617 research outputs found
Process for purification of solids
A process for purifying solids, especially silicon, by melting and subsequent resolidification, is described. Silicon used in solar cell manufacturing is processed more efficiently and cost effectively
DC bias immune nanocrystalline magnetic cores made of Fe73Nb3Cu1B7Si16 ribbon with induced transverse magnetic anisotropy
Fundamental Magnetic Properties and Structural Implications for Nanocrystalline Fe-Ti-N Thin Films
The magnetization (M) as a function of temperature (T) from 2 to 300 K and
in-plane field (H) up to 1 kOe, room temperature easy and hard direction
in-plane field hysteresis loops for fields between -100 and +100 Oe, and 10 GHz
ferromagnetic resonance (FMR) profiles have been measured for a series of
soft-magnetic nano-crystalline 50 nm thick Fe-Ti-N films made by magnetron
sputtering in an in-plane field. The nominal titanium concentration was 3 at. %
and the nitrogen concentrations (xN) ranged from zero to 12.7 at. %. The
saturation magnetization (Ms) vs. T data and the extracted exchange parameters
as a function of xN are consistent with a lattice expansion due to the addition
of interstitial nitrogen in the body-centered-cubic (bcc) lattice and a
structural transition to body-centered-tetragonal (bct) in the 6-8 at. %
nitrogen range. The hysteresis loop and FMR data show a consistent picture of
the changes in both the uniaxial and cubic anisotropy as a function of xN.
Films with xN > 1.9 at. % show an overall uniaxial anisotropy, with an
anisotropy field parameter Hu that increases with xN. The corresponding
dispersion averaged uniaxial anisotropy energy density parameter = HuMs/2
is a linear function of xN, with a rate of increase of 950 erg/cm3 per at. %
nitrogen. The estimated uniaxial anisotropy energy per nitrogen atom is 30
J/mol, a value consistent with other systems. For xN below 6 at. %, the scaling
of coercive force Hc data with the sixth power of the grain size D indicate a
grain averaged effective cubic anisotropy energy density parameter that is
about an order of magnitude smaller that the nominal K1 values for iron, and
give a quantitative vs. D response that matches predictions for exchange
coupled random grains with cubic anisotropy.Comment: 13 pages, 7 figure
Projective Ring Line of an Arbitrary Single Qudit
As a continuation of our previous work (arXiv:0708.4333) an algebraic
geometrical study of a single -dimensional qudit is made, with being
{\it any} positive integer. The study is based on an intricate relation between
the symplectic module of the generalized Pauli group of the qudit and the fine
structure of the projective line over the (modular) ring \bZ_{d}. Explicit
formulae are given for both the number of generalized Pauli operators commuting
with a given one and the number of points of the projective line containing the
corresponding vector of \bZ^{2}_{d}. We find, remarkably, that a perp-set is
not a set-theoretic union of the corresponding points of the associated
projective line unless is a product of distinct primes. The operators are
also seen to be structured into disjoint `layers' according to the degree of
their representing vectors. A brief comparison with some multiple-qudit cases
is made
The Projective Line Over the Finite Quotient Ring GF(2)[]/ and Quantum Entanglement I. Theoretical Background
The paper deals with the projective line over the finite factor ring
GF(2)[]/. The line is endowed with 18
points, spanning the neighbourhoods of three pairwise distant points. As
is not a local ring, the neighbour (or parallel) relation is
not an equivalence relation so that the sets of neighbour points to two distant
points overlap. There are nine neighbour points to any point of the line,
forming three disjoint families under the reduction modulo either of two
maximal ideals of the ring. Two of the families contain four points each and
they swap their roles when switching from one ideal to the other; the points of
the one family merge with (the image of) the point in question, while the
points of the other family go in pairs into the remaining two points of the
associated ordinary projective line of order two. The single point of the
remaining family is sent to the reference point under both the mappings and its
existence stems from a non-trivial character of the Jacobson radical, , of the ring. The factor ring is isomorphic to GF(2)
GF(2). The projective line over features nine
points, each of them being surrounded by four neighbour and the same number of
distant points, and any two distant points share two neighbours. These
remarkable ring geometries are surmised to be of relevance for modelling
entangled qubit states, to be discussed in detail in Part II of the paper.Comment: 8 pages, 2 figure
Projective Ring Line Encompassing Two-Qubits
The projective line over the (non-commutative) ring of two-by-two matrices
with coefficients in GF(2) is found to fully accommodate the algebra of 15
operators - generalized Pauli matrices - characterizing two-qubit systems. The
relevant sub-configuration consists of 15 points each of which is either
simultaneously distant or simultaneously neighbor to (any) two given distant
points of the line. The operators can be identified with the points in such a
one-to-one manner that their commutation relations are exactly reproduced by
the underlying geometry of the points, with the ring geometrical notions of
neighbor/distant answering, respectively, to the operational ones of
commuting/non-commuting. This remarkable configuration can be viewed in two
principally different ways accounting, respectively, for the basic 9+6 and 10+5
factorizations of the algebra of the observables. First, as a disjoint union of
the projective line over GF(2) x GF(2) (the "Mermin" part) and two lines over
GF(4) passing through the two selected points, the latter omitted. Second, as
the generalized quadrangle of order two, with its ovoids and/or spreads
standing for (maximum) sets of five mutually non-commuting operators and/or
groups of five maximally commuting subsets of three operators each. These
findings open up rather unexpected vistas for an algebraic geometrical
modelling of finite-dimensional quantum systems and give their numerous
applications a wholly new perspective.Comment: 8 pages, three tables; Version 2 - a few typos and one discrepancy
corrected; Version 3: substantial extension of the paper - two-qubits are
generalized quadrangles of order two; Version 4: self-dual picture completed;
Version 5: intriguing triality found -- three kinds of geometric hyperplanes
within GQ and three distinguished subsets of Pauli operator
Projective Ring Line of a Specific Qudit
A very particular connection between the commutation relations of the
elements of the generalized Pauli group of a -dimensional qudit, being a
product of distinct primes, and the structure of the projective line over the
(modular) ring \bZ_{d} is established, where the integer exponents of the
generating shift () and clock () operators are associated with submodules
of \bZ^{2}_{d}. Under this correspondence, the set of operators commuting
with a given one -- a perp-set -- represents a \bZ_{d}-submodule of
\bZ^{2}_{d}. A crucial novel feature here is that the operators are also
represented by {\it non}-admissible pairs of \bZ^{2}_{d}. This additional
degree of freedom makes it possible to view any perp-set as a {\it
set-theoretic} union of the corresponding points of the associated projective
line
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