43,938 research outputs found
Dirac Sea for Bosons I -- Formulation of Negative Energy Sea for Bosons
It is proposed to make formulation of second quantizing a bosonic theory by
generalizing the method of filling the Dirac negative energy sea for fermions.
We interpret that the correct vacuum for the bosonic theory is obtained by
adding minus one boson to each single particle negative energy states while the
positive energy states are empty. The boson states are divided into two sectors
; the usual positive sector with positive and zero numbers of bosons and the
negative sector with negative numbers of bosons. Once it comes into the
negative sector it cannot return to the usual positive sector by ordinary
interaction due to a barrier. It is suggested to use as a playground model in
which the filling of empty fermion Dirac sea and the removal of boson from the
negative energy states are not yet performed. We put forward such a naive
vacuum world in the present paper. The successive paper will concern a CPT-like
Theorem in the naive vacuum world.Comment: 24 pages, 2 figures, Latex; added refereces, corrected typo
Simple proof of the robustness of Gaussian entanglement in bosonic noisy channels
The extremality of Gaussian states is exploited to show that Gaussian states
are the most robust, among all possible bipartite continuous-variable states at
fixed energy, against disentanglement due to noisy evolutions in Markovian
Gaussian channels involving dissipation and thermal hopping. This proves a
conjecture raised recently in [M. Allegra, P. Giorda, and M. G. A. Paris, Phys.
Rev. Lett. {\bf 105}, 100503 (2010)], providing a rigorous validation of the
conclusions of that work. The problem of identifying continuous variable states
with maximum resilience to entanglement damping in more general bosonic open
system dynamical evolutions, possibly including correlated noise and
non-Markovian effects, remains open.Comment: 3 pages, 1 figure, brief repor
Local unitary equivalence and entanglement of multipartite pure states
The necessary and sufficient conditions for the equivalence of arbitrary
n-qubit pure quantum states under Local Unitary (LU) operations derived in [B.
Kraus Phys. Rev. Lett. 104, 020504 (2010)] are used to determine the different
LU-equivalence classes of up to five-qubit states. Due to this classification
new parameters characterizing multipartite entanglement are found and their
physical interpretation is given. Moreover, the method is used to derive
examples of two n-qubit states (with n>2 arbitrary) which have the properties
that all the entropies of any subsystem coincide, however, the states are
neither LU-equivalent nor can be mapped into each other by general local
operations and classical communication
Local unitary equivalence of multipartite pure states
Necessary and sufficient conditions for the equivalence of arbitrary n-qubit
pure quantum states under Local Unitary (LU) operations are derived. First, an
easily computable standard form for multipartite states is introduced. Two
generic states are shown to be LU-equivalent iff their standard forms coincide.
The LU-equivalence problem for non--generic states is solved by presenting a
systematic method to determine the LU operators (if they exist) which
interconvert the two states.Comment: 5 page
On sphaleron deformations induced by Yukawa interactions
Due to the presence of the chiral anomaly sphalerons with Chern-Simons number
a half (CS=1/2) are the only static configurations that allow for a fermion
level crossing in the two-dimensional Abelian-Higgs model with massless
fermions, i.e. in the absence of Yukawa interactions. In the presence of
fermion-Higgs interactions we demonstrate the existence of zero energy
solutions to the one-dimensional Dirac equation at deformed sphalerons with
CS Induced level crossing due to Yukawa interactions illustrates a
non-trivial generalization of the Atiyah-Patodi-Singer index theorem and of the
equivalence between parity anomaly in odd and the chiral anomaly in even
dimensions. We discuss a subtle manifestation of this effect in the standard
electroweak theory at finite temperatures.Comment: 14 pages, Latex, NBI-HE-93-7
A model for the anisotropic response of fibrous soft tissues using six discrete fibre bundles
The development of accurate constitutive models of fibrous soft-tissues is a challenging problem. Many consider the tissue to be a collection of fibres with a continuous distribution function representing their orientations. A novel discrete fibre model is presented consisting of six weighted fibre bundles. Each bundle is oriented such that they pass through opposing vertices of a regular icosahedron. A novel aspect of the model is the use of simple analytical distribution functions to simulate the undulated collagen fibres. This approach yields a closed form analytical expression for the strain energy function for the collagen fibre bundle that avoids the sometimes costly numerical integration of some statistical distribution functions. The elastin fibres are characterized by a neo-Hookean strain energy function. The model accurately simulates the biaxial stretching of rabbit-skin (error-of-fit 8.7%), the uniaxial stretching of pig-skin (error-of-fit 7.6%), equibiaxial loading of aortic valve cusp (error-of-fit 0.8%), and the simple shear of rat septal myocardium (error-of-fit 9.1%). The proposed model compares favourably with previously published soft-tissue models and alternative methods of representing undulated collagen fibres. The stiffness of collagen fibres predicted by the model ranges from 8.0 MPa to 0.93 GPa. The stiffness of elastin fibres ranges from 2.5 kPa to 154.4 kPa. The anisotropy of model resulting from the representation of the fibre field with a discrete number of fibres is also explored
Ginsparg-Wilson Relation and Ultralocality
It is shown that it is impossible to construct a free theory of fermions on
infinite hypercubic Euclidean lattice in four dimensions that is: (a)
ultralocal, (b) respects symmetries of hypercubic lattice, (c) corresponding
kernel satisfies D gamma5 + gamma5 D = D gamma5 D (Ginsparg-Wilson relation),
(d) describes single species of massless Dirac fermions in the continuum limit.Comment: 4 pages, REVTEX; few minor change
Entanglement Detection Using Majorization Uncertainty Bounds
Entanglement detection criteria are developed within the framework of the
majorization formulation of uncertainty. The primary results are two theorems
asserting linear and nonlinear separability criteria based on majorization
relations, the violation of which would imply entanglement. Corollaries to
these theorems yield infinite sets of scalar entanglement detection criteria
based on quasi-entropic measures of disorder. Examples are analyzed to probe
the efficacy of the derived criteria in detecting the entanglement of bipartite
Werner states. Characteristics of the majorization relation as a comparator of
disorder uniquely suited to information-theoretical applications are emphasized
throughout.Comment: 10 pages, 1 figur
Products of Random Matrices
We derive analytic expressions for infinite products of random 2x2 matrices.
The determinant of the target matrix is log-normally distributed, whereas the
remainder is a surprisingly complicated function of a parameter characterizing
the norm of the matrix and a parameter characterizing its skewness. The
distribution may have importance as an uncommitted prior in statistical image
analysis.Comment: 9 pages, 1 figur
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