Biorthogonal quantum mechanics

The Hermiticity condition in quantum mechanics required for the characterization of (a) physical observables and (b) generators of unitary motions can be relaxed into a wider class of operators whose eigenvalues are real and whose eigenstates are complete. In this case, the orthogonality of eigenstates is replaced by the notion of biorthogonality that defines the relation between the Hilbert space of states and its dual space. The resulting quantum theory, which might appropriately be called 'biorthogonal quantum mechanics', is developed here in some detail in the case for which the Hilbert-space dimensionality is finite. Specifically, characterizations of probability assignment rules, observable properties, pure and mixed states, spin particles, measurements, combined systems and entanglements, perturbations, and dynamical aspects of the theory are developed. The paper concludes with a brief discussion on infinite-dimensional systems. © 2014 IOP Publishing Ltd

Orthonormal sequences in L2(Rd)L^2(R^d) and time frequency localization

We study uncertainty principles for orthonormal bases and sequences in $L^2(\R^d)$. As in the classical Heisenberg inequality we focus on the product of the dispersions of a function and its Fourier transform. In particular we prove that there is no orthonormal basis for $L^2(\R)$ for which the time and frequency means as well as the product of dispersions are uniformly bounded. The problem is related to recent results of J. Benedetto, A. Powell, and Ph. Jaming. Our main tool is a time frequency localization inequality for orthonormal sequences in $L^2(\R^d)$. It has various other applications.Comment: 18 page

Group Strategyproof Pareto-Stable Marriage with Indifferences via the Generalized Assignment Game

We study the variant of the stable marriage problem in which the preferences of the agents are allowed to include indifferences. We present a mechanism for producing Pareto-stable matchings in stable marriage markets with indifferences that is group strategyproof for one side of the market. Our key technique involves modeling the stable marriage market as a generalized assignment game. We also show that our mechanism can be implemented efficiently. These results can be extended to the college admissions problem with indifferences

Matching structure and bargaining outcomes in buyer–seller networks

We examine the relationship between the matching structure of a bipartite (buyer-seller) network and the (expected) shares of the unit surplus that each connected pair in this network can create. We show that in different bargaining environments, these shares are closely related to the Gallai-Edmonds Structure Theorem. This theorem characterizes the structure of maximum matchings in an undirected graph. We show that the relationship between the (expected) shares and the tructure Theorem is not an artefact of a particular bargaining mechanism or trade centralization. However, this relationship does not necessarily generalize to non-bipartite networks or to networks with heterogeneous link values

A new expedited approach to evaluate the importance of different crystal growth parameters on laser damage performance in KDP and DKDP

In this work, we investigate the laser-induced damage resistance at 355 nm in DKDP crystals grown with varying growth parameters, including temperature, speed of growth and impurity concentration. In order to perform this work, a DKDP crystal was grown over 34 days by the rapid-growth technique with varied growth conditions. By using the same crystal, we are able to isolate growth-related parameters affecting LID from raw material or other variations that are encountered when testing in different crystals. The objective is to find correlations of damage performance to growth conditions and reveal the key parameters for achieving DKDP material in which the number of damage initiating defects is reduced. This approach can lead to reliable and expedite information regarding the importance of different crystal growth parameters on the laser damage characteristics of these crystals

Genome characteristics of facultatively symbiotic Frankia sp. strains reflect host range and host plant biogeography

Soil bacteria that also form mutualistic symbioses in plants encounter two major levels of selection. One occurs during adaptation to and survival in soil, and the other occurs in concert with host plant speciation and adaptation. Actinobacteria from the genus Frankia are facultative symbionts that form N2-fixing root nodules on diverse and globally distributed angiosperms in the “actinorhizal” symbioses. Three closely related clades of Frankia sp. strains are recognized; members of each clade infect a subset of plants from among eight angiosperm families. We sequenced the genomes from three strains; their sizes varied from 5.43 Mbp for a narrow host range strain (Frankia sp. strain HFPCcI3) to 7.50 Mbp for a medium host range strain (Frankia alni strain ACN14a) to 9.04 Mbp for a broad host range strain (Frankia sp. strain EAN1pec.) This size divergence is the largest yet reported for such closely related soil bacteria (97.8%–98.9% identity of 16S rRNA genes). The extent of gene deletion, duplication, and acquisition is in concert with the biogeographic history of the symbioses and host plant speciation. Host plant isolation favored genome contraction, whereas host plant diversification favored genome expansion. The results support the idea that major genome expansions as well as reductions can occur in facultative symbiotic soil bacteria as they respond to new environments in the context of their symbioses

Oriented coloring: complexity and approximation

International audienceThis paper is devoted to an oriented coloring problem motivated by a task assignment model. A recent result established the NP-completeness of deciding whether a digraph is k-oriented colorable; we extend this result to the classes of bipartite digraphs and circuit-free digraphs. Finally, we investigate the approximation of this problem: both positive and negative results are devised

Temperature activated absorption during laser-induced damage: the evolution of laser-supported solid-state absorption fronts

Previously we have shown that the size of laser induced damage sites in both KDP and SiO{sub 2} is largely governed by the duration of the laser pulse which creates them. Here we present a model based on experiment and simulation that accounts for this behavior. Specifically, we show that solid-state laser-supported absorption fronts are generated during a damage event and that these fronts propagate at constant velocities for laser intensities up to 4 GW/cm{sup 2}. It is the constant absorption front velocity that leads to the dependence of laser damage site size on pulse duration. We show that these absorption fronts are driven principally by the temperature-activated deep sub band-gap optical absorptivity, free electron transport, and thermal diffusion in defect-free silica for temperatures up to 15,000K and pressures < 15GPa. In addition to the practical application of selecting an optimal laser for pre-initiation of large aperture optics, this work serves as a platform for understanding general laser-matter interactions in dielectrics under a variety of conditions

Different precursor populations revealed by microscopic studies of bulk damage in KDP and DKDP crystals

We present experimental results aiming to reveal the relationship between damage initiating defect populations in KDP and DKDP crystals under irradiation at different wavelengths. Our results indicate that there is more than one type of defects leading to damage initiation, each defect acting as damage initiators over a different wavelength range. Results showing disparities in the morphology of damage sites from exposure at different wavelengths provides additional evidence for the presence of multiple types of defects responsible for damage initiation