140 research outputs found
On the geometry of four qubit invariants
The geometry of four-qubit entanglement is investigated. We replace some of
the polynomial invariants for four-qubits introduced recently by new ones of
direct geometrical meaning. It is shown that these invariants describe four
points, six lines and four planes in complex projective space . For
the generic entanglement class of stochastic local operations and classical
communication they take a very simple form related to the elementary symmetric
polynomials in four complex variables. Moreover, their magnitudes are
entanglement monotones that fit nicely into the geometric set of -qubit ones
related to Grassmannians of -planes found recently. We also show that in
terms of these invariants the hyperdeterminant of order 24 in the four-qubit
amplitudes takes a more instructive form than the previously published
expressions available in the literature. Finally in order to understand two,
three and four-qubit entanglement in geometric terms we propose a unified
setting based on furnished with a fixed quadric.Comment: 19 page
On the geometry of a class of N-qubit entanglement monotones
A family of N-qubit entanglement monotones invariant under stochastic local
operations and classical communication (SLOCC) is defined. This class of
entanglement monotones includes the well-known examples of the concurrence, the
three-tangle, and some of the four, five and N-qubit SLOCC invariants
introduced recently. The construction of these invariants is based on bipartite
partitions of the Hilbert space in the form with . Such partitions can be given
a nice geometrical interpretation in terms of Grassmannians Gr(L,l) of l-planes
in that can be realized as the zero locus of quadratic polinomials
in the complex projective space of suitable dimension via the Plucker
embedding. The invariants are neatly expressed in terms of the Plucker
coordinates of the Grassmannian.Comment: 7 pages RevTex, Submitted to Physical Review
Quelques remarques sur une épidémie de grippe équine qui sévit en décembre 1965 à l’annexe de l’Institut Pasteur de Carches
Au début du mois de décembre 1965 une épidémie de grippe équine a éclaté dans les écuries de l’Institut Pasteur de Carches où 22 p. 100 de l’effectif furent atteints. Le taux de mortalité fut de 4 p. 100. Dix souches furent isolées ; l’étude antigénique de ces souches fut effectuée comparativement aux diverses souches équines antérieurement isolées en Europe et en Amérique. Un vaccin quadrivalent a été préparé, il est en cours d’expérimen tation
A Hopf laboratory for symmetric functions
An analysis of symmetric function theory is given from the perspective of the
underlying Hopf and bi-algebraic structures. These are presented explicitly in
terms of standard symmetric function operations. Particular attention is
focussed on Laplace pairing, Sweedler cohomology for 1- and 2-cochains, and
twisted products (Rota cliffordizations) induced by branching operators in the
symmetric function context. The latter are shown to include the algebras of
symmetric functions of orthogonal and symplectic type. A commentary on related
issues in the combinatorial approach to quantum field theory is given.Comment: 29 pages, LaTeX, uses amsmat
Algebraic invariants of five qubits
The Hilbert series of the algebra of polynomial invariants of pure states of
five qubits is obtained, and the simplest invariants are computed.Comment: 4 pages, revtex. Short discussion of quant-ph/0506073 include
Wigner transform and pseudodifferential operators on symmetric spaces of non-compact type
We obtain a general expression for a Wigner transform (Wigner function) on
symmetric spaces of non-compact type and study the Weyl calculus of
pseudodifferential operators on them
Superelastic Behavior of Biomedical Metallic Alloys
In this this work, superelastic NiTi and Ni-free Ti-23Hf-3Mo-4Sn biomedical alloys were investigated by tensile tests in relationship with their microstructures. To follow the stress-induced martensitic transformations occurring in these alloys, in situ tensile tests under synchrotron beam were conducted. In NiTi, an intermediate trigonal R phase, which is first stress-induced before the B19 ' martensitic phase, was identified. However, the Ti-23Hf-3Mo-4Sn alloy does not present a transitional phase, and a direct beta into alpha '' reversible stress-induced martensitic transformation was observed. With NiTi, all the applied strain is recovered after unloading, and no residual plastic deformation occurs. However, the strain is not completely recovered with the Ti-23Hf-3Mo-4Sn alloy, and residual plastic strain was observed to prevent a complete recovery, thus explaining why the strain recovery is lower for Ti-23Hf-3Mo-4Sn compared with NiTi. We also showed that the maximum strain recovery depends on the texture in the Ti-23Hf-3Mo-4Sn alloy. The favorable texture leading to the highest strain recovery (4.6 pct) is the {111}< 110 and rang;(beta) texture, which can be obtained by a short-time solution treatment (0.3 ks) at 1073 K with this alloy
Crystal Graphs and -Analogues of Weight Multiplicities for the Root System
We give an expression of the -analogues of the multiplicities of weights
in irreducible \sl_{n+1}-modules in terms of the geometry of the crystal
graph attached to the corresponding U_q(\sl_{n+1})-modules. As an
application, we describe multivariate polynomial analogues of the
multiplicities of the zero weight, refining Kostant's generalized exponents.Comment: LaTeX file with epic, eepic pictures, 17 pages, November 1994, to
appear in Lett. Math. Phy
Quadratic pseudosupersymmetry in two-level systems
Using the intertwining relation we construct a pseudosuperpartner for a
(non-Hermitian) Dirac-like Hamiltonian describing a two-level system
interacting in the rotating wave approximation with the electric component of
an electromagnetic field. The two pseudosuperpartners and pseudosupersymmetry
generators close a quadratic pseudosuperalgebra. A class of time dependent
electric fields for which the equation of motion for a two level system placed
in this field can be solved exactly is obtained. New interesting phenomenon is
observed. There exists such a time-dependent detuning of the field frequency
from the resonance value that the probability to populate the excited level
ceases to oscillate and becomes a monotonically growing function of time
tending to 3/4. It is shown that near this fixed excitation regime the
probability exhibits two kinds of oscillations. The oscillations with a small
amplitude and a frequency close to the Rabi frequency (fast oscillations) take
place at the background of the ones with a big amplitude and a small frequency
(slow oscillations). During the period of slow oscillations the minimal value
of the probability to populate the excited level may exceed 1/2 suggesting for
an ensemble of such two-level atoms the possibility to acquire the inverse
population and exhibit lasing properties.Comment: 5 figure
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