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$\neq 1/2 .$ 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