相关论文: Diagonalization of Sp(2) matrices
We show that the method of stochastic reduction of linear superpositions can be applied to the process of disentanglement for the spin-0 state of two spin-1/2 particles. We describe the geometry of this process in the framework of the…
Relativistic quantum effects on physical observables of scalar charged particles are studied. Possible peculiarities of their behavior that can be verified in an experiment can confirm several fundamental conceptions of quantum mechanics.…
In this paper, we introduce a deterministic approach of quantum mechanics for particles with spin 1 2 moving in one dimension. We present a Lagrangian of a spinning particle ($s ={1 \over 2} $), and deduce the expression of the conjugate…
An SL-invariant extension of the concurrence to higher local Hilbert-space dimension is due to its relation with the determinant of the matrix of a $d\times d$ two qudits state, which is the only SL-invariant of polynomial degree $d$. This…
A symmetric doubly stochastic matrix A is said to be determined by its spectra if the only symmetric doubly stochastic matrices that are similar to A are of the form $P^TAP$ for some permutation matrix P. The problem of characterizing such…
Having in mind the significance of parity (reflection) in various areas of physics, the single-mode and two-mode Wigner algebras are considered adding to them a reflection operator. The associated deformed $sl(2, R)$ algebra,…
The calculation of particle decay widths and scattering cross sections naturally decomposes into a quantum mechanical amplitude and a relativistic phase space (PS). This PS can be formulated in terms of parallelotopes providing frame…
By expressing the time-independent Schrodinger equation in one dimension as a system of two first-order differential equations, the transfer matrix for a rectangular potential barrier is obtained making use of the matrix exponential. It is…
Recently it has been advocated [1] that for describing nature within the minimal symmetry requirement, certain subgroups of Lorentz group may play a fundamental role. One such group is E(2) which induces a Lie algebraic Non-Commutative…
A semi-infinite weighted Hankel matrix with entries defined in terms of basic hypergeometric series is explicitly diagonalized as an operator on $\ell^{2}(\mathbb{N}_{0})$. The approach uses the fact that the operator commutes with a…
Different bases for the spin-1 density matrix are discussed to clarify the connection between its components and observables measured in heavy-ion collisions. The theoretical advantage of using the adjoint representation for spin matrices…
We propose for the spin density matrix two parametrizations which automatically fulfil the non-negativity conditions, without setting any bound on the parameters. The first one relies on a theorem, that we prove, and it is rather simple and…
We introduce a spin polarization-scaling map for spin-$j$ particles, whose physical meaning is the decrease of spin polarization along three mutually orthogonal axes. We find conditions on three scaling parameters under which the map is…
We consider a relativistic superalgebra in the picture in which the time and spatial derivative cannot be presented in the operators of the particle. The supersymmetry generators as well as the Hamilton operators for the massive…
A review of methods for finding general expressions for matrix elements (non-diagonal with respect to configurations included) of any one- and two-particle operator for an arbitrary number of shells in an atomic configuration is given.…
The second part of the article is devoted to field transfers by diffraction that are represented by fractional Fourier transformations whose orders are complex numbers. The corresponding effects on the Wigner distributions associated with…
We present an explicit expression for the topological invariants associated to $SU(2)$ monopoles in the fundamental representation on spin four-manifolds. The computation of these invariants is based on the analysis of their corresponding…
We analyze the entanglement of SU(2)-invariant density matrices of two spins $\vec S_{1}$, $\vec S_{2}$ using the Peres-Horodecki criterion. Such density matrices arise from thermal equilibrium states of isotropic spin systems. The partial…
We show that Calogero-Sutherland models for interacting particles have a natural supersymmetric extension. For the construction, we use Jacobians which appear in certain superspaces. Some of the resulting Hamiltonians have a direct physics…
We introduce the triangulant of two matrices, and relate it to the existence of orthogonal eigenvectors. We also use it for a new characterization of mutually unbiased bases. Generalizing the notion, we introduce higher order triangulants…