相关论文: The Bloch Vector for N-Level Systems

We study previously un-researched second order statistics - correlation function of spectral staircase and global level number variance - in generic integrable systems with no extra degeneracies. We show that the global level number…

The difference variational bicomplex, which is the natural setting for systems of difference equations, is constructed and used to examine the geometric and algebraic properties of various systems. Exactness of the bicomplex gives a…

We derive a simple analytical expression for the level correlation function of an integrable system. It accounts for both the lack of correlations at smaller energy scales and for global rigidity (level number conservation) at larger…

We extend the concept of eigenvector centrality to multiplex networks, and introduce several alternative parameters that quantify the importance of nodes in a multi-layered networked system, including the definition of vectorial-type…

As Physics did in previous centuries, there is currently a common dream of extracting generic laws of nature in economics, sociology, neuroscience, by focalising the description of phenomena to a minimal set of variables and parameters,…

Recently there has been theoretical and experimental interest in Bloch-Siegert shifts in an intense photon field. A perturbative treatment becomes difficult in this multiphoton regime. We present a unitary transform and rotated model, which…

We present a novel inequality on the purity of a bipartite state depending solely on the difference of the local Bloch vector lengths. For two qubits this inequality is tight for all marginal states and so extends the previously known…

We determine the multiplicities of a class of roots for Nichols algebras of diagonal type of rank two, and identify the corresponding root vectors. Our analysis is based on a precise description of the relations of the Nichols algebra in…

Poly-Cauchy numbers with level $2$ are defined by inverse sine hyperbolic functions with the inverse relation from sine hyperbolic functions. In this paper, we show several convolution identities of poly-Cauchy numbers with level $2$. In…

We consider the behavior of level lines of two-dimensional potentials, which play an important role in the physics of ``two-layer'' systems. Potentials of this type are quasiperiodic and, at the same time, can also be considered as a model…

The new concept of multilevel network is introduced in order to embody some topological properties of complex systems with structures in the mesoscale which are not completely captured by the classical models. This new model, which…

Since the experimental observation of the violation of the Bell-CHSH inequalities, much has been said about the non-local and contextual character of the underlying system. But the hypothesis from which Bell's inequalities are derived…

For a large class of linear neutral type systems the problem of eigenvalues and eigenvectors assignment is investigated, i.e. finding the system which has the given spectrum and almost all, in some sense, eigenvectors.

Noise is often considered to be a nuisance. Here we argue that it can be a useful probe of fluctuating two level systems in glasses. It can be used to: (1) shed light on whether the fluctuations are correlated or independent events; (2)…

Seeking the convex hull of an object is a very fundamental problem arising from various tasks. In this work, we propose two variational convex hull models using level set representation for 2-dimensional data. The first one is an exact…

Multilevel methods are among the most efficient numerical methods for solving large-scale linear systems that arise from discretized partial differential equations. The fundamental module of such methods is a two-level procedure, which…

A two-sphere ("Bloch" or "Poincare") is familiar for describing the dynamics of a spin-1/2 particle or light polarization. Analogous objects are derived for unitary groups larger than SU(2) through an iterative procedure that constructs…

In this paper, we study several type of point derivations for Banach algebras. We investigate how our definition of point derivations are related to each others.

We consider redundant analogues of the f- and h-vectors of simplicial complexes and present bases of R^{m+1} related to these ``long'' f- and h-vectors describing the face systems from 2^{1,...,m}; we list the corresponding change of basis…

The (2 + 1)-dimensional gauge model describing two complex scalar fields that interact through a common Abelian gauge field is considered. It is shown that the model has a soliton solution that describes a system consisting of a vortex and…