1,929 research outputs found
Quantum and approximation algorithms for maximum witnesses of Boolean matrix products
The problem of finding maximum (or minimum) witnesses of the Boolean product
of two Boolean matrices (MW for short) has a number of important applications,
in particular the all-pairs lowest common ancestor (LCA) problem in directed
acyclic graphs (dags). The best known upper time-bound on the MW problem for
n\times n Boolean matrices of the form O(n^{2.575}) has not been substantially
improved since 2006. In order to obtain faster algorithms for this problem, we
study quantum algorithms for MW and approximation algorithms for MW (in the
standard computational model). Some of our quantum algorithms are input or
output sensitive. Our fastest quantum algorithm for the MW problem, and
consequently for the related problems, runs in time
\tilde{O}(n^{2+\lambda/2})=\tilde{O}(n^{2.434}), where \lambda satisfies the
equation \omega(1, \lambda, 1) = 1 + 1.5 \, \lambda and \omega(1, \lambda, 1)
is the exponent of the multiplication of an n \times n^{\lambda}$ matrix by an
n^{\lambda} \times n matrix. Next, we consider a relaxed version of the MW
problem (in the standard model) asking for reporting a witness of bounded rank
(the maximum witness has rank 1) for each non-zero entry of the matrix product.
First, by adapting the fastest known algorithm for maximum witnesses, we obtain
an algorithm for the relaxed problem that reports for each non-zero entry of
the product matrix a witness of rank at most \ell in time
\tilde{O}((n/\ell)n^{\omega(1,\log_n \ell,1)}). Then, by reducing the relaxed
problem to the so called k-witness problem, we provide an algorithm that
reports for each non-zero entry C[i,j] of the product matrix C a witness of
rank O(\lceil W_C(i,j)/k\rceil ), where W_C(i,j) is the number of witnesses for
C[i,j], with high probability. The algorithm runs in
\tilde{O}(n^{\omega}k^{0.4653} +n^2k) time, where \omega=\omega(1,1,1).Comment: 14 pages, 3 figure
Magnetization steps in Zn_(1-x)Mn_xO: Four largest exchange constants and single-ion anisotropy
Magnetization steps (MST's) from Mn pairs in several single crystals of
Zn_(1-x)Mn_xO (0.0056<=x<=0.030, and in one powder (x=0.029), were observed.
The largest two exchange constants, J1/kB=-18.2+/-0.5K and J1'/kB=-24.3+/-0.6K,
were obtained from large peaks in the differential susceptibility, dM/dH,
measured in pulsed magnetic fields, H, up to 500 kOe. These two largest J's are
associated with the two inequivalent classes of nearest neighbors (NN's) in the
wurtzite structure. The 29% difference between J1 and J1' is substantially
larger than 13% in CdS:Mn, and 15% in CdSe:Mn. The pulsed-field data also
indicate that, despite the direct contact between the samples and a
superfluid-helium bath, substantial departures from thermal equilibrium
occurred during the 7.4 ms pulse. The third- and fourth-largest J's were
determined from the magnetization M at 20 mK, measured in dc magnetic fields H
up to 90 kOe. Both field orientations H||c and H||[10-10] were studied. (The
[10-10] direction is perpendicular to the c-axis, [0001].) By definition,
neighbors which are not NN's are distant neighbors (DN's). The largest DN
exchange constant (third-largest overall), has the value J/kB=-0.543+/-0.005K,
and is associated with the DN at r=c. Because this is not the closest DN, this
result implies that the J's do not decrease monotonically with the distance r.
The second-largest DN exchange constant (fourth-largest overall), has the value
J/kB=-0.080 K. It is associated with one of the two classes of neighbors that
have a coordination number z=12, but the evidence is insufficient for a
definite unique choice. The dependence of M on the direction of H gives
D/kB=-0.039+/-0.008K, in fair agreement with -0.031 K from earlier EPR work.Comment: 12 pages, 10 figures. Submitted to PR
Magnetization steps in a diluted Heisenberg antiferromagnetic chain: Theory and experiments on TMMC:Cd
A theory for the equilibrium low-temperature magnetization M of a diluted
Heisenberg antiferromagnetic chain is presented. The magnetization curve, M
versus B, is calculated using the exact contributions of finite chains with 1
to 5 spins, and the "rise and ramp approximation" for longer chains. Some
non-equilibrium effects that occur in a rapidly changing B, are also
considered. Specific non-equilibrium models based on earlier treatments of the
phonon bottleneck, and of spin flips associated with cross relaxation and with
level crossings, are discussed. Magnetization data on powders of TMMC diluted
with cadmium [i.e., (CH_3)_4NMn_xCd_(1-x)Cl_3, with 0.16<=x<=0.50 were measured
at 0.55 K in 18 T superconducting magnets. The field B_1 at the first MST from
pairs is used to determine the NN exchange constant, J, which changes from -5.9
K to -6.5 K as x increases from 0.16 to 0.50. The magnetization curves obtained
in the superconducting magnets are compared with simulations based on the
equilibrium theory. Data for the differential susceptibility, dM/dB, were taken
in pulsed magnetic fields (7.4 ms duration) up to 50 T, with the powder samples
in a 1.5 K liquid-helium bath. Non-equilibrium effects, which became more
severe as x decreased, were observed. The non-equilibrium effects are
tentatively interpreted using the "Inadequate Heat Flow Scenario," or to
cross-relaxation, and crossings of energy levels, including those of excited
states.Comment: 16 pages, 14 figure
Processing of strong flux trapping high T(subc) oxide superconductors: Center director's discretionary fund
Magnetic suspension effect was first observed in samples of YBa2Cu3O7/AgO(Y-123/AgO) composites. Magnetization measurements of these samples show a much larger hysteresis which corresponds to a large critical current density. In addition to the Y-123AgO composites, recently similar suspension effects in other RE-123/AgO, where RE stands for rare-Earth elements, were also observed. Some samples exhibit even stronger flux pinning than that of the Y-123/AgO sample. An interesting observation was that in order to form the composite which exhibits strong flux trapping effect the sintering temperature depends on the particular RE-123 compound used. The paper presents the detailed processing conditions for the formation of these RE-123/AgO composites, as well as the magnetization and critical field data
"Quasi two-dimensional" spin distributions in II-VI magnetic semiconductor heterostructures: Clustering and dimensionality
Spin clustering in diluted magnetic semiconductors (DMS) arises from
antiferromagnetic exchange between neighboring magnetic cations and is a strong
function of reduced dimensionality. Epitaxially-grown single monolayers and
abrupt interfaces of DMS are, however, never perfectly two-dimensional (2D) due
to the unavoidable inter-monolayer mixing of atoms during growth. Thus the
magnetization of DMS heterostructures, which is strongly modified by spin
clustering, is intermediate between that of 2D and 3D spin distributions. We
present an exact calculation of spin clustering applicable to arbitrary
distributions of magnetic spins in the growth direction. The results reveal a
surprising insensitivity of the magnetization to the form of the intermixing
profile, and identify important limits on the maximum possible magnetization.
High-field optical studies of heterostructures containing "quasi-2D" spin
distributions are compared with calculation.Comment: 5 pages (RevTeX), 5 embedded EPS figs, published in PRB v61 p1736
(2000
Magnetic structures and reorientation transitions in noncentrosymmetric uniaxial antiferromagnets
A phenomenological theory of magnetic states in noncentrosymmetric tetragonal
antiferromagnets is developed, which has to include homogeneous and
inhomogeneous terms (Lifshitz-invariants) derived from Dzyaloshinskii-Moriya
couplings. Magnetic properties of this class of antiferromagnets with low
crystal symmetry are discussed in relation to its first known members, the
recently detected compounds Ba2CuGe2O7 and K2V3O8. Crystallographic symmetry
and magnetic ordering in these systems allow the simultaneous occurrence of
chiral inhomogeneous magnetic structures and weak ferromagnetism. New types of
incommensurate magnetic structures are possible, namely, chiral helices with
rotation of staggered magnetization and oscillations of the total
magnetization. Field-induced reorientation transitions into modulated states
have been studied and corresponding phase diagrams are constructed. Structures
of magnetic defects (domain-walls and vortices) are discussed. In particular,
vortices, i.e. localized non-singular line defects, are stabilized by the
inhomogeneous Dzyaloshinskii-Moriya interactions in uniaxial noncentrosymmetric
antiferromagnets.Comment: 18 pages RevTeX4, 13 figure
Colossal Magnetoresistance in the Mn2+ Oxypnictides NdMnAsO1-xFx
Colossal magnetoresistance (CMR) is a rare phenomenon in which the electronic
resistivity of a material can be decreased by orders of magnitude upon
application of a magnetic field. Such an effect could be the basis of the next
generation of magnetic memory devices. Here we report CMR in the
antiferromagnetic oxypnictide NdMnAsO1-xFx as a result of competition between
an antiferromagnetic insulating phase with strong electron correlations and a
paramagnetic semiconductor upon application of a magnetic field. The discovery
of CMR in antiferromagnetic Mn2+ oxypnictide materials could open up an array
of materials for further investigation and optimisation for technological
applications
Quantum analogue of the spin-flop transition for a spin pair
Quantum (step-like) magnetization curves are studies for a spin pair with
antiferromagnetic coupling in the presence of a magnetic field parallel to the
easy axis of the magnetic anisotropy. The consideration is done both
analytically and numerically for a wide range of the anisotropy constants and
spins up to . Depending on the origin of the anisotropy
(exchange or single-ion), the magnetization curve can demonstrate the jumps
more than unity and the concentration of the unit jumps in a narrow range of
the field. We also point the region of the problem parameters, where the
behavior is quasiclassical for , and where system is substantially
quantum in the limit .Comment: 5 pages, 5 figure
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