Quantum cohomology via vicious and osculating walkers

We relate the counting of rational curves intersecting Schubert varieties of the Grassmannian to the counting of certain non-intersecting lattice paths on the cylinder, so-called vicious and osculating walkers. These lattice paths form exactly solvable statistical mechanics models and are obtained from solutions to the Yang–Baxter equation. The eigenvectors of the transfer matrices of these models yield the idempotents of the Verlinde algebra of the gauged u^(n)k -WZNW model. The latter is known to be closely related to the small quantum cohomology ring of the Grassmannian. We establish further that the partition functions of the vicious and osculating walker model are given in terms of Postnikov’s toric Schur functions and can be interpreted as generating functions for Gromov–Witten invariants. We reveal an underlying quantum group structure in terms of Yang–Baxter algebras and use it to give a generating formula for toric Schur functions in terms of divided difference operators which appear in known representations of the nil-Hecke algebra

Functional relations from the Yang-Baxter algebra: Eigenvalues of the XXZ model with non-diagonal twisted and open boundary conditions

In this work we consider a functional method in the theory of exactly solvable models based on the Yang-Baxter algebra. Using this method we derive the eigenvalues of the XXZ model with non-diagonal twisted and open boundary conditions for general values of the anisotropy and boundary parameters.Comment: 26 page

Atmospheric neutrons

Contributions to fast neutron measurements in the atmosphere are outlined. The results of a calculation to determine the production, distribution and final disappearance of atmospheric neutrons over the entire spectrum are presented. An attempt is made to answer questions that relate to processes such as neutron escape from the atmosphere and C-14 production. In addition, since variations of secondary neutrons can be related to variations in the primary radiation, comment on the modulation of both radiation components is made

Noncommutative Schur polynomials and the crystal limit of the U_q sl(2)-vertex model

Starting from the Verma module of U_q sl(2) we consider the evaluation module for affine U_q sl(2) and discuss its crystal limit (q=0). There exists an associated integrable statistical mechanics model on a square lattice defined in terms of vertex configurations. Its transfer matrix is the generating function for noncommutative complete symmetric polynomials in the generators of the affine plactic algebra, an extension of the finite plactic algebra first discussed by Lascoux and Sch\"{u}tzenberger. The corresponding noncommutative elementary symmetric polynomials were recently shown to be generated by the transfer matrix of the so-called phase model discussed by Bogoliubov, Izergin and Kitanine. Here we establish that both generating functions satisfy Baxter's TQ-equation in the crystal limit by tying them to special U_q sl(2) solutions of the Yang-Baxter equation. The TQ-equation amounts to the well-known Jacobi-Trudy formula leading naturally to the definition of noncommutative Schur polynomials. The latter can be employed to define a ring which has applications in conformal field theory and enumerative geometry: it is isomorphic to the fusion ring of the sl(n)_k -WZNW model whose structure constants are the dimensions of spaces of generalized theta-functions over the Riemann sphere with three punctures.Comment: 24 pages, 6 figures; v2: several typos fixe

Optical inter-site spin transfer probed by energy and spin-resolved transient absorption spectroscopy

Optically driven spin transport is the fastest and most efficient process to manipulate macroscopic magnetization as it does not rely on secondary mechanisms to dissipate angular momentum. In the present work, we show that such an optical inter-site spin transfer (OISTR) from Pt to Co emerges as a dominant mechanism governing the ultrafast magnetization dynamics of a CoPt alloy. To demonstrate this, we perform a joint theoretical and experimental investigation to determine the transient changes of the helicity dependent absorption in the extreme ultraviolet spectral range. We show that the helicity dependent absorption is directly related to changes of the transient spin-split density of states, allowing us to link the origin of OISTR to the available minority states above the Fermi level. This makes OISTR a general phenomenon in optical manipulation of multi-component magnetic systems. Optically driven spin transfer is the fastest process to manipulate magnetism. Here, the authors show that this process emerges as the dominant mechanism in femtosecond spin dynamics enabling to the engineering of functional magnetic systems for future all optical technologies

Exactly solvable potentials of Calogero type for q-deformed Coxeter groups

We establish that by parameterizing the configuration space of a one-dimensional quantum system by polynomial invariants of q-deformed Coxeter groups it is possible to construct exactly solvable models of Calogero type. We adopt the previously introduced notion of solvability which consists of relating the Hamiltonian to finite dimensional representation spaces of a Lie algebra. We present explicitly the $G_2^q$-case for which we construct the potentials by means of suitable gauge transformations.Comment: 22 pages Late

BMPix and PEAK tools: New methods for automated laminae recognition and counting — Application to glacial varves from Antarctic marine sediment

We present tools for rapid and quantitative detection of sediment lamination. The BMPix tool extracts color and gray-scale curves from images at pixel resolution. The PEAK tool uses the gray-scale curve and performs, for the first time, fully automated counting of laminae based on three methods. The maximum count algorithm counts every bright peak of a couplet of two laminae (annual resolution) in a smoothed curve. The zero-crossing algorithm counts every positive and negative halfway-passage of the curve through a wide moving average, separating the record into bright and dark intervals (seasonal resolution). The same is true for the frequency truncation method, which uses Fourier transformation to decompose the curve into its frequency components before counting positive and negative passages. We applied the new methods successfully to tree rings, to well-dated and already manually counted marine varves from Saanich Inlet, and to marine laminae from the Antarctic continental margin. In combination with AMS14C dating, we found convincing evidence that laminations in Weddell Sea sites represent varves, deposited continuously over several millennia during the last glacial maximum. The new tools offer several advantages over previous methods. The counting procedures are based on a moving average generated from gray-scale curves instead of manual counting. Hence, results are highly objective and rely on reproducible mathematical criteria. Also, the PEAK tool measures the thickness of each year or season. Since all information required is displayed graphically, interactive optimization of the counting algorithms can be achieved quickly and conveniently

Reducing Interanalyst Variability in Photovoltaic Degradation Rate Assessments

The economic return on investment of a commercial photovoltaic system depends greatly on its performance over the long term and, hence, its degradation rate. Many methods have been proposed for assessing system degradation rates from outdoor performance data. However, comparing reported values from one analyst and research group to another requires a common baseline of performance; consistency between methods and analysts can be a challenge. An interlaboratory study was conducted involving different volunteer analysts reporting on the same photovoltaic performance data using different methodologies. Initial variability of the reported degradation rates was so high that analysts could not come to a consensus whether a system degraded or not. More consistent values are received when written guidance is provided to each analyst. Further improvements in analyst variance was accomplished by using the free open-source software RdTools, allowing a reduction in variance between analysts by more than two orders of magnitude over the first round, where multiple analysis methods are allowed. This article highlights many pitfalls in conducting 'routine' degradation analysis, and it addresses some of the factors that must be considered when comparing degradation results reported by different analysts or methods

Transforming European Water Governance? Participation and River Basin Management under the EU Water Framework Directive in 13 Member States

The European Union (EU) Water Framework Directive (WFD) requires EU member states to produce and implement river basin management plans, which are to be designed and updated via participatory processes that inform, consult with, and actively involve all interested stakeholders. The assumption of the European Commission is that stakeholder participation, and institutional adaptation and procedural innovation to facilitate it, are essential to the effectiveness of river basin planning and, ultimately, the environmental impact of the Directive. We analyzed official documents and the WFD literature to compare implementation of the Directive in EU member states in the initial WFD planning phase (2000–2009). Examining the development of participatory approaches to river basin management planning, we consider the extent of transformation in EU water governance over the period. Employing a mixed quantitative and qualitative approach, we map the implementation “trajectories” of 13 member states, and then provide a detailed examination of shifts in river basin planning and participation in four member states (Germany, Sweden, Poland and France) to illustrate the diversity of institutional approaches observed. We identify a general tendency towards increased, yet circumscribed, stakeholder participation in river basin management in the member states examined, alongside clear continuities in terms of their respective pre-WFD institutional and procedural arrangements. Overall, the WFD has driven a highly uneven shift to river basin-level planning among the member states, and instigated a range of efforts to institutionalize stakeholder involvement—often through the establishment of advisory groups to bring organized stakeholders into the planning process