595 research outputs found
Excitation basis for (3+1)d topological phases
We consider an exactly solvable model in 3+1 dimensions, based on a finite
group, which is a natural generalization of Kitaev's quantum double model. The
corresponding lattice Hamiltonian yields excitations located at
torus-boundaries. By cutting open the three-torus, we obtain a manifold bounded
by two tori which supports states satisfying a higher-dimensional version of
Ocneanu's tube algebra. This defines an algebraic structure extending the
Drinfel'd double. Its irreducible representations, labeled by two fluxes and
one charge, characterize the torus-excitations. The tensor product of such
representations is introduced in order to construct a basis for (3+1)d gauge
models which relies upon the fusion of the defect excitations. This basis is
defined on manifolds of the form , with a
two-dimensional Riemann surface. As such, our construction is closely related
to dimensional reduction from (3+1)d to (2+1)d topological orders.Comment: 33 pages; v2 references added; v3 minor change
An Investigation of Ancient Hebrew Music During the Time of the Old Testament: Especially the Role of Music in the Lives of Israel\u27s First Two Kings, Saul and David
Music has always been an inextricable component of Jewish culture from its beginnings. Even before the construction of the Temple, music was used for worship, feasts, festivals, and various other cultural activities. Since much of this music involves the singing of texts, poetry was also a central part of the Jewish music culture. Singing in ancient Israel often involved instrumental accompaniment. The Bible records the texts of much musical activity. Instrumental music, vocal music, and accompanied vocal music are found throughout the Bible. Instrumental music is found in 1 Samuel 16 when David played his harp to soothe Saul and in 1 Samuel 19 when Saul tried to kill David when a troubling spirit came upon him. When men were coming back from battle in 1 Samuel 18, women played instruments and sang songs of David’s greatness. Psalms 16, 24, and 64 are great representations of Hebrew vocal music written by David. Music played a central role in the lives of the first two kings of Israel. This study will encompass a discussion of the role of music in the lives of the first two kings of Israel, Saul and David
Towards a dual spin network basis for (3+1)d lattice gauge theories and topological phases
Using a recent strategy to encode the space of flat connections on a
three-manifold with string-like defects into the space of flat connections on a
so-called 2d Heegaard surface, we propose a novel way to define gauge invariant
bases for (3+1)d lattice gauge theories and gauge models of topological phases.
In particular, this method reconstructs the spin network basis and yields a
novel dual spin network basis. While the spin network basis allows to interpret
states in terms of electric excitations, on top of a vacuum sharply peaked on a
vanishing electric field, the dual spin network basis describes magnetic (or
curvature) excitations, on top of a vacuum sharply peaked on a vanishing
magnetic field (or flat connection). This technique is also applicable for
manifolds with boundaries. We distinguish in particular a dual pair of boundary
conditions, namely of electric type and of magnetic type. This can be used to
consider a generalization of Ocneanu's tube algebra in order to reveal the
algebraic structure of the excitations associated with certain 3d manifolds.Comment: 45 page
Essential patents in pools: Is value intrinsinc or induced ?
This paper analyzes empirically the value - as measured by patent citations - of a set of 1363 essential patents belonging to 9 different patent pools. We find that pooled patents receive more cites than control patents having the same characteristics but not included in a pool. This difference stems only partly from the pools' ability to select the most cited patents. Indeed we show that being included in a pool also tends to increase the value of patents. This induced effect reflects the incentive for patent owners to join a pool. We analyze it in details in order to better understand the drivers of enhanced patent value.
Tube algebras, excitations statistics and compactification in gauge models of topological phases
We consider lattice Hamiltonian realizations of (+1)-dimensional
Dijkgraaf-Witten theory. In (2+1)d, it is well-known that the Hamiltonian
yields point-like excitations classified by irreducible representations of the
twisted quantum double. This can be confirmed using a tube algebra approach. In
this paper, we propose a generalization of this strategy that is valid in any
dimensions. We then apply the tube algebra approach to derive the algebraic
structure of loop-like excitations in (3+1)d, namely the twisted quantum
triple. The irreducible representations of the twisted quantum triple algebra
correspond to the simple loop-like excitations of the model. Similarly to its
(2+1)d counterpart, the twisted quantum triple comes equipped with a compatible
comultiplication map and an -matrix that encode the fusion and the braiding
statistics of the loop-like excitations, respectively. Moreover, we explain
using the language of loop-groupoids how a model defined on a manifold that is
-times compactified can be expressed in terms of another model in -lower
dimensions. This can in turn be used to recast higher-dimensional tube algebras
in terms of lower dimensional analogues.Comment: 71 page
On 2-form gauge models of topological phases
We explore various aspects of 2-form topological gauge theories in (3+1)d.
These theories can be constructed as sigma models with target space the second
classifying space of the symmetry group , and they are classified by
cohomology classes of . Discrete topological gauge theories can typically
be embedded into continuous quantum field theories. In the 2-form case, the
continuous theory is shown to be a strict 2-group gauge theory. This embedding
is studied by carefully constructing the space of -form connections using
the technology of Deligne-Beilinson cohomology. The same techniques can then be
used to study more general models built from Postnikov towers. For finite
symmetry groups, 2-form topological theories have a natural lattice
interpretation, which we use to construct a lattice Hamiltonian model in (3+1)d
that is exactly solvable. This construction relies on the introduction of a
cohomology, dubbed 2-form cohomology, of algebraic cocycles that are identified
with the simplicial cocycles of as provided by the so-called
-construction of Eilenberg-MacLane spaces. We show algebraically and
geometrically how a 2-form 4-cocycle reduces to the associator and the braiding
isomorphisms of a premodular category of -graded vector spaces. This is used
to show the correspondence between our 2-form gauge model and the Walker-Wang
model.Comment: 78 page
Essential patents in pools: Is value intrinsinc or induced ?
CERNA WORKING PAPER SERIES 2010-04This paper analyzes empirically the value - as measured by patent citations - of a set of 1363 essential patents belonging to 9 different patent pools. We find that pooled patents receive more cites than control patents having the same characteristics but not included in a pool. This difference stems only partly from the pools' ability to select the most cited patents. Indeed we show that being included in a pool also tends to increase the value of patents. This induced effect reflects the incentive for patent owners to join a pool. We analyze it in details in order to better understand the drivers of enhanced patent value
Tensor network approach to electromagnetic duality in (3+1)d topological gauge models
Given the Hamiltonian realisation of a topological (3+1)d gauge theory with
finite group , we consider a family of tensor network representations of its
ground state subspace. This family is indexed by gapped boundary conditions
encoded into module 2-categories over the input spherical fusion 2-category.
Individual tensors are characterised by symmetry conditions with respect to
non-local operators acting on entanglement degrees of freedom. In the case of
Dirichlet and Neumann boundary conditions, we show that the symmetry operators
form the fusion 2-categories of -graded 2-vector spaces
and of 2-representations of , respectively. In virtue of
the Morita equivalence between and --
which we explicitly establish -- the topological order can be realised as the
Drinfel'd centre of either 2-category of operators; this is a realisation of
the electromagnetic duality of the theory. Specialising to the case , we recover tensor network representations that were recently
introduced, as well as the relation between the electromagnetic duality of a
pure (3+1)d gauge theory and the Kramers-Wannier duality of a
boundary (2+1)d Ising model
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