2014

EQUIVALENCE AND HERMITICITY OF DIRAC HAMILTONIANS IN THE KERR GRAVITATIONAL FIELD / M. V. Gorbatenko, V. P. Neznamov // VANT. Ser.: Theoret. i prikl. fizika. 2014. N 1. P. 3–11.
In the paper, for the Kerr field, we prove that Chandrasekhar’s Dirac Hamiltonian and the self-adjoint Hamiltonian   with a flat scalar product of the wave functions are physically equivalent.
Operators of transformation of Chandrasekhar’s Hamiltonian and wave functions to the η representation with a flat scalar product are defined explicitly.
If the domain of the wave functions of Dirac’s equation in the Kerr field is bounded by two-dimensional surfaces of revolution around the z axis, Chandrasekhar’s Hamiltonian and the self-adjoint Hamiltonian in the η representation are Hermitian with equality of the scalar products,  .

ON DENSITY JUMPS IN THE EXPERIMENTS ON HYDROGEN ISOTOPES DYNAMIC COMPRESSION / R. F. Trunin, A. B. Medvedev // VANT. Ser.: Theoret. i prikl. fizika. 2014. N 1. P. 12–18.
The available experimental data on shock-wave protium and deuterium quasi-isentropic compression in wide pressure and density variation ranges have been compared. It is shown that the discovered density jumps on the initial liquid deuterium Hugoniot curve under ≈30 GPa and on the deuterium compression isentrope under ≈150 GPa are not confirmed by other probes. The existing data do not deny the peculiarities of hydrogen behavior at isentropic compression under ≈300 GPa.

NONEVAPORATING BLACK HOLES, ELEMENTARY PARTICLES, DARK MATTER…
/ V. P. Neznamov // VANT. Ser.: Theoret. i prikl. fizika. 2014. N 1. P. 19–26.
A toy model of elementary particles of light and dark matter is proposed. The model is based on the assumption that there exist relict nonevaporating black holes with Schwarzschild, Reissner – Nordström, Kerr and Kerr – Newman metrics.
The maximum possible mass of elementary particles of the Standard Model is defined. The maximum mass for fermions and bosons is close to the Planck mass  
The LHC boson of mass   within this model can be the Higgs boson, if it is a composite particle of fermion matter.
Within the framework of the model proposed, the paper discusses possible reasons for the baryon asymmetry of the universe and possible causes of powerful gamma-ray bursts in the universe.

COMPUTATIONAL RESEARCH OF X-RAY TEMPERATURE INCREASE POSSIBILITY IN ICF TARGETS / M. A. Barinov, V. V. Vatulin, K. A. Volkova, D. N. Golishnikov, A. S. Gnutov, G. M. Eliseyev, P. G. Kuznetsov, L. Z. Morenko, E. A. Novikova, N. P. Pleteneva, A. V. Kharitonov // VANT. Ser.: Theoret. i prikl. fizika. 2014. N 1. P. 27–34.
The paper presents the results of the numerical study of forming, in the target interior, the X-ray field with effective temperature above 300 eV typical for the X-ray in the NIF targets. The NIF facility uses laser radiation with 0,32 µm wave length (3-rd harmonics of neodymium laser). The X-ray field parameters of a laser with the shorter wave length are considered. Using a shorter-wave-length laser allows significant increase of the limiting laser intensity, thus making possible reaching higher effective X-ray temperatures of 350 eV and higher.
The laser energy conversion calculation results for different laser wave lengths, as well as effective temperature, energy and spectral X-ray composition inside the various designs of hohlraum calculational pre-estimations are shown.

EVOLUTION OF LOCAL PERTURBATIONS ON THE LIQUID CYLINDRICAL AND SEMI-SPHERICAL SURFACES IN THE PRESENCE OF RAYLEIGH – TAYLOR INSTABILITY / N. V. Nevmerzhitsky, E. A. Sotskov, O. L. Krivonos // VANT. Ser.: Theoret. i prikl. fizika. 2014. N 1. P. 35–41.
The paper presents the experimental study results on the evolution of local perturbations along with the RT-instability development on internal and external cylindrical and semi-spherical surfaces in the implosion and explosion conditions.
The low-strength gelatin water solution shells (the failure strain σ ≈ 0,001 MPa) were accelerated with acetylene-oxygen mixture explosion products (pressure ~13,5 atm). In the realized loading conditions the gelatin behaved as a liquid. Local perturbations were pre-set on unstable surfaces in the form of cylindrical caverns (Ø 2,5x3 mm) or were generated by the shock-wave interference. The process was filmed. The results of similar perturbation development on plane interface are given for comparison.
We have discovered that on the external surfaces, at the cylindrical and spherical shell implosion, the radial velocity of perturbation penetration into liquid is higher while on the internal surfaces at explosion – it is lower in comparison with the perturbation velocity on a plane interface.

ANALYSIS OF THE QUANTUM-MECHANICAL EQUIVALENCE OF THE METRICS OF A CENTRALLY SYMMETRIC UNCHARGED GRAVITATIONAL FIELD / M. V. Gor¬ba¬ten-ko, V. P. Neznamov // VANT. Ser.: Theoret. i prikl. fizika. 2014. N 1. P. 42–57.
In the paper we analyze the quantum-mechanical equivalence of the metrics of a centrally symmetric uncharged gravitational field. The scope of the analysis includes domains of the wave functions of Dirac’s equation, hermiticity of Hamiltonians, and the possibility of existence of stationary bound states of spin-half particles. We prove the existence of the self-adjoint Hamiltonians for: 1) the Schwarzschild metrics in the spherical, isotropic and harmonic coordinates; 2) the Eddington – Finkelstein and Painleve – Gullstrand metrics; 3) the Lemaitre – Finkelstein and Kruskal metrics.
For (1) the Hamiltonians are Hermitian, and for them the existence of stationary bound states of spin-half particles is possible. For (2) the self-adjoint Hamiltonians are non-Hermitian, and only states with complex energy levels decaying with time are possible for them. For (3) the self-adjoint Hamiltonians are Hermitian, but, because of the explicit dependence on the temporal coordinate, stationary bound states of spin-half particles cannot exist for these Hamiltonians.