Sum rules for multi-photon spectroscopy of ions in finite symmetry

Models describing one- and two-photon transitions for ions in crystalline environments are unified and extended to the case of parity-allowed and parity-forbiddenp-photon transitions. The number of independent parameters for characterizing the polarization dependence is shown to depend on an ensemble of properties and rules which combine symmetry considerations and physical models.     

Dynamical generation of quasicrystals

We present a new general mechanism for a dynamical generation (growth) of quasicrystals (and crystals) in any dimension. The growth process proceeds in elementary steps starting from a chosen seed and the notion of an ideal local configuration. Each step is governed by local information inside of the physical space of the quasicrystal: A point is added to existing quasicrystal points only if its locally defined phase matches at that point a freely chosen continuous phase (gauge) in the quasicrystal space within a given precision. Some 2D examples are shown.Work supported in part by the Natural Science and Engineering Research Council of Canada and by the FCAR of Quebec.     

On the periodic orbits of perturbed Hooke Hamiltonian systems with three degrees of freedom

We study periodic orbits of Hamiltonian differential systems with three degrees of freedom using the averaging theory. We have chosen the classical integrable Hamiltonian system with the Hooke potential and we study periodic orbits which bifurcate from the periodic orbits of the integrable system perturbed with a non-autonomous potential.     

On coherent states for the simplest quantum groups

The coherent states for the simplest quantum groups (q-Heisenberg-Weyl, SU _q (2) and the discrete series of representations of SU _q (1, 1)) are introduced and their properties investigated. The corresponding analytic representations, path integrals, and q-deformation of Berezin's quantization on , a sphere, and the Lobatchevsky plane are discussed.     

Localization for random potentials supported on a subspace

We consider the lattice Schrödinger operator acting onl ² ( ^d ) with random potential (independent, identically distributed random variables), supported on a subspace of dimension 1 v <d. We use the multiscale analyses scheme to prove that this operator exhibits exponential localization at the edges of the spectrum for any disorder or outside the interval [-2d, 2d] for sufficiently high disorder.     

Upper bound on the free energy of the spin 1/2 Heisenberg ferromagnet

The authors obtain an upper bound on the free energy of the spin 1/2 Heisenberg ferromagnet. The zero field bound is, at low temperature, similar to the formula given by the magnon approximation. That is, its functional dependence on temperature is the same but the constant is different.Work partially supported by U.S. National Science Foundation grants DMS 9196047 (JGC) and DMS 9002416 (JPS).     

The blob algebra and the periodic Temperley-Lieb algebra

We determine the structure of two variations on the Temperley-Lieb algebra, both used for dealing with special kinds of boundary conditions in statistical mechanics models. The first is a new algebra, the blob algebra. We determine both the generic and all the exceptional structures for this two parameter algebra. The second is the periodic Temperley-Lieb algebra. The generic structure and part of the exceptional structure of this algebra have already been studied. We complete the analysis using results from the study of the blob algebra.     

Improved lower bound on the thermodynamic pressure of the spin 1/2 Heisenberg ferromagnet

We introduce a new stochastic representation of the partition function of the spin 1/2 Heisenberg ferromagnet. We express some of the relevant thermodynamic quantities in terms of expectations of functionals of so-called random stirrings on ^d . By use of this representation, we improve the lower bound on the pressure given by Conlon and Solovej inLett. Math. Phys. 23, 223–231 (1991).Work supported by the Hungarian National Foundation for Scientific Research, grant No. 1902.     

Differential calculus on quantized simple lie groups

Differential calculi, generalizations of Woronowicz's four-dimensional calculus on SU _q (2), are introduced for quantized classical simple Lie groups in a constructive way. For this purpose, the approach of Faddeev and his collaborators to quantum groups was used. An equivalence of Woronowicz's enveloping algebra generated by the dual space to the left-invariant differential forms and the corresponding quantized universal enveloping algebra, is obtained for our differential calculi. Real forms for q are also discussed.     

Two-dimensional superintegrable metrics with one linear and one cubic integral

We describe all local Riemannian metrics on surfaces whose geodesic flows are superintegrable with one integral linear in momenta and one integral cubic in momenta.     

Dolbeault cohomology groups of compact pseudo-Kähler homogeneous manifolds

It is well known that a pseudo-Kähler structure is one of the natural generalizations of a Kähler structure. In this paper, we consider the Dolbeault cohomology groups of compact pseudo-Kähler homogeneous manifolds.     

Geometric crystals on flag varieties and unipotent subgroups of classical groups

For a classical simple algebraic group G$G$, we obtain the affirmative answer for the conjecture in Nakashima (2005) [3] that there exists an isomorphism between the geometric crystal on the flag variety and the one on the maximal unipotent subgroup U⁻$U^{-}$.     

Dijkgraaf–Witten invariants of surfaces and projective representations of groups

We compute the Dijkgraaf–Witten invariants of surfaces in terms of projective representations of groups. As an application we prove that the complex Dijkgraaf–Witten invariants of surfaces of positive genus are positive integers.     

A remark about static space times

We discuss a differential equation, whose unknowns are a function and a Riemannian metric. This equation occurs both in general relativity (static space times) and in the study of the space of Riemannian metrics on a manifold (singularities of the map from the space of metrics into the space of functions, which assigns to any metric its scalar curvature).     

Invariant characterization of Liouville metrics and polynomial integrals

In this paper a criterion for a metric on a surface to be Liouville is established, and it is given in terms of differential invariants of the metric. Moreover, here we completely solve in invariant terms the local mobility problem of a 2D metric, considered by Darboux: How many quadratic in momenta integrals the geodesic flow of a given metric possesses? The method is also applied to recognition of higher degree polynomial integrals of geodesic flows.     

Existence of almost periodic solutions for SICNNs with time-varying delays

In this Letter, the shunting inhibitory cellular neural networks with time-varying delays are considered. We establish some new results about the existence and stability of almost periodic solutions for SICNNs without the global Lipschitz conditions on the activity functions. An example is given to illustrate the effectiveness of our results.     

内掺过渡金属富勒烯衍生物Ni@C20H20几何结构、成键和电磁性质的密度泛函计算研究

采用密度泛函理论中的广义梯度近似对Ni@C20H20的几何结构、成键和电磁性质进行密度泛函计算研究.结构优化发现位于偏离笼子中心三种位置处的Ni原子优化之后均回到笼子中心.结合能和能隙分析表明C20H20的中心位置是Ni原子热力学和动力学最稳定的位置.成键分析表明:Ni原子位于C20H20中心时,和C原子之间几乎没有相互作用,保持自己的孤立状态.电磁分析表明:原子磁矩为2μB的Ni原子内掺到C20H20中心后磁性完全猝灭,而本来无磁性的笼子由于与Ni原子之间没有发生电子转移仍然无磁性.     

The bosonic string measure at two and three loops and symplectic transformations of the volume form

Symplectic modular invariance of the string integral has been verified at genus 2 and 3 using the period matrix coordinatization of moduli space. A calculation of the transformation of the product of holomorphic coordinates _ij d _ij shows that an extra phase arises together with the factor associated with a specific modular weight; the phase is cancelled in the transformation of the entire volume element including the complex conjugate. An argument is given for modular invariance of the reggeon measure at genus 12.     

Differential Galois obstructions for non-commutative integrability

We show that if a holomorphic Hamiltonian system is holomorphically integrable in the non-commutative sense in a neighbourhood of a non-equilibrium phase curve which is located at a regular level of the first integrals, then the identity component of the differential Galois group of the variational equations along the phase curve is Abelian. Thus necessary conditions for the commutative and non-commutative integrability given by the differential Galois approach are the same.     

Normal Bundles to Laufer Rational Curves in Local Calabi–Yau Threefolds

We prove a conjecture by F. Ferrari. Let X be the total space of a nonlinear deformation of a rank two holomorphic vector bundle on a smooth rational curve, such that X has trivial canonical bundle and has sections. Then the normal bundle to such sections is computed in terms of the rank of the Hessian of a suitably defined superpotential at its critical points.