42,526 research outputs found
Tetrahedratic mesophases, chiral order, and helical domains induced by quadrupolar and octupolar interactions
We present an exhaustive account of phases and phase transitions that can be stabilized in the recently introduced generalized Lebwohl-Lasher model with quadrupolar and octupolar microscopic interactions [ L. Longa, G. Pająk and T. Wydro Phys. Rev. E 79 040701 (2009)]. A complete mean-field analysis of the model, along with Monte Carlo simulations allows us to identify four distinct classes of the phase diagrams with a number of multicritical points where, in addition to the standard uniaxial and biaxial nematic phases, the other nematic like phases are stabilized. These involve, among the others, tetrahedratic (T), nematic tetrahedratic (NT), and chiral nematic tetrahedratic (NT*) phases of global Td, D2d, and D2 symmetry, respectively. Molecular order parameters and correlation functions in these phases are determined. We conclude with generalizations of the model that give a simple molecular interpretation of macroscopic regions with opposite optical activity (ambidextrous chirality), observed, e.g., in bent-core systems. An estimate of the helical pitch in the NT* phase is also given
Contextuality in Measurement-based Quantum Computation
We show, under natural assumptions for qubit systems, that measurement-based
quantum computations (MBQCs) which compute a non-linear Boolean function with
high probability are contextual. The class of contextual MBQCs includes an
example which is of practical interest and has a super-polynomial speedup over
the best known classical algorithm, namely the quantum algorithm that solves
the Discrete Log problem.Comment: Version 3: probabilistic version of Theorem 1 adde
From ab initio quantum chemistry to molecular dynamics: The delicate case of hydrogen bonding in ammonia
The ammonia dimer (NH3)2 has been investigated using high--level ab initio
quantum chemistry methods and density functional theory (DFT). The structure
and energetics of important isomers is obtained to unprecedented accuracy
without resorting to experiment. The global minimum of eclipsed C_s symmetry is
characterized by a significantly bent hydrogen bond which deviates from
linearity by about 20 degrees. In addition, the so-called cyclic C_{2h}
structure is extremely close in energy on an overall flat potential energy
surface. It is demonstrated that none of the currently available (GGA,
meta--GGA, and hybrid) density functionals satisfactorily describe the
structure and relative energies of this nonlinear hydrogen bond. We present a
novel density functional, HCTH/407+, designed to describe this sort of hydrogen
bond quantitatively on the level of the dimer, contrary to e.g. the widely used
BLYP functional. This improved functional is employed in Car-Parrinello ab
initio molecular dynamics simulations of liquid ammonia to judge its
performance in describing the associated liquid. Both the HCTH/407+ and BLYP
functionals describe the properties of the liquid well as judged by analysis of
radial distribution functions, hydrogen bonding structure and dynamics,
translational diffusion, and orientational relaxation processes. It is
demonstrated that the solvation shell of the ammonia molecule in the liquid
phase is dominated by steric packing effects and not so much by directional
hydrogen bonding interactions. In addition, the propensity of ammonia molecules
to form bifurcated and multifurcated hydrogen bonds in the liquid phase is
found to be negligibly small.Comment: Journal of Chemical Physics, in press (305335JCP
Quantum algorithms for highly non-linear Boolean functions
Attempts to separate the power of classical and quantum models of computation
have a long history. The ultimate goal is to find exponential separations for
computational problems. However, such separations do not come a dime a dozen:
while there were some early successes in the form of hidden subgroup problems
for abelian groups--which generalize Shor's factoring algorithm perhaps most
faithfully--only for a handful of non-abelian groups efficient quantum
algorithms were found. Recently, problems have gotten increased attention that
seek to identify hidden sub-structures of other combinatorial and algebraic
objects besides groups. In this paper we provide new examples for exponential
separations by considering hidden shift problems that are defined for several
classes of highly non-linear Boolean functions. These so-called bent functions
arise in cryptography, where their property of having perfectly flat Fourier
spectra on the Boolean hypercube gives them resilience against certain types of
attack. We present new quantum algorithms that solve the hidden shift problems
for several well-known classes of bent functions in polynomial time and with a
constant number of queries, while the classical query complexity is shown to be
exponential. Our approach uses a technique that exploits the duality between
bent functions and their Fourier transforms.Comment: 15 pages, 1 figure, to appear in Proceedings of the 21st Annual
ACM-SIAM Symposium on Discrete Algorithms (SODA'10). This updated version of
the paper contains a new exponential separation between classical and quantum
query complexit
Magnetic-field asymmetry of electron wave packet transmission in bent channels capacitively coupled to a metal gate
We study the electron wave packet moving through a bent channel. We
demonstrate that the packet transmission probability becomes an uneven function
of the magnetic field when the electron packet is capacitively coupled to a
metal plate. The coupling occurs through a non-linear potential which
translates a different kinetics of the transport for opposite magnetic field
orientations into a different potential felt by the scattered electron
On the normality of -ary bent functions
Depending on the parity of and the regularity of a bent function from
to , can be affine on a subspace of dimension
at most , or . We point out that many -ary bent
functions take on this bound, and it seems not easy to find examples for which
one can show a different behaviour. This resembles the situation for Boolean
bent functions of which many are (weakly) -normal, i.e. affine on a
-dimensional subspace. However applying an algorithm by Canteaut et.al.,
some Boolean bent functions were shown to be not - normal. We develop an
algorithm for testing normality for functions from to . Applying the algorithm, for some bent functions in small dimension we
show that they do not take on the bound on normality. Applying direct sum of
functions this yields bent functions with this property in infinitely many
dimensions.Comment: 13 page
Spatially resolved stress measurements in materials with polarization-sensitive optical coherence tomography: image acquisition and processing aspects
We demonstrate that polarization-sensitive optical coherence tomography
(PS-OCT) is suitable to map the stress distribution within materials in a
contactless and non-destructive way. In contrast to transmission
photoelasticity measurements the samples do not have to be transparent but can
be of scattering nature. Denoising and analysis of fringe patterns in single
PS-OCT retardation images are demonstrated to deliver the basis for a
quantitative whole-field evaluation of the internal stress state of samples
under investigation.Comment: 10 pages, 6 figures; Copyright: Blackwell Publishing Ltd 2008; The
definitive version is available at: www.blackwell-synergy.co
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