3,655 research outputs found
Constructions of complex Hadamard matrices via tiling Abelian groups
Applications in quantum information theory and quantum tomography have raised
current interest in complex Hadamard matrices. In this note we investigate the
connection between tiling Abelian groups and constructions of complex Hadamard
matrices. First, we recover a recent very general construction of complex
Hadamard matrices due to Dita via a natural tiling construction. Then we find
some necessary conditions for any given complex Hadamard matrix to be
equivalent to a Dita-type matrix. Finally, using another tiling construction,
due to Szabo, we arrive at new parametric families of complex Hadamard matrices
of order 8, 12 and 16, and we use our necessary conditions to prove that these
families do not arise with Dita's construction. These new families complement
the recent catalogue of complex Hadamard matrices of small order.Comment: 15 page
Ab-initio elastic tensor of cubic TiAlN alloy: the dependence of the elastic constants on the size and shape of the supercell model
In this study we discuss the performance of approximate SQS supercell models
in describing the cubic elastic properties of B1 (rocksalt)
TiAlN alloy by using a symmetry based projection technique. We
show on the example of TiAlN alloy, that this projection
technique can be used to align the differently shaped and sized SQS structures
for a comparison in modeling elasticity. Moreover, we focus to accurately
determine the cubic elastic constants and Zener's type elastic anisotropy of
TiAlN. Our best supercell model, that captures accurately both
the randomness and cubic elastic symmetry, results in GPa,
GPa and GPa with 3% of error and for Zener's
elastic anisotropy with 6% of error. In addition, we establish the general
importance of selecting proper approximate SQS supercells with symmetry
arguments to reliably model elasticity of alloys. In general, we suggest the
calculation of nine elastic tensor elements - , , ,
, , , , and , to evaluate and
analyze the performance of SQS supercells in predicting elasticity of cubic
alloys via projecting out the closest cubic approximate of the elastic tensor.
The here described methodology is general enough to be applied in discussing
elasticity of substitutional alloys with any symmetry and at arbitrary
composition.Comment: Submitted to Physical Review
New fixed point action for SU(3) lattice gauge theory
We present a new fixed point action for SU(3) lattice gauge theory, which has --- compared to earlier published fixed point actions --- shorter interaction range and smaller violations of rotational symmetry in the static q\bar{q}-potential even at shortest distances
Crackling noise in three-point bending of heterogeneous materials
We study the crackling noise emerging during single crack propagation in a
specimen under three-point bending conditions. Computer simulations are carried
out in the framework of a discrete element model where the specimen is
discretized in terms of convex polygons and cohesive elements are represented
by beams. Computer simulations revealed that fracture proceeds in bursts whose
size and waiting time distributions have a power law functional form with an
exponential cutoff. Controlling the degree of brittleness of the sample by the
amount of disorder, we obtain a scaling form for the characteristic quantities
of crackling noise of quasi-brittle materials. Analyzing the spatial structure
of damage we show that ahead of the crack tip a process zone is formed as a
random sequence of broken and intact mesoscopic elements. We characterize the
statistics of the shrinking and expanding steps of the process zone and
determine the damage profile in the vicinity of the crack tip.Comment: 11 pages, 15 figure
Logarithmic delocalization of end spins in the S=3/2 antiferromagnetic Heisenberg chain
Using the DMRG method we calculate the surface spin correlation function,
, in the spin antiferromagnetic Heisenberg
chain. For comparison we also investigate the chain with S=1 impurity
end spins and the S=1 chain. In the half-integer spin models the end-to-end
correlations are found to decay to zero logarithmically, , with . We find no surface order, in clear contrast with
the behavior of the S=1 chain, where exponentially localized end spins induce
finite surface correlations. The lack of surface order implies that end spins
do not exist in the strict sense. However, the system possesses a
logarithmically weakly delocalizing boundary excitation, which, for any chain
lengths attainable numerically or even experimentally, creates the illusion of
an end spin. This mode is responsible for the first gap, which vanishes
asymptotically as , where is the
sound velocity and is the logarithmic decay exponent. For the half-integer
spin models our results on the surface correlations and on the first gap
support universality. Those for the second gap are less conclusive, due to
strong higher-order corrections.Comment: 10 pages, 8 figure
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