figure
Joint measurement of complementary observables in moment tomography
Wigner and Husimi quasi-distributions, owing to their functional regularity,
give the two archetypal and equivalent representations of all
observable-parameters in continuous-variable quantum information. Balanced
homodyning and heterodyning that correspond to their associated sampling
procedures, on the other hand, fare very differently concerning their state or
parameter reconstruction accuracies. We present a general theory of a now-known
fact that heterodyning can be tomographically more powerful than balanced
homodyning to many interesting classes of single-mode quantum states, and
discuss the treatment for two-mode sources.Comment: 15 pages, 4 figures, conference proceedings for Quantum 2017 in
Torin
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