相关论文: State space decomposition and classification of te…

The relativistic 20-component wave equation, describing particles with spin 1/2 and two mass states, is analyzed. The projection operators extracting states with definite energy and spin projections, and density matrix are obtained. The…

We construct and investigate a family of two-band unitary systems living on a cylinder geometry and presenting localized edge states. Using the transfer matrix formalism, we solve and investigate in details such states in the thermodynamic…

Decomposition spaces are a class of function spaces constructed out of well-behaved coverings and partitions of unity of a set. The structure of the covering of the set determines the properties of the decomposition space. Besov spaces,…

We present a description of finite dimensional quantum entanglement, based on a study of the space of all convex decompositions of a given density matrix. On this space we construct a system of real polynomial equations describing separable…

This paper introduces a new approach toward characterizing local structural features of two-dimensional particle systems. The approach can accurately identify and characterize defects in high-temperature crystals, distinguish a wide range…

Analyzing the properties of entanglement in many-particle spin-1/2 systems is generally difficult because the system's Hilbert space grows exponentially with the number of constituent particles, $N$. Fortunately, it is still possible to…

By estimating 3D shape and instances from a single view, we can capture information about an environment quickly, without the need for comprehensive scanning and multi-view fusion. Solving this task for composite scenes (such as object…

We propose a new 2D shape decomposition method based on the short-cut rule. The short-cut rule originates from cognition research, and states that the human visual system prefers to partition an object into parts using the shortest possible…

In this paper we prove, extend and review possible mappings between the two-dimensional Cluster state, Wen's model, the two-dimensional Ising chain and Kitaev's toric code model. We introduce a two-dimensional duality transformation to map…

We consider Wave Maps into the sphere and give a new proof of small data global well-posedness and scattering in the critical Besov space, in any space dimension $n \geq 2$. We use an adapted version of the atomic space $U^2$ as the single…

Sampling from distributions of implicitly defined shapes enables analysis of various energy functionals used for image segmentation. Recent work describes a computationally efficient Metropolis-Hastings method for accomplishing this task.…

This paper introduces a comprehensive formalism for decomposing the state space of a quantum field into several entangled subobjects, i.e., fields generating a subspace of states. Projecting some of the subobjects onto degenerate background…

Document structure extraction has been a widely researched area for decades with recent works performing it as a semantic segmentation task over document images using fully-convolution networks. Such methods are limited by image resolution…

Using the information geometry approach, we determine the volume of the set of two-qubit states with maximally disordered subsystems. Particular attention is devoted to the behavior of the volume of sub-manifolds of separable and entangled…

We use the method of atomic decomposition to build new families of function spaces, similar to Besov spaces, in measure spaces with grids, a very mild assumption. Besov spaces with low regularity are considered in measure spaces with good…

The paper gives a categorical approach to generalized manifolds such as orbit spaces and leaf spaces of foliations. It is suggested to consider these spaces as sets equipped with some additional structure which generalizes the notion of…

This article describes how the ideas promoted by the fundamental papers published by M. Frazier and B. Jawerth in the eighties have influenced subsequent developments related to the theory of atomic decompositions and Banach frames for…

The dually flat structure of statistical manifolds can be derived in a non-parametric way from a particular case of affine space defined on a qualified set of probability measures. The statistically natural displacement mapping of the…

There are a least uncountably many diffeomorphism types for open manifolds. Hence the classification problem is extremely difficult. We proceed as follows: We define several uniform structures of proper metric spaces and consider their arc…

The aim of the paper is to propose geometric descriptions of multipartite entangled states using algebraic geometry. In the context of this paper, geometric means each stratum of the Hilbert space, corresponding to an entangled state, is an…