abstract

For the case of a pair repulsive potential, certain integral identities between conditioned correlation functions describing the grand canonical Gibbs ensemble of the Gonchar type are derived and some applications of them are described. In particular we prove the uniqueness of the grand canonical Gibbs whenever sufficiently strong external field is switched on.

abstract

Using the properties of the so-called fundamental solutions to the one-dimensional Schroedinger equation having Fröman and Fröman form the rules are formulated which allow one to evaluate matrix elements in the JWKB approximation and its generalizations. The rules apply to operators \(M(x, d/dx)\), \(M\) being polynomial functions of their arguments. The applicability of the rules depends on the properties of the so-called canonical indices introduced in this paper. The canonical indices are global characteristics of underlying Stokes graphs. If sufficiently small in comparison with unity they allow one to apply safely the JWKB approximation within the so-called \(\varepsilon \)-reduced canonical domains of a given Stokes graph. The 0th canonical index for the nth energy level Stokes graph corresponding to the harmonic oscillator potential is found to be \(\varepsilon ^{\rm CAN} = 0.678/(2n+1)\). If the application of the rules is allowed then approximated matrix elements are obtained in an unambiguous way and with an accuracy controlled by corresponding canonical indices. Several examples of matrix elements are considered to illustrate how the rules should be used. Limitations to the rules are also discussed with the aid of suitably chosen examples.

abstract

Mathematics underlying the structure of spacetime at experimentally available energy range should be based on the field of real numbers. At the Planck scale we are unable to examine experimentally the geometry of spacetime. If the concept of spacetime has any physical meaning in the Planckian region, its mathematical model might be based on the adelic number system. Physical motivation is given for such proposal.

abstract

It is suggested to experimental physicists to look for a magnetic-type deviation from the familiar magnetic interaction between nucleons. Such a deviation would give us a strong indication that quarks would be composed of some more elementary constituants bound by a new Abelian gauge force, since then quarks and hence also nucleons should display a new magnetic-type interaction.

abstract

The elastic scattering differential cross sections of intermediate energy protons, antiprotons and charged pions on \(^{12}\)C and \(^{16}\)O nuclei and the elastic scattering polarization observables of protons on these nuclei have been calculated on the basis of the \(\alpha \)-particle model with dispersion and multipole diffraction scattering theory. The results of these calculations contain no fitting parameters and are in agreement with the experimental data.

abstract

The properties of neutron matter are studied using several existing parametrizations of the Skyrme interaction SK. Relations for energy per particle, effective mass, magnetic susceptibility, … etc. for neutron matter are derived using the Skyrme interaction, it is found that the ratio \(\chi _{\rm F}/\chi \) of the magnetic susceptibility of a Fermi gas of non-interacting neutrons to that of a neutron matter increases with density up to \(k_{\rm f}\) 1.1 fm\(^{-1}\) and then decreases. in order to obtain a similar behaviour to that of realistic interactions we varied the SK parameters to produce values of \(\chi _{\rm F}/\chi \) which increase steadily with \(k_{\rm f}\). The thermal properties of neutron matter are calculated also using SK force. The temperature dependences of the volume and spin pressure are determined. The results show a similar trend as previous theoretical estimates using realistic forces.