Area law violations in a supersymmetric model

We study the structure of entanglement in a supersymmetric lattice model of fermions on certain types of decorated graphs with quenched disorder. In particular, we construct models with controllable ground state degeneracy protected by supersymmetry and the choice of Hilbert space. We show that in certain special limits these degenerate ground states are associated with local impurities and that there exists a basis of the ground state manifold in which every basis element satisfies a boundary law for entanglement entropy. On the other hand, by considering incoherent mixtures or coherent superpositions of these localized ground states, we can find regions that violate the boundary law for entanglement entropy over a wide range of length scales. More generally, we discuss various desiderata for constructing violations of the boundary law for entanglement entropy and discuss possible relations of our work to recent holographic studies.Comment: 20 pages, 1 figure, 1 appendi

Biofouling in water systems

The paper describes the mechanisms in the development of biofouling layers (initial surface conditioning, microbial transport and attachment, mass transfer of nutrients to the biofilm surface and through the microbial layer, cell metabolism, and detachment of cells and of larger parts of the biofilm) and summarizes the effects of several factors on the buildup and stability of biofilms (nutrient availability, fluid velocity and turbulence, temperature, surface condition, and nonliving particles). Mass transfer within biofilms is treated in more detail. A biofouling model applied to the development of biofilms in heat exchangers is presented. Finally, references are made to biofouling control methods (biocide and the proper design and operation of heat exchangers) and to future research needs in this area

Exact ground states of a staggered supersymmetric model for lattice fermions

We study a supersymmetric model for strongly interacting lattice fermions in the presence of a staggering parameter. The staggering is introduced as a tunable parameter in the manifestly supersymmetric Hamiltonian. We obtain analytic expressions for the ground states in the limit of small and large staggering for the model on the class of doubly decorated lattices. On this type of lattice there are two ground states, each with a different density. In one limit we find these ground states to be a simple Wigner crystal and a valence bond solid (VBS) state. In the other limit we find two types of quantum liquids. As a special case, we investigate the quantum liquid state on the one dimensional chain in detail. It is characterized by a massless kink that separates two types of order.Comment: 21 pages, 6 figures, v2: largely rewritten version with more emphasis on physical interpretatio

The Standard Model Fermion Spectrum From Complex Projective spaces

It is shown that the quarks and leptons of the standard model, including a right-handed neutrino, can be obtained by gauging the holonomy groups of complex projective spaces of complex dimensions two and three. The spectrum emerges as chiral zero modes of the Dirac operator coupled to gauge fields and the demonstration involves an index theorem analysis on a general complex projective space in the presence of topologically non-trivial SU(n)xU(1) gauge fields. The construction may have applications in type IIA string theory and non-commutative geometry.Comment: 13 pages. Typset using LaTeX and JHEP3 style files. Minor typos correcte

Time for Ontology? The Role of Ontological Time in Anticipation

In this contribution, I will argue for an ontological understanding of time as temporality. This, however, implies that in a certain sense being is temporality, by which I mean that (1) on an ontological level temporality is nothing but the process of change, i.e. the dynamic aspect of being in its becoming, changing, and perishing, and (2) that concrete beings are not merely in time, but they are temporal. This leads to the conclusion that actual time is the process of change that becoming beings are, as well as the conclusion that reality is fundamentally temporal as argued by process metaphysicians like Alfred North Whitehead, Henri Bergson, Martin Heidegger, and Gilles Deleuze. The investigation begins with first establishing the methodological difficulties involved in thinking temporality as an ontological feature. In a second step, dynamic ontologies are introduced as the conceptual background best suited to think ontological temporality and their difference to event-ontologies is explained. Finally, the distinction between temporality and linear time is clarified. This introduction of temporality ends with some arguments for the existence of temporality that are inspired by Aristotle’s famous investigations into the nature of time. After having thus introduced temporality as an ontological feature and argued for the existence and relevance of it, its implications for our understanding of the dimensions of time and especially for anticipation are discussed.</p

Geometric quantization of Hamiltonian actions of Lie algebroids and Lie groupoids

We construct Hermitian representations of Lie algebroids and associated unitary representations of Lie groupoids by a geometric quantization procedure. For this purpose we introduce a new notion of Hamiltonian Lie algebroid actions. The first step of our procedure consists of the construction of a prequantization line bundle. Next, we discuss a version of K\"{a}hler quantization suitable for this setting. We proceed by defining a Marsden-Weinstein quotient for our setting and prove a ``quantization commutes with reduction'' theorem. We explain how our geometric quantization procedure relates to a possible orbit method for Lie groupoids. Our theory encompasses the geometric quantization of symplectic manifolds, Hamiltonian Lie algebra actions, actions of families of Lie groups, foliations, as well as some general constructions from differential geometry.Comment: 40 pages, corrected version 11-01-200

Representations of p-brane topological charge algebras

The known extended algebras associated with p-branes are shown to be generated as topological charge algebras of the standard p-brane actions. A representation of the charges in terms of superspace forms is constructed. The charges are shown to be the same in standard/extended superspace formulations of the action.Comment: 22 pages. Typos fixed, refs added. Minor additions to comments sectio

A super-analogue of Kontsevich's theorem on graph homology

In this paper we will prove a super-analogue of a well-known result by Kontsevich which states that the homology of a certain complex which is generated by isomorphism classes of oriented graphs can be calculated as the Lie algebra homology of an infinite-dimensional Lie algebra of symplectic vector fields.Comment: 15 page

Cyclic cocycles on twisted convolution algebras

We give a construction of cyclic cocycles on convolution algebras twisted by gerbes over discrete translation groupoids. For proper \'etale groupoids, Tu and Xu provide a map between the periodic cyclic cohomology of a gerbe-twisted convolution algebra and twisted cohomology groups which is similar to a construction of Mathai and Stevenson. When the groupoid is not proper, we cannot construct an invariant connection on the gerbe; therefore to study this algebra, we instead develop simplicial techniques to construct a simplicial curvature 3-form representing the class of the gerbe. Then by using a JLO formula we define a morphism from a simplicial complex twisted by this simplicial curvature 3-form to the mixed bicomplex computing the periodic cyclic cohomology of the twisted convolution algebras. The results in this article were originally published in the author's Ph.D. thesis.Comment: 39 page