7,127 research outputs found
Noncommutative tori and universal sets of non-binary quantum gates
A problem of universality in simulation of evolution of quantum system and in
theory of quantum computations is related with the possibility of expression or
approximation of arbitrary unitary transformation by composition of specific
unitary transformations (quantum gates) from given set. In an earlier paper
(quant-ph/0010071) application of Clifford algebras to constructions of
universal sets of binary quantum gates was shown. For
application of a similar approach to non-binary quantum gates
in present work is used rational noncommutative torus . A
set of universal non-binary two-gates is presented here as one example.Comment: 5 pages, REVTeX3.1, v2: spelling and misprints, 4 new ref
Mode mixing in asymmetric double trench photonic crystal waveguides
e investigate both experimentally and theoretically the waveguiding
properties of a novel double trench waveguide where a conventional single-mode
strip waveguide is embedded in a two dimensional photonic crystal (PhC) slab
formed in silicon on insulator (SOI) wafers. We demonstrate that the bandwidth
for relatively low-loss (50dB/cm) waveguiding is significantly expanded to
250nm covering almost all the photonic band gap owing to nearly linear
dispersion of the TE-like waveguiding mode. The flat transmission spectrum
however is interrupted by numerous narrow stop bands. We found that these stop
bands can be attributed to anti-crossing between TE-like (positive parity) and
TM-like (negative parity) modes. This effect is a direct result of the strong
asymmetry of the waveguides that have an upper cladding of air and lower
cladding of oxide. To our knowledge this is the first demonstration of the
effects of cladding asymmetry on the transmission characteristics of the PhC
slab waveguides.Comment: 7 pages, 6 figure
New and Old Results in Resultant Theory
Resultants are getting increasingly important in modern theoretical physics:
they appear whenever one deals with non-linear (polynomial) equations, with
non-quadratic forms or with non-Gaussian integrals. Being a subject of more
than three-hundred-year research, resultants are of course rather well studied:
a lot of explicit formulas, beautiful properties and intriguing relationships
are known in this field. We present a brief overview of these results,
including both recent and already classical. Emphasis is made on explicit
formulas for resultants, which could be practically useful in a future physics
research.Comment: 50 pages, 15 figure
Spatial Solitons in Media with Delayed-Response Optical Nonlinearities
Near-soliton scanning light-beam propagation in media with both
delayed-response Kerr-type and thermal nonlinearities is analyzed. The
delayed-response part of the Kerr nonlinearity is shown to be competitive as
compared to the thermal nonlinearity, and relevant contributions to a
distortion of the soliton form and phase can be mutually compensated. This
quasi-soliton beam propagation regime keeps properties of the incli- ned
self-trapped channel.Comment: 7 pages, to be published in Europhys. Let
Changes of Granite Rapakivi under the Biofouling Influence
Interdisciplinary study of granite rapakivi biofouling in the natural and anthropogenic environment (St. Petersburg, Vyborg, Southern Finland) was carried out. The biodiversity of microorganisms (cyanobacteria, micromycetes, and organotrophic bacteria) and various types of biofilms are characterized. The influence of external factors on the changes of cyanobacterial biofilms is shown. The features of biofilms localization on the granite surface in an urban environment and in natural outcrops are studied. Differences in the biofilms metabolites composition at the granite quarries and monuments of St. Petersburg are shown. The behavior of chemical elements during the bioweathering of granite is estimated. The role of biofilms in the accumulation of chemical elements on the surface of granite is established. The dynamics of chemical elements leaching from granite may depend on the type of biofilm developing on granite
Correlations in Transmission of Light through a Disordered Amplifying Medium
The angular and frequency correlation functions of the transmission
coefficient for light propagation through a strongly scattering amplifying
medium are considered. It is found that just as in the case of an elastic
scattering medium the correlation function consists of three terms. However,
the structure of the terms is rather different. Angular correlation has a
power-law decay and exhibits oscillations. There is no "memory effect" as in
the case of an elastic medium. Interaction between diffusion modes is strongly
enhanced near the lasing threshold. Frequency correlation scale decreases close
to the lasing threshold.
We also consider time correlations of the transmission in the case of
nonstationary inhomogeneities. We find short- and long-range time correlations.
The scale of the short-range correlation decreases, while the long-range
correlation scale becomes infinite near the threshold.Comment: 16 pages, 7 postscript figure
Clifford algebras and universal sets of quantum gates
In this paper is shown an application of Clifford algebras to the
construction of computationally universal sets of quantum gates for -qubit
systems. It is based on the well-known application of Lie algebras together
with the especially simple commutation law for Clifford algebras, which states
that all basic elements either commute or anticommute.Comment: 4 pages, REVTeX (2 col.), low-level language corrections, PR
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