Related papers: On construction of projection operators
We describe the representation of arbitrary density operators in terms of expectation values of simple projection operators. Two representations are presented which yield non--recursive schemes for experimentally determining the density…
The purpose of this article is to study operators whose kernel share some key features of Bergman kernels from complex analysis, and are approximate projectors. It turns out that they must be associated with a rich set of geometric data, on…
In quantum mechanics, symmetry groups can be realized by projective, as well as by ordinary unitary, representations. For the permutation symmetry relevant to quantum statistics of N indistinguishable particles, the simplest properly…
Consider an elliptic self-adjoint pseudodifferential operator $A$ acting on $m$-columns of half-densities on a closed manifold $M$, whose principal symbol is assumed to have simple eigenvalues. We show existence and uniqueness of $m$…
In this paper we study the Weihrauch complexity of projection operators onto closed subsets of the Euclidean space. We show that some fundamental degrees of the Weihrauch lattice can be characterized in terms of such operators.
We provide formulas for projectors onto a polyhedral set, i.e. the intersection of a finite number of halfspaces. To this aim we formulate the problem of finding the projection as a convex optimization problem and we solve explicitly…
The spherically symmetric volume operator is discussed and all its eigenstates and eigenvalues are computed. Even though the operator is more complicated than its homogeneous analog, the spectra are related in the sense that the larger…
Considering homogeneous four-dimensional space-time geometries within real projective geometry provides a mathematically well-defined framework to discuss their deformations and limits without the appearance of coordinate singularities. On…
Solution and analysis of mathematical programming problems may be simplified when these problems are symmetric under appropriate linear transformations. In particular, a knowledge of the symmetries may help reduce the problem dimension, cut…
In investigations of the emergence of classicality from quantum theory, a useful step is the construction of quantum operators corresponding to the classical notion that the system resides in a region of phase space. The simplest such…
The idea that symmetries simplify or reduce the complexity of a system has been remarkably fruitful in physics, and especially in quantum mechanics. On a mathematical level, symmetry groups single out a certain structure in the Hilbert…
This paper studies the eigenvalue problem $K \psi = \lambda \psi$ associated with a Fredholm integral operator $K$ defined by a smooth kernel. The focus is on analyzing the convergence behaviour of numerical approximations to eigenvalues…
Projection operators are central to the algebraic formulation of quantum theory because both wavefunction and hermitian operators(observables) have spectral decomposition in terms of the spectral projections. Projection operators are…
Quantum constraints of the type Q \psi = 0 can be straightforwardly implemented in cases where Q is a self-adjoint operator for which zero is an eigenvalue. In that case, the physical Hilbert space is obtained by projecting onto the kernel…
This paper develops an analytical approach to the study of the geometry of projective maps using the theory of elliptic differential operators. We construct two elliptic operators of second and fourth order, whose kernels characterize…
Recently, much research has been carried out on Hamiltonians that are not Hermitian but are symmetric under space-time reflection, that is, Hamiltonians that exhibit PT symmetry. Investigations of the Sturm-Liouville eigenvalue problem…
Proper splittings of operators are commonly used to study the convergence of iterative processes. In order to approximate solutions of operator equations, in this article we deal with proper splittings of closed range bounded linear…
Several algebraic and topological properties of subgradient projection operators are investigated and various examples are provided. Connections with Moreau's proximity operator are also made and acceleration schemes for subgradient…
Nonlinear quantum optical systems are of paramount relevance for modern quantum technologies, as well as for the study of dissipative phase transitions. Their nonlinear nature makes their theoretical study very challenging and hence they…
To develop a unitary quantum theory with probabilistic description for pseudo- Hermitian systems one needs to consider the theories in a different Hilbert space endowed with a positive definite metric operator. There are different…