Formal rigidity of the Witt and Virasoro Algebra

The formal rigidity of the Witt and Virasoro algebras was first established by the author in [4]. The proof was based on some earlier results of the author and Goncharowa, and was not presented there. In this paper we give an elementary proof of these facts.Comment: 5 page

Constraints on the relativistic mean field of Δ\Delta-isobar in nuclear matter

The effects of the presence of $\Delta$-isobars in nuclear matter are studied in the framework of relativistic mean-field theory. The existence of stable nuclei at saturation density imposes constraints on the $\Delta$-isobar self-energy and thereby on the mean-field coupling constants of the scalar and vector mesons with $\Delta$-isobars. The range of possible values for the scalar and vector coupling constants of $\Delta$-isobars with respect to the nucleon coupling is investigated and compared to recent predictions of QCD sum-rule calculations.Comment: 8 pages, Latex using Elsevier style, 2 PS figures, minor changes in revised versio

Vector magnetic field microscopy using nitrogen vacancy centers in diamond

The localized spin triplet ground state of a nitrogen vacancy (NV) center in diamond can be used in atomic-scale detection of local magnetic fields. Here we present a technique using these defects in diamond to image fields around magnetic structures. We extract the local magnetic field vector by probing resonant transitions of the four fixed tetrahedral NV orientations. In combination with confocal microscopy techniques, we construct a 2-dimensional image of the local magnetic field vectors. Measurements are done in external fields less than 50 G and under ambient conditions.Comment: 9 pages, 3 figure

Cohomology of osp(1∣2)\frak {osp}(1|2) acting on the space of bilinear differential operators on the superspace R1∣1\mathbb{R}^{1|1}

We compute the first cohomology of the ortosymplectic Lie superalgebra $\mathfrak{osp}(1|2)$ on the (1,1)-dimensional real superspace with coefficients in the superspace $\frak{D}_{\lambda,\nu;\mu}$ of bilinear differential operators acting on weighted densities. This work is the simplest superization of a result by Bouarroudj [Cohomology of the vector fields Lie algebras on $\mathbb{R}\mathbb{P}^1$ acting on bilinear differential operators, International Journal of Geometric Methods in Modern Physics (2005), {\bf 2}; N 1, 23-40]

Deformations of modules of differential forms

We study non-trivial deformations of the natural action of the Lie algebra $\mathrm{Vect}({\mathbb R}^n)$ on the space of differential forms on ${\mathbb R}^n$. We calculate abstractions for integrability of infinitesimal multi-parameter deformations and determine the commutative associative algebra corresponding to the miniversal deformation in the sense of \cite{ff}.Comment: Published by JNMP at http://www.sm.luth.se/math/JNM

Quantum criticality and minimal conductivity in graphene with long-range disorder

We consider the conductivity $\sigma_{xx}$ of graphene with negligible intervalley scattering at half filling. We derive the effective field theory, which, for the case of a potential disorder, is a symplectic-class $\sigma$-model including a topological term with $\theta=\pi$. As a consequence, the system is at a quantum critical point with a universal value of the conductivity of the order of $e^2/h$. When the effective time reversal symmetry is broken, the symmetry class becomes unitary, and $\sigma_{xx}$ acquires the value characteristic for the quantum Hall transition.Comment: 4 pages, 1 figur

Reducing Time for the Product Development Process by Evaluation in the Phase of Solution Searching

Less and less time is available for product development process. To prevent product failures and the resulting time intensive and cost intensive iteration steps, some preventive measures must be taken. Within the scope of quality management, FMEA anticipates possible problems concerning product and process properties. Nevertheless, in industrial practice designed products can have failures which were not considered within FMEA. The time pressure is immense, and efforts which do not make a contribution to a successful solution are regarded as lost time.This paper introduces a systematic approach to troubleshooting, with the aim of reducing the time for solution searching by considering the feasibility of ideas at an early stage

Two qubit copying machine for economical quantum eavesdropping

We study the mapping which occurs when a single qubit in an arbitrary state interacts with another qubit in a given, fixed state resulting in some unitary transformation on the two qubit system which, in effect, makes two copies of the first qubit. The general problem of the quality of the resulting copies is discussed using a special representation, a generalization of the usual Schmidt decomposition, of an arbitrary two-dimensional subspace of a tensor product of two 2-dimensional Hilbert spaces. We exhibit quantum circuits which can reproduce the results of any two qubit copying machine of this type. A simple stochastic generalization (using a ``classical'' random signal) of the copying machine is also considered. These copying machines provide simple embodiments of previously proposed optimal eavesdropping schemes for the BB84 and B92 quantum cryptography protocols.Comment: Minor changes. 26 pages RevTex including 7 PS figure

The relativistic self-energy in nuclear dynamics

It is a well known fact that Dirac phenomenology of nuclear forces predicts the existence of large scalar and vector mean fields in matter. To analyse the relativistic self-energy in a model independent way, modern high precision nucleon-nucleon ($NN$) potentials are mapped on a relativistic operator basis using projection techniques. This allows to compare the various potentials at the level of covariant amplitudes were a remarkable agreement is found. It allows further to calculate the relativistic self-energy in nuclear matter in Hartree-Fock approximation. Independent of the choice of the nucleon-nucleon interaction large scalar and vector mean fields of several hundred MeV magnitude are generated at tree level. In the framework of chiral EFT these fields are dominantly generated by contact terms which occur at next-to-leading order in the chiral expansion. Consistent with Dirac phenomenology the corresponding low energy constants which generate the large fields are closely connected to the spin-orbit interaction in $NN$ scattering. The connection to QCD sum rules is discussed as well.Comment: 49 pages, 13 figure

Model independent study of the Dirac structure of the nucleon-nucleon interaction

Relativistic and non-relativistic modern nucleon-nucleon potentials are mapped on a relativistic operator basis using projection techniques. This allows to compare the various potentials at the level of covariant amplitudes were a remarkable agreement is found. In nuclear matter large scalar and vector mean fields of several hundred MeV magnitude are generated at tree level. This is found to be a model independent feature of the nucleon-nucleon interaction.Comment: 5 pages, 2 figures, results for V_lowk added, to appear in PR