Random matrix theory and analysis of nucleus-nucleus collision at high energies

We propose a novel method for analysis of experimental data obtained in relativistic nucleus—nucleus collisions. The method, based on the ideas of random matrix theory, is applied to detect systematic errors that occur in measurements of momentum distributions of emitted particles. The unfolded momentum distribution is well described by the Gaussian orthogonal ensemble of random matrices, when the uncertainty in the momentum distribution is maximal. The method is free from unwanted background contributions. The text was submitted by the authors in English.     

On electromagnetic properties of rotating nuclei in crpa

An analysis of quasiparticle correlations with special emphasis on transition matrix elements have been done for a self-consistent cranking model. It is pointed out that a second order of the boson representation of a transition operator leads to a signature dependence of transition probabilities between excited one-phonon states in even-even nuclei. Moreover, it brings about the new contribution to an expectation value of electromagnetic moments in the yrast line states of deformed nuclei.     

Triaxial octupole deformations and shell structure

Manifestations of pronounced shell effects are discovered when non-axial octupole deformations are added to a harmonic oscillator model. The degeneracies of the quantum spectra are in good agreement with the corresponding main periodic orbits and winding number ratios which are found by classical analysis. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 8, 525–530 (25 April 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Conformal Hamiltonian dynamics of general relativity

The General Relativity formulated with the aid of the spin connection coefficients is considered in the finite space geometry of similarity with the Dirac scalar dilaton. We show that the redshift evolution of the General Relativity describes the vacuum creation of the matter in the empty Universe at the electroweak epoch and the dilaton vacuum energy plays a role of the dark energy.     

Quantum phase transitions and backbending in even-even N ∼ 90 nuclei

We extend the classical Landau theory for rotating nuclei and show that the backbending in ¹⁶²Yb, which comes about as a result of the two-quasiparticle alignment, is identified with the second-order phase transition. We found that the backbending in ¹⁵⁶Dy, caused by the instability of γ vibrations in the rotating frame, corresponds to the first-order phase transition. We suggest an empirical rule to determine the type of the phase transition in rotating nuclei undergoing backbending. The text was submitted by the authors in English.     

Collective excitations and a backbending phenomenon in <Superscript>156</Superscript>Dy

We propose a self-consistent practical method to study collective excitations in rotating nuclei within the cranking + random phase approximation approach. It consists in solving the cranking Hartree-Bogolyubov equations for the modified Nilsson potential + monopole pairing forces. Further, the mean field results are used to construct collective vibrations treated in the random phase approximation (RPA). Special attention is paid to fulfill all conservation laws in the RPA to separate spurious and physical solutions. We demonstrate that the backbending in ¹⁵⁶Dy can be explained as a result of the disappearance of collective γ vibrations of the positive signature in the rotating frame.     

On the confinement potential formation in a two-electron quantum dot

A model of a quantum dot for two interacting electrons is proposed and analyzed. The properties of the ambient determining the form of the confinement potential for electrons are simulated using the electrostatic field of the image charge. Analytic expressions for the eigenvalues of each subsystem are derived taking into account the external magnetic field and using the representation of the system Hamiltonian as the sum of the Hamiltonians of the center of mass and of relative motion on the basis of the method of oscillator representation [M. Dineykhan and G. V. Efimov, Element. Chast. At. Yadra 26, 651 (1995); M. Dineykhan, G. V. Efimov, G. Ganbold, and S. N. Nedelko, Oscillator Representation in Quantum Physics, Lecture Notes in Physics, Vol. 26, Springer, Berlin (1995)]. The relative motion of electrons is responsible for a confinement potential which differs from the parabolic confinement potential and is a function of the electron effective mass as well as the characteristics of the image charge.     

Applying a new method for analyzing experimental data on nuclear reactions at high energies

A new statistical method is proposed for the analysis of experimental data obtained in nucleus-nucleus collisions at high energies which borrows from ideas developed using the Random Matrix Theory. The method allows us to detect regions with correlation effects in the momentum distributions of secondary particles.     

Spin-orbit effects in carbon nanotubes – Analytical results

We report a study of the normal and superconducting state properties of the Ti _x V_1?x alloys for x = 0.4, 0.6, 0.7 and 0.8 with the help of dc magnetization, electrical resistivity and heat capacity measurements along with the electronic structure calculation. The superconducting transition temperature T _c of these alloys is higher than that of elemental Ti and is also higher than elemental V for x ≤ 0.7. The roles of electron density of states, electron-phonon coupling and spin fluctuations in the normal and superconducting state properties of these alloys have been investigated in detail. The experimentally observed value of T _c is found to be considerably lower than that estimated on the basis of electron density of states and electron-phonon coupling in the x = 0.4, 0.6 and 0.7 alloys. There is some evidence as well for the preformed Cooper pair in all these Ti-V alloys in the temperature regime well above T _c . Similar to x = 0.6 [Md. Matin, L.S. Sharath Chandra, R.K. Meena, M.K. Chattopadhyay, A.K. Sinha, M.N. Singh, S.B. Roy, Physica B 436, 20 (2014)], the normal state properties of the x = 0.4 alloy showed the signature of the presence of spin fluctuations. The difference between the experimentally observed T _c and that estimated by considering electron density of states and electron-phonon coupling in the x = 0.4, 0.6 and 0.7 alloys is attributed to the possible influence of these spin fluctuations. We show that the non-monotonous variation of T _c as a function of x in the Ti _x V_1?x alloys is due to the combined effects of the electron-phonon coupling and the spin fluctuations.