The generator coordinate method as an approximation to the exact diagonalization in a given model space

The low-lying states of the nuclei ¹⁶O and ²⁰Ne are calculated with the generator coordinate method. For ¹⁶O two generator coordinates are used, which are related to the quadrupole and to the octupole deformation of the single-particle potential. For ²⁰Ne the generator coordinates are related to the parameters β and D of the Nilsson potential. In both cases six pairs of coordinate values are chosen. The results are compared with those of the complete diagonalization. The agreement is, for both cases, better than 0.5 MeV for most low-lying states.     

Stationary Generalization of the Bonnor Magnetic Dipole Solution

An exact asymptotically flat 3-parameter solution of the Einstein-Maxwell equations is presented that reduces to the Bonnor magnetic dipole solution in the magnetostatic limit, and to the Tomimatsu-Sato = 2 solution in the stationary pure vacuum limit. This solution is the simplest possible one admitting the polynomial representation in the spheroidal coordinates (x, y) and able to describe the exterior field of a magnetized spinning mass. A multipole criterion for the choice of the parameters in the Einstein-Maxwell spacetimes is also formulated.     

Generating Techniques and Analytically Extended Solutions of the Einstein–Maxwell Equations

The correspondence of arbitrary parameters inexact axisymmetric solutions of the Einstein-Maxwellequations constructed with the aid of differentgenerating methods to the analytically extendedparameter sets is discussed and examples of the extendedsolutions are given.     

On a general static axisymmetric solution of the Einstein vacuum equations

It is shown that a generalization of the procedure given in [1] for construction of the gravitational multipoles leads to the same Newtonian limit as the generalized Erez-Rosen solution [2].     

Unitary and Nonunitary Evolution of Qubit States in Probability Representation of Quantum Mechanics

Review of the probability representation of qubit states and observables is presented as well as the picture of states of two-level systems in terms of Triada of Malevich’s squares. A new relation of introduced probability parameters is obtained. Also, it is offered a method to visualize the quantum channel’s maps of qubit states. Evolution of the two-level system is considered in terms of Triada of Malevich’s squares in case of Rabi and Demkov models.