Postmodern String Theory: Stochastic Formulation

In this paper we study the dynamics of a statistical ensemble of strings, building on a recently proposed gauge theory of the string geodesic field. We show that this stochastic approach is equivalent to the Carath\'eodory formulation of the Nambu-Goto action, supplemented by an averaging procedure over the family of classical string world-sheets which are solutions of the equation of motion. In this new framework, the string geodesic field is reinterpreted as the Gibbs current density associated with the string statistical ensemble. Next, we show that the classical field equations derived from the string gauge action, can be obtained as the semi-classical limit of the string functional wave equation. For closed strings, the wave equation itself is completely analogous to the Wheeler-DeWitt equation used in quantum cosmology. Thus, in the string case, the wave function has support on the space of all possible spatial loop configurations. Finally, we show that the string distribution induces a multi-phase, or {\it cellular} structure on the spacetime manifold characterized by domains with a purely Riemannian geometry separated by domain walls over which there exists a predominantly Weyl geometry.Comment: 24pages, ReVTe

Normal forms and entanglement measures for multipartite quantum states

A general mathematical framework is presented to describe local equivalence classes of multipartite quantum states under the action of local unitary and local filtering operations. This yields multipartite generalizations of the singular value decomposition. The analysis naturally leads to the introduction of entanglement measures quantifying the multipartite entanglement (as generalizations of the concurrence and the 3-tangle), and the optimal local filtering operations maximizing these entanglement monotones are obtained. Moreover a natural extension of the definition of GHZ-states to e.g. $2\times 2\times N$ systems is obtained.Comment: Proof of uniqueness of normal form adde

Produktorienteret miljøindsats i landbrugssektoren - forudsætninger

For at styrke den produktorienterede miljøindsats i landbruget nedsatte Miljøstyrelsen primo 2003 et produktkædepanel for landbrugsområdet. Panelets primære mål er at fremme udvikling og afsætning af landbrugsprodukter, der set i et livscyklusperspektiv ("fra jord til jord") er mindre miljøbelastende end tilsvarende traditionelle produkter. Som fundament for panelets arbejde er udarbejdet denne rapport, som beskriver de eksisterende forudsætninger for en produktorienteret indsats i sektoren - i form af en kortlægning af relevante projekter/tiltag. Denne rapport har dannet udgangspunkt for udarbejdelsen af et såkaldt fremsyn på området, som er publiceret særskilt. Fremsynet og information om panelets arbejde i øvrigt kan fås på www.produktpanel-landbrug.dk. En produktorienteret indsats vil altid være et supplement til de eksisterende overordnede reguleringer af samfundets adfærd, forbrug og udledninger. Vi vil stadig i fremtiden opleve berettiget miljøarbejde, der tager udgangspunkt i en konkret produktion eller proces eller i ønsket om at reducere en arealbelastning. Med produktorientering følger en anderledes og mere nuanceret opfattelse af, hvad der er "godt og dårligt" for miljøet, hvilke områder, der skal prioriteres i fødevaresektorens miljøindsats, og hvad miljøarbejdet kan omfatte i alle led i fødevarernes produktkæde. Et produktorienteret miljøarbejde stiller krav til og udfordrer alle aktører i produktkæderne. Der skal ikke alene udveksles og håndteres oplysninger om produktets miljøpåvirkning bagud og fremad i produktkæden, men der skal også ageres på baggrund af de erkendelser, denne udveksling af oplysninger giver anledning til. Helhedsorienteringen skaber også muligheder for at synliggøre og dokumentere valg undervejs i produktkæden. Produktorientering giver dermed en enestående mulighed for aktører/virksomheder for at dokumentere adfærd og valg overfor aftagere (herunder forbrugeren). Også for landbrugs- og gartnerierhvervet er produktorienteringen en udfordring. En kvalificeret diskussion af muligheder og perspektiver i produktorienteringen i landbrugserhvervet er derfor langt fra kun et spørgsmål om værktøjer, opgørelsesmetoder og mulighederne for afsætning af miljødokumenterede varer. Produktorienteringen er i langt højere grad den ramme, hvori f.eks. nedenstående spørgsmål kan diskuteres: Hvilke langsigtede scenarier for landbrugserhvervet er tænkelige? Hvilke strategier kan anlægges for erhvervsudvikling, forskning, kompetenceudvikling etc. for bedst muligt at sigte på de mest attraktive scenarier? Hvordan bringes aktørerne i spil, og hvordan skal ansvar fordeles? De hidtidige erfaringer med produktorientering viser, at en væsentlig forudsætning for succes er åbenhed og kommunikation i produktkæderne

Classification of multipartite entangled states by multidimensional determinants

We find that multidimensional determinants "hyperdeterminants", related to entanglement measures (the so-called concurrence or 3-tangle for the 2 or 3 qubits, respectively), are derived from a duality between entangled states and separable states. By means of the hyperdeterminant and its singularities, the single copy of multipartite pure entangled states is classified into an onion structure of every closed subset, similar to that by the local rank in the bipartite case. This reveals how inequivalent multipartite entangled classes are partially ordered under local actions. In particular, the generic entangled class of the maximal dimension, distinguished as the nonzero hyperdeterminant, does not include the maximally entangled states in Bell's inequalities in general (e.g., in the $n \geq 4$ qubits), contrary to the widely known bipartite or 3-qubit cases. It suggests that not only are they never locally interconvertible with the majority of multipartite entangled states, but they would have no grounds for the canonical n-partite entangled states. Our classification is also useful for the mixed states.Comment: revtex4, 10 pages, 4 eps figures with psfrag; v2 title changed, 1 appendix added, to appear in Phys. Rev.

Generalised quantum weakest preconditions

Generalisation of the quantum weakest precondition result of D'Hondt and Panangaden is presented. In particular the most general notion of quantum predicate as positive operator valued measure (POVM) is introduced. The previously known quantum weakest precondition result has been extended to cover the case of POVM playing the role of a quantum predicate. Additionally, our result is valid in infinite dimension case and also holds for a quantum programs defined as a positive but not necessary completely positive transformations of a quantum states.Comment: 7 pages, no figures, added references, changed conten

Classification of qubit entanglement: SL(2,C) versus SU(2) invariance

The role of SU(2) invariants for the classification of multiparty entanglement is discussed and exemplified for the Kempe invariant I_5 of pure three-qubit states. It is found to being an independent invariant only in presence of both W-type entanglement and threetangle. In this case, constant I_5 admits for a wide range of both threetangle and concurrences. Furthermore, the present analysis indicates that an SL^3 orbit of states with equal tangles but continuously varying I_5 must exist. This means that I_5 provides no information on the entanglement in the system in addition to that contained in the tangles (concurrences and threetangle) themselves. Together with the numerical evidence that I_5 is an entanglement monotone this implies that SU(2) invariance or the monotone property are too weak requirements for the characterization and quantification of entanglement for systems of three qubits, and that SL(2,C) invariance is required. This conclusion can be extended to general multipartite systems (including higher local dimension) because the entanglement classes of three-qubit systems appear as subclasses.Comment: 9 pages, 10 figures, revtex

General structure of the photon self-energy in non-commutative QED

We study the behavior of the photon two point function, in non-commutative QED, in a general covariant gauge and in arbitrary space-time dimensions. We show, to all orders, that the photon self-energy is transverse. Using an appropriate extension of the dimensional regularization method, we evaluate the one-loop corrections, which show that the theory is renormalizable. We also prove, to all orders, that the poles of the photon propagator are gauge independent and briefly discuss some other related aspects.Comment: 16 pages, revtex4. This is the final version to be published in Phys. Rev.

Viking Age garden plants from southern Scandinavia: diversity, taphonomy and cultural aspects

Plant finds recovered from archaeological sites in southern Scandinavia dated to the Viking Age reflect the diversity of useful plants that were cultivated and collected. This review presents the results of 14 investigations of deposits that are dated between AD 775 and 1050. The site types are categorized as agrarian, urban, military and burials. Garden plants are unevenly distributed, as the greatest diversity is recorded in features from urban contexts. We argue that taphonomic processes played an important role in the picture displayed. Archaeobotanical research results from neighbouring regions suggest that Viking Age horticulture has its roots in older traditions, and that the spectrum of garden plants is influenced by central and north-western European horticultural customs, which were to a great extent shaped by Roman occupation

Magnetism in Dense Quark Matter

We review the mechanisms via which an external magnetic field can affect the ground state of cold and dense quark matter. In the absence of a magnetic field, at asymptotically high densities, cold quark matter is in the Color-Flavor-Locked (CFL) phase of color superconductivity characterized by three scales: the superconducting gap, the gluon Meissner mass, and the baryonic chemical potential. When an applied magnetic field becomes comparable with each of these scales, new phases and/or condensates may emerge. They include the magnetic CFL (MCFL) phase that becomes relevant for fields of the order of the gap scale; the paramagnetic CFL, important when the field is of the order of the Meissner mass, and a spin-one condensate associated to the magnetic moment of the Cooper pairs, significant at fields of the order of the chemical potential. We discuss the equation of state (EoS) of MCFL matter for a large range of field values and consider possible applications of the magnetic effects on dense quark matter to the astrophysics of compact stars.Comment: To appear in Lect. Notes Phys. "Strongly interacting matter in magnetic fields" (Springer), edited by D. Kharzeev, K. Landsteiner, A. Schmitt, H.-U. Ye

Quantum walks: a comprehensive review

Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a solid field of research of quantum computation full of exciting open problems for physicists, computer scientists, mathematicians and engineers. In this paper we review theoretical advances on the foundations of both discrete- and continuous-time quantum walks, together with the role that randomness plays in quantum walks, the connections between the mathematical models of coined discrete quantum walks and continuous quantum walks, the quantumness of quantum walks, a summary of papers published on discrete quantum walks and entanglement as well as a succinct review of experimental proposals and realizations of discrete-time quantum walks. Furthermore, we have reviewed several algorithms based on both discrete- and continuous-time quantum walks as well as a most important result: the computational universality of both continuous- and discrete- time quantum walks.Comment: Paper accepted for publication in Quantum Information Processing Journa