Formalization of Complex Vectors in Higher-Order Logic

Complex vector analysis is widely used to analyze continuous systems in many disciplines, including physics and engineering. In this paper, we present a higher-order-logic formalization of the complex vector space to facilitate conducting this analysis within the sound core of a theorem prover: HOL Light. Our definition of complex vector builds upon the definitions of complex numbers and real vectors. This extension allows us to extensively benefit from the already verified theorems based on complex analysis and real vector analysis. To show the practical usefulness of our library we adopt it to formalize electromagnetic fields and to prove the law of reflection for the planar waves.Comment: 15 pages, 1 figur

Vacuum energy, spectral determinant and heat kernel asymptotics of graph Laplacians with general vertex matching conditions

We consider Laplace operators on metric graphs, networks of one-dimensional line segments (bonds), with matching conditions at the vertices that make the operator self-adjoint. Such quantum graphs provide a simple model of quantum mechanics in a classically chaotic system with multiple scales corresponding to the lengths of the bonds. For graph Laplacians we briefly report results for the spectral determinant, vacuum energy and heat kernel asymptotics of general graphs in terms of the vertex matching conditions.Comment: 5 pages, submitted to proceedings of QFEXT09, minor corrections made

A pilot study examining garment severance damage caused by a trained sharp-weapon user

The pilot study summarized in this paper aimed to raise awareness of a gap that exists in the forensic textile science literature about damage caused to clothing by trained sharp-weapon users. A male trained in the Filipino martial arts discipline of Eskrima performed attack techniques on a physical model of a male torso covered with a 97% cotton/3% elastane knitted T-shirt, that is, a garment commonly worn by males. Fabric severance appearance created by three different, but commonly available, knives was evaluated. High-speed video was used to capture each attack. After each attack the resulting damage to the garment was assessed. This pilot study highlighted differences in severances associated with weapon selection, that is, not all knives resulted in similar patterns of textile damage. In addition, a mixture of stab and slash severances were observed. The findings demonstrated the possible misinterpretation of textile damage under these circumstances compared to damage patterns reported in the existing forensic textile science literature for more commonly occurring knife attacks (i.e. stabbings)

Heisenberg exchange in magnetic monoxides

The superexchange intertacion in transition-metal oxides, proposed initially by Anderson in 1950, is treated using contemporary tight-binding theory and existing parameters. We find also a direct exchange for nearest-neighbor metal ions, larger by a factor of order five than the superexchange. This direct exchange arises from Vddm coupling, rather than overlap of atomic charge densities, a small overlap exchange contribution which we also estimate. For FeO and CoO there is also an important negative contribution, related to Stoner ferromagnetism, from the partially filled minority-spin band which broadens when ionic spins are aligned. The corresponding J1 and J2 parameters are calculated for MnO, FeO, CoO, and NiO. They give good accounts of the Neel and the Curie-Weiss temperatures, show appropriate trends, and give a reasonable account of their volume dependences. For MnO the predicted value for the magnetic susceptibility at the Neel temperature and the crystal distortion arising from the antiferromagnetic transition were reasonably well given. Application to CuO2 planes in the cuprates gives J=1220oK, compared to an experimental 1500oK, and for LiCrO2 gives J1=4 50oK compared to an experimental 230oK.Comment: 21 pages, 1 figure, submitted to Phys. Rev. B 1/19/07. Realized J=4V^2/U applies generally, as opposed to J=2V^2/U from one-electron theory (1/28 revision

Spectral determinants and zeta functions of Schr\"odinger operators on metric graphs

A derivation of the spectral determinant of the Schr\"odinger operator on a metric graph is presented where the local matching conditions at the vertices are of the general form classified according to the scheme of Kostrykin and Schrader. To formulate the spectral determinant we first derive the spectral zeta function of the Schr\"odinger operator using an appropriate secular equation. The result obtained for the spectral determinant is along the lines of the recent conjecture.Comment: 16 pages, 2 figure

Information propagation for interacting particle systems

We show that excitations of interacting quantum particles in lattice models always propagate with a finite speed of sound. Our argument is simple yet general and shows that by focusing on the physically relevant observables one can generally expect a bounded speed of information propagation. The argument applies equally to quantum spins, bosons such as in the Bose-Hubbard model, fermions, anyons, and general mixtures thereof, on arbitrary lattices of any dimension. It also pertains to dissipative dynamics on the lattice, and generalizes to the continuum for quantum fields. Our result can be seen as a meaningful analogue of the Lieb-Robinson bound for strongly correlated models.Comment: 4 pages, 1 figure, minor change

Augmented paper applications: Initial user tests of a wireless pattern reader

A handheld pattern reader has been developed to read low visibility conductive patterns on paper. The patterns are formed by masking conductive paper with a non-conductive, printed lacquer. The reader was developed as part of an EU-funded project investigating methods of augmenting paper. Data read from the patterns was used to trigger events in the digital domain. Usability tests were undertaken to investigate the performance of the prototype. Results showed that at this stage of development there was significant variation in performance of the prototype from user to user. Further work is being undertaken to determine the causes of this variability