Related papers: Kippenhahn's Theorem for joint numerical ranges an…
A set of $n$ coherent states is introduced in a quantum system with $d$-dimensional Hilbert space $H(d)$. It is shown that they resolve the identity, and also have a discrete isotropy property. A finite cyclic group acts on the set of these…
Realistic quantum mechanics based on complex probability theory is shown to have a frequency interpretation, to coexist with Bell's theorem, to be linear, to include wavefunctions which are expansions in eigenfunctions of Hermitian…
Methods of Harder and Narasimhan from the theory of moduli of vector bundles are applied to moduli of quiver representations. Using the Hall algebra approach to quantum groups, an analog of the Harder-Narasimhan recursion is constructed…
Symmetries of trigonometric integrable two dimensional statistical face models are considered. The corresponding symmetry operators on the Hilbert space of states of the quantum version of these models define a weak *-Hopf algebra…
We explore the relation between noncommutative geometry, in the spectral triple formulation, and quantum mechanics. To this aim, we consider a dynamical theory of a noncommutative geometry defined by a spectral triple, and study its…
The purpose of this paper is to show that the mathematics of quantum mechanics (QM) is the mathematics of set partitions (which specify indefiniteness and definiteness) linearized to vector spaces, particularly in Hilbert spaces. That is,…
A geometric quantization using the topological recursion is established for the compactified cotangent bundle of a smooth projective curve of an arbitrary genus. In this quantization, the Hitchin spectral curve of a rank $2$ meromorphic…
We prove that a bounded linear Hilbert space operator has the unit circle in its essential approximate point spectrum if and only if it admits an orbit satisfying certain orthogonality and almost-orthogonality relations. This result is…
We prove that the rank-one convex hull of finitely many $2\times 2$ triangular matrices is a semialgebraic set, defined by linear and quadratic polynomials. We present explicit constructions for five-point configurations and offer evidence…
All correlation measures, classical and quantum, must be monotonic under local operations. In this paper, we characterize monotonic formulas that are linear combinations of the von Neumann entropies associated with the quantum state of a…
In this note we investigate the convex hull of those $n \times n$-permutation matrices that correspond to symmetries of a regular $n$-gon. We give the complete facet description. As an application, we show that this yields a Gorenstein…
The convex hull on three points in two dimensional euclidean space of three flat edges (trihedron) was studied. The Bohr-Sommerfeld quantization of the area of space is performed. It is shown that it reproduces exactly the equidistant…
We establish equivalences of derived categories of the following 3 categories: (1) Principal block of representations of the quantum at a root of 1; (2) G-equivariant coherent sheaves on the Springer resolution; (3) Perverse sheaves on the…
It is shown that the geometric measure of entanglement of a pure multipartite state satisfies a polynomial equation, generalising the characteristic equation of the matrix of coefficients of a bipartite state. The equation is solved for a…
The modelling of electrical connections of single, or several, multiterminal quantum Hall effect (QHE) devices is relevant for electrical metrology: it is known, in fact, that certain particular connections allow i) the realization of…
A quantum system's state is identified with a density matrix. Though their probabilistic interpretation is rooted in ensemble theory, density matrices embody a known shortcoming. They do not completely express an ensemble's physical…
Quantum matrix models in the large-N limit arise in many physical systems like Yang-Mills theory with or without supersymmetry, quantum gravity, string-bit models, various low energy effective models of string theory, M(atrix) theory,…
The boundary of the convex hull of a compact algebraic curve in real 3-space defines a real algebraic surface. For general curves, that boundary surface is reducible, consisting of tritangent planes and a scroll of stationary bisecants. We…
Matrix product states play an important role in quantum information theory to represent states of many-body systems. They can be seen as low-dimensional subvarieties of a high-dimensional tensor space. In these notes, we consider two…
Which convex subsets of the complex plane are the numerical range W(A of some matrix A? This paper gives a precise characterization of these sets. In addition to this we show that for any A there exists a symmetric matrix B of the same size…