Toric K\"ahler metrics seen from infinity, quantization and compact tropical amoebas

We consider the metric space of all toric K\"ahler metrics on a compact toric manifold; when "looking at it from infinity" (following Gromov), we obtain the tangent cone at infinity, which is parametrized by equivalence classes of complete geodesics. In the present paper, we study the associated limit for the family of metrics on the toric variety, its quantization, and degeneration of generic divisors. The limits of the corresponding K\"ahler polarizations become degenerate along the Lagrangian fibration defined by the moment map. This allows us to interpolate continuously between geometric quantizations in the holomorphic and real polarizations and show that the monomial holomorphic sections of the prequantum bundle converge to Dirac delta distributions supported on Bohr-Sommerfeld fibers. In the second part, we use these families of toric metric degenerations to study the limit of compact hypersurface amoebas and show that in Legendre transformed variables they are described by tropical amoebas. We believe that our approach gives a different, complementary, perspective on the relation between complex algebraic geometry and tropical geometry.Comment: v1: 32 pages, 5 figures; v2: 1 figure added; v3: 1 reference added; v4: some reorganization, 1 theorem (now 1.1) added; v5: final version, to appear in JD

Stability of Affine G-varieties and Irreducibility in Reductive Groups

Let $G$ be a reductive affine algebraic group, and let $X$ be an affine algebraic $G$-variety. We establish a (poly)stability criterion for points $x\in X$ in terms of intrinsically defined closed subgroups $H_{x}$ of $G$, and relate it with the numerical criterion of Mumford, and with Richardson and Bate-Martin-R\"ohrle criteria, in the case $X=G^{N}$. Our criterion builds on a close analogue of a theorem of Mundet and Schmitt on polystability and allows the generalization to the algebraic group setting of results of Johnson-Millson and Sikora about complex representation varieties of finitely presented groups. By well established results, it also provides a restatement of the non-abelian Hodge theorem in terms of stability notions.Comment: 29 pages. To appear in Int. J. Math. Note: this version 4 is identical with version 2 (version 3 is empty

Loss of coherence in double-slit diffraction experiments

7 págs.; 3 figs.; PACS numberssd: 03.65.Yz, 03.65.Ta, 03.75.DgThe effects of incoherence and decoherence in a double-slit experiment are studied using both optical and quantum-phenomenological models. The results are compared with experimental data obtained with cold neutrons. ©2005 American Physical SocietyThis work was supported in part by MCyT Spaind under Contracts No. BFM2000-347 and No. BQU2003-8212. A.S.S. gratefully acknowledges partial support from the Consejería de Educación y Cultura of the Comunidad Autónoma de Madrid.Peer Reviewe

Correspondence between classical and quantum resonances

Bifurcations take place in molecular Hamiltonian nonlinear systems as the excitation energy increases, leading to the appearance of different classical resonances. In this paper, we study the quantum manifestations of these classical resonances in the isomerizing system CN-Li Li-CN. By using a correlation diagram of eigenenergies versus Planck constant, we show the existence of different series of avoided crossings, leading to the corresponding series of quantum resonances, which represent the quantum manifestations of the classical resonances. Moreover, the extrapolation of these series to h = 0 unveils the correspondence between the bifurcation energy of classical resonances and the energy of the series of quantum resonances in the semiclassical limit → 0. Additionally, in order to obtain analytical expressions for our results, a semiclassical theory is develope

An analysis on neck and upper limb musculoskeletal symptoms in Portuguese automotive assembly line workers

publishersversionpublishe

Coherent state transforms and vector bundles on elliptic curves

AbstractWe extend the coherent state transform (CST) of Hall to the context of the moduli spaces of semistable holomorphic vector bundles with fixed determinant over elliptic curves. We show that by applying the CST to appropriate distributions, we obtain the space of level k, rank n and genus one non-abelian theta functions with the unitarity of the CST transform being preserved. Furthermore, the shift in the level k→k+n appears in a natural way in this finite-dimensional framework

Using basis sets of scar functions

We present a method to efficiently compute the eigenfunctions of classically chaotic systems. The key point is the definition of a modified Gram-Schmidt procedure which selects the most suitable elements from a basis set of scar functions localized along the shortest periodic orbits of the system. In this way, one benefits from the semiclassical dynamical properties of such functions. The performance of the method is assessed by presenting an application to a quartic two-dimensional oscillator whose classical dynamics are highly chaotic. We have been able to compute the eigenfunctions of the system using a small basis set. An estimate of the basis size is obtained from the mean participation ratio. A thorough analysis of the results using different indicators, such as eigenstate reconstruction in the local representation, scar intensities, participation ratios, and error bounds, is also presentedThis work was supported by MINECO (Spain), under projects MTM2009-14621 and ICMAT Severo Ochoa SEV-2011-0087, and by CEAL Banco de Santander–UAM. F.R. is grateful for the support from a doctoral fellowship from UPM and the hospitality of the members of the Departamento de Física in the Laboratorio TANDAR–Comisión Nacional de la Energía Atómica, where part of this work was don

Unraveling the highly nonlinear dynamics of KCN molecular system using Lagrangian descriptors

In this work, we identify the phase-space structures which are responsible for the chaotic dynamics observed in KCN molecular system using the Lagrangian descriptors. We show that the vibrational dynamics of this molecule is strongly determined by the invariant manifolds associated with a particular stretching periodic orbit previously described (Párraga et al., 2018). Likewise, the representation of these invariant manifolds on a Poincaré surface of section is also studied, concluding that the intricate depiction that is observed has its origin in the complex behavior of the manifolds, which is a consequence of the strong anharmonicities in the potential energy surfaceThis work has been partially supported by the Grants PID2021-122711NB-C21 and CEX2019-000904-S funded by MCIN/AEI/10.13039/501100011033, by the People Programme (Marie Curie Actions) of the European Union’s Horizon 2020 Research and Innovation Program under Grant No. 734557, and by the Comunidad de Madrid, Spain under the Grant APOYO-JOVENES-4L2UB6-53-29443N (GeoCoSiM) financed within the Plurianual Agreement with the Universidad Politécnica de Madrid, Spain in the line to improve the research of young doctor