Combinatorial Topology Of Multipartite Entangled States

With any state of a multipartite quantum system its separability polytope is associated. This is an algebro-topological object (non-trivial only for mixed states) which captures the localisation of entanglement of the state. Particular examples of separability polytopes for 3-partite systems are explicitly provided. It turns out that this characterisation of entanglement is associated with simulation of arbitrary unitary operations by 1- and 2-qubit gates. A topological description of how entanglement changes in course of such simulation is provided.Comment: 14 pages, LaTeX2e. Slightly revised version of the poster resented on the International Conference on Quantum Information, Oviedo, Spain, 13-18 July, 2002. To appear in the special issue of Journal of Modern Optic

Spacetime topology from the tomographic histories approach: Part II

As an inverse problem, we recover the topology of the effective spacetime that a system lies in, in an operational way. This means that from a series of experiments we get a set of points corresponding to events. This continues the previous work done by the authors. Here we use the existence of upper bound in the speed of transfer of matter and information to induce a partial order on the set of events. While the actual partial order is not known in our operational set up, the grouping of events to (unordered) subsets corresponding to possible histories, is given. From this we recover the partial order up to certain ambiguities that are then classified. Finally two different ways to recover the topology are sketched and their interpretation is discussed.Comment: 21 pages, slight change in title and certain minor corrections in this second version. To apear in IJT

Backpropagation training in adaptive quantum networks

We introduce a robust, error-tolerant adaptive training algorithm for generalized learning paradigms in high-dimensional superposed quantum networks, or \emph{adaptive quantum networks}. The formalized procedure applies standard backpropagation training across a coherent ensemble of discrete topological configurations of individual neural networks, each of which is formally merged into appropriate linear superposition within a predefined, decoherence-free subspace. Quantum parallelism facilitates simultaneous training and revision of the system within this coherent state space, resulting in accelerated convergence to a stable network attractor under consequent iteration of the implemented backpropagation algorithm. Parallel evolution of linear superposed networks incorporating backpropagation training provides quantitative, numerical indications for optimization of both single-neuron activation functions and optimal reconfiguration of whole-network quantum structure.Comment: Talk presented at "Quantum Structures - 2008", Gdansk, Polan

Algebraic description of spacetime foam

A mathematical formalism for treating spacetime topology as a quantum observable is provided. We describe spacetime foam entirely in algebraic terms. To implement the correspondence principle we express the classical spacetime manifold of general relativity and the commutative coordinates of its events by means of appropriate limit constructions.Comment: 34 pages, LaTeX2e, the section concerning classical spacetimes in the limit essentially correcte

Thermal effects on electron-phonon interaction in silicon nanostructures

Raman spectra from silicon nanostructures, recorded using excitation laser power density of 1.0 kW/cm^2, is employed here to reveal the dominance of thermal effects at temperatures higher than the room temperature. Room temperature Raman spectrum shows only phonon confinement and Fano effects. Raman spectra recorded at higher temperatures show increase in FWHM and decrease in asymmetry ratio with respect to its room temperature counterpart. Experimental Raman scattering data are analyzed successfully using theoretical Raman line-shape generated by incorporating the temperature dependence of phonon dispersion relation. Experimental and theoretical temperature dependent Raman spectra are in good agreement. Although quantum confinement and Fano effects persists, heating effects start dominating at higher temperatures than room tempaerature.Comment: 9 Pages, 3 Figures and 1 Tabl

`Iconoclastic', Categorical Quantum Gravity

This is a two-part, `2-in-1' paper. In Part I, the introductory talk at `Glafka--2004: Iconoclastic Approaches to Quantum Gravity' international theoretical physics conference is presented in paper form (without references). In Part II, the more technical talk, originally titled ``Abstract Differential Geometric Excursion to Classical and Quantum Gravity'', is presented in paper form (with citations). The two parts are closely entwined, as Part I makes general motivating remarks for Part II.Comment: 34 pages, in paper form 2 talks given at ``Glafka--2004: Iconoclastic Approaches to Quantum Gravity'' international theoretical physics conference, Athens, Greece (summer 2004

`Third' Quantization of Vacuum Einstein Gravity and Free Yang-Mills Theories

Based on the algebraico-categorical (:sheaf-theoretic and sheaf cohomological) conceptual and technical machinery of Abstract Differential Geometry, a new, genuinely background spacetime manifold independent, field quantization scenario for vacuum Einstein gravity and free Yang-Mills theories is introduced. The scheme is coined `third quantization' and, although it formally appears to follow a canonical route, it is fully covariant, because it is an expressly functorial `procedure'. Various current and future Quantum Gravity research issues are discussed under the light of 3rd-quantization. A postscript gives a brief account of this author's personal encounters with Rafael Sorkin and his work.Comment: 43 pages; latest version contributed to a fest-volume celebrating Rafael Sorkin's 60th birthday (Erratum: in earlier versions I had wrongly written that the Editor for this volume is Daniele Oriti, with CUP as publisher. I apologize for the mistake.

Reversible Pressure-Induced Amorphization in Solid C70 : Raman and Photoluminescence Study

We have studied single crystals of $C_{70}$ by Raman scattering and photoluminescence in the pressure range from 0 to 31.1 GPa. The Raman spectrum at 31.1 GPa shows only a broad band similar to that of the amorphous carbon without any trace of the Raman lines of $C_{70}$. After releasing the pressure from 31.1 GPa, the Raman and the photoluminescence spectra of the recovered sample are that of the starting $C_{70}$ crystal. These results indicate that the $C_{70}$ molecules are stable upto 31.1 GPa and the amorphous carbon high pressure phase is reversible, in sharp contrast to the results on solid $C_{60}$. A qualitative explaination is suggested in terms of inter- versus intra-molecular interactions.Comment: To appear in Phys. Rev. Lett., 12 pages, RevTeX (preprint format), 3 figures available upon reques