On the magnitude of a finite dimensional algebra

There is a general notion of the magnitude of an enriched category, defined subject to hypotheses. In topological and geometric contexts, magnitude is already known to be closely related to classical invariants such as Euler characteristic and dimension. Here we establish its significance in an algebraic context. Specifically, in the representation theory of an associative algebra $A$, a central role is played by the indecomposable projective $A$-modules, which form a category enriched in vector spaces. We show that the magnitude of that category is a known homological invariant of the algebra: writing $\chi_A$ for the Euler form of $A$ and $S$ for the direct sum of the simple $A$-modules, it is $\chi_A(S,S)$

Direct vs. indirect optical recombination in Ge films grown on Si substrates

The optical emission spectra from Ge films on Si are markedly different from their bulk Ge counterparts. Whereas bulk Ge emission is dominated by the material's indirect gap, the photoluminescence signal from Ge films is mainly associated with its direct band gap. Using a new class of Ge-on-Si films grown by a recently introduced CVD approach, we study the direct and indirect photoluminescence from intrinsic and doped samples and we conclude that the origin of the discrepancy is the lack of self-absorption in thin Ge films combined with a deviation from quasi-equilibrium conditions in the conduction band. The latter is confirmed by a simple model suggesting that the deviation from quasi-equilibrium is caused by the much shorter recombination lifetime in the films relative to bulk Ge

Where are the Hedgehogs in Nematics?

In experiments which take a liquid crystal rapidly from the isotropic to the nematic phase, a dense tangle of defects is formed. In nematics, there are in principle both line and point defects (``hedgehogs''), but no point defects are observed until the defect network has coarsened appreciably. In this letter the expected density of point defects is shown to be extremely low, approximately $10^{-8}$ per initially correlated domain, as result of the topology (specifically, the homology) of the order parameter space.Comment: 6 pages, latex, 1 figure (self-unpacking PostScript)

Cryogenic-coolant He4-superconductor dynamic and static interactions

A composite superconducting material (NbTi-Cu) was evaluated with emphasis on post quench solid cooling interaction regimes. The quasi-steady runs confirm the existence of a thermodynamic limiting thickness for insulating coatings. Two distinctly different post quench regimes of coated composites are shown to relate to the limiting thickness. Only one regime,, from quench onset to the peak value, revealed favorable coolant states, in particular in He2. Transient recovery shows favorable recovery times from this post quench regime (not drastically different from bare conductors) for both single coated specimens and a coated conductor bundle

Quantum Bit Regeneration

Decoherence and loss will limit the practicality of quantum cryptography and computing unless successful error correction techniques are developed. To this end, we have discovered a new scheme for perfectly detecting and rejecting the error caused by loss (amplitude damping to a reservoir at T=0), based on using a dual-rail representation of a quantum bit. This is possible because (1) balanced loss does not perform a ``which-path'' measurement in an interferometer, and (2) balanced quantum nondemolition measurement of the ``total'' photon number can be used to detect loss-induced quantum jumps without disturbing the quantum coherence essential to the quantum bit. Our results are immediately applicable to optical quantum computers using single photonics devices.Comment: 4 pages, postscript only, figures available at http://feynman.stanford.edu/qcom

Geometric quantum computation using fictitious spin- 1/2 subspaces of strongly dipolar coupled nuclear spins

Geometric phases have been used in NMR, to implement controlled phase shift gates for quantum information processing, only in weakly coupled systems in which the individual spins can be identified as qubits. In this work, we implement controlled phase shift gates in strongly coupled systems, by using non-adiabatic geometric phases, obtained by evolving the magnetization of fictitious spin-1/2 subspaces, over a closed loop on the Bloch sphere. The dynamical phase accumulated during the evolution of the subspaces, is refocused by a spin echo pulse sequence and by setting the delay of transition selective pulses such that the evolution under the homonuclear coupling makes a complete $2\pi$ rotation. A detailed theoretical explanation of non-adiabatic geometric phases in NMR is given, by using single transition operators. Controlled phase shift gates, two qubit Deutsch-Jozsa algorithm and parity algorithm in a qubit-qutrit system have been implemented in various strongly dipolar coupled systems obtained by orienting the molecules in liquid crystal media.Comment: 37 pages, 17 figure

Carrier dynamics and coherent acoustic phonons in nitride heterostructures

We model generation and propagation of coherent acoustic phonons in piezoelectric InGaN/GaN multi-quantum wells embedded in a \textit{pin} diode structure and compute the time resolved reflectivity signal in simulated pump-probe experiments. Carriers are created in the InGaN wells by ultrafast pumping below the GaN band gap and the dynamics of the photoexcited carriers is treated in a Boltzmann equation framework. Coherent acoustic phonons are generated in the quantum well via both deformation potential electron-phonon and piezoelectric electron-phonon interaction with photogenerated carriers, with the latter mechanism being the dominant one. Coherent longitudinal acoustic phonons propagate into the structure at the sound speed modifying the optical properties and giving rise to a giant oscillatory differential reflectivity signal. We demonstrate that coherent optical control of the differential reflectivity can be achieved using a delayed control pulse.Comment: 14 pages, 11 figure

Evidence for Duality of Conifold from Fundamental String

We study the spectrum of BPS D5-D3-F1 states in type IIB theory, which are proposed to be dual to D4-D2-D0 states on the resolved conifold in type IIA theory. We evaluate the BPS partition functions for all values of the moduli parameter in the type IIB side, and find them completely agree with the results in the type IIA side which was obtained by using Kontsevich-Soibelman's wall-crossing formula. Our result is a quite strong evidence for string dualities on the conifold.Comment: 24 pages, 13 figures, v2: typos corrected, v3: explanations about wall-crossing improved and figures adde