相关论文: The Bloch Vector for N-Level Systems
We present some new Poisson bivectors that are invariants by the Clebsch system flow. Symplectic integrators on their symplectic leaves exactly preserve the corresponding Casimir functions, which have different physical meanings. The Kahan…
We develop a ready-to-use comprehensive theory for (super) 2-vector bundles over smooth manifolds. It is based on the bicategory of (super) algebras, bimodules, and intertwiners as a model for 2-vector spaces. We discuss symmetric monoidal…
Nonlinear eigenvalue problems arise in a wide range of physical systems, in which system parameters depend on the eigenvalue. Such systems have been proposed to exhibit an extreme sensitivity of their spectra to boundary conditions, which…
We study $h$-vectors and graded Betti numbers of level modules up to multiplication by a rational number. Assuming a conjecture on the possible graded Betti numbers of Cohen-Macaulay modules we get a description of the possible $h$-vectors…
We study vector-valued Siegel modular forms of genus 2 and level 2. We describe the structure of certain modules of vector-valued modular forms over rings of scalar-valued modular forms.
With the completion of human genome mapping, the focus of scientists seeking to explain the biological complexity of living systems is shifting from analyzing the individual components (such as a particular gene or biochemical reaction) to…
Structured light is attracting significant attention for its diverse applications in both classical and quantum optics. The so-called vector vortex beams display peculiar properties in both contexts due to the non-trivial correlations…
Network classification aims to group networks (or graphs) into distinct categories based on their structure. We study the connection between classification of a network and of its constituent nodes, and whether nodes from networks in…
In this paper, we prove some normality criteria concerning transitivity of normality from one family of meromorphic functions to another which improve and generalize some recent results. We also prove some value distribution results for…
The division between two vectors belonging to the same vector space is obtained by elementary procedures of vector algebra and is defined by a matrix. This representation is obtained for two and three dimensional vector spaces. A new vector…
General birth-and-death as well as hopping stochastic dynamics of infinite multicomponent particle systems in the continuum are considered. We derive the corresponding evolution equations for quasi-observables and correlation functions. We…
The soliton structure of a gauge theory proposed to describe chiral excitations in the multi-Layer Fractional Quantum Hall Effect is investigated. A new type of derivative multi-component nonlinear Schr\"{o}dinger equation emerges as…
We introduce a Hermitian generalization of Pauli matrices to higher dimensions which is based on Heisenberg-Weyl operators. The complete set of Heisenberg-Weyl observables allows us to identify a real-valued Bloch vector for an arbitrary…
In the first part of this note, we review and compare various instances of the notion of twisted coefficient system, a.k.a. polynomial functor, appearing in the literature. This notion hinges on how one defines the degree of a functor from…
Two-band Hamiltonians provide a typical description of topological band structures, in which the eigenfunctions can be characterized by a %Bloch vector field whose winding number that defines an integer topological invariant. This winding…
This work predicts that individual Bloch points can be created and stabilized by magnetostatic and chiral interactions in nanocuboids, confined in between two chiral bobbers of opposing polarity. The Bloch point can be moved by an external…
Monte Carlo methods play important part in modern statistical physics. The application of these methods suffer from two main difficulties.The first is caused by the relatively small number of particles that can participate in any numerical…
In this paper, we characterize all possible h-vectors of 2-dimensional Buchsbaum simplicial complexes.
In this note we recall the relations between the barcodes in level and sub-level persistence and make precise their relation with the Morse-Novikov complex of a Morse real- or angle-valued map. The results in this papers are implicit in my…
We proove a Bloch's theorem in an almost complex projective plane.