Integrability and action operators in quantum Hamiltonian systems

For a (classically) integrable quantum mechanical system with two degrees of freedom, the functional dependence $\hat{H}=H_Q(\hat{J}_1,\hat{J}_2)$ of the Hamiltonian operator on the action operators is analyzed and compared with the corresponding functional relationship $H(p_1,q_1;p_2,q_2) = H_C(J_1,J_2)$ in the classical limit of that system. The former is shown to converge toward the latter in some asymptotic regime associated with the classical limit, but the convergence is, in general, non-uniform. The existence of the function $\hat{H}=H_Q(\hat{J}_1,\hat{J}_2)$ in the integrable regime of a parametric quantum system explains empirical results for the dimensionality of manifolds in parameter space on which at least two levels are degenerate. The comparative analysis is carried out for an integrable one-parameter two-spin model. Additional results presented for the (integrable) circular billiard model illuminate the same conclusions from a different angle.Comment: 9 page

Possibility of local pair existence in optimally doped SmFeAsO(1-x) in pseudogap regime

We report the analysis of pseudogap Delta* derived from resistivity experiments in FeAs-based superconductor SmFeAsO(0.85), having a critical temperature T_c = 55 K. Rather specific dependence Delta*(T) with two representative temperatures followed by a minimum at about 120 K was observed. Below T_s = 147 K, corresponding to the structural transition in SmFeAsO, Delta*(T) decreases linearly down to the temperature T_AFM = 133 K. This last peculiarity can likely be attributed to the antiferromagnetic (AFM) ordering of Fe spins. It is believed that the found behavior can be explained in terms of Machida, Nokura, and Matsubara (MNM) theory developed for the AFM superconductors.Comment: 5 pages, 2 figure

Langmuir wave linear evolution in inhomogeneous nonstationary anisotropic plasma

Equations describing the linear evolution of a non-dissipative Langmuir wave in inhomogeneous nonstationary anisotropic plasma without magnetic field are derived in the geometrical optics approximation. A continuity equation is obtained for the wave action density, and the conditions for the action conservation are formulated. In homogeneous plasma, the wave field E universally scales with the electron density N as E ~ N^{3/4}, whereas the wavevector evolution varies depending on the wave geometry

Evaluation of the current state of aquatic ecosystems and the problems of the protection of biological resources during development of kruzenshternskoye gcf

The results of studies of the current state of freshwater ecosystems and their biotic components in the western part of the Yamal Peninsula are presented in the article. Based on the evaluation of the structure of communities of phytoplankton, zooplankton, benthos, and whitefishes, the range of problems related to the protection of biological resources during the development of the Kruzenshternskoye gas field is defined. The data on species composition and quantitative indicators of hydrobionts of different types of waterbodies and watercourses in the lower reaches of the Mordyyakha and Naduyyakha Rivers basins is the basis for environmental monitoring of water objects during development and exploitation of the Kruzenshternskoye gas field. Estimation of the fish fauna state and their food base in the territory of the Kruzenshternskoye GCF according to the monitoring program is present. The river delta zones are the most important feeding areas of the salmonid and whitefishes valuable fish species in the territory of Kruzenshternskoye GCF. In cases where water bodies and watercourses are not completely demolished for the construction of GCF facilities, changes of quantitative and qualitative characteristics of communities of hydrobionts after the end of operations are reversible. River ecosystems are restored within a shorter period of time in comparison to lacustrine ones. Proposals for the protection of fisheries resources and monitoring of aquatic ecosystems on the basis of comprehensive studies are reported. Recommendations on reducing the anthropogenic impact on aquatic ecosystems in the development period are present. The results of the investigation were used in the development of the environmental protection part of the Kruzenshternskoye deposit project. Anthropogenic disturbances present now on the gas deposit territory of Kruzenshternskoye does not influence the aquatic ecosystems.The article have been prepared within the Project of the Presidium of the Russian Academy of Sciences № 12-P-47-2013 and "The Arctic" Project of the Presidium of the Ural Branch of the Russian Academy of Sciences № 12-4-3-012

Two-particle multiplets splitting as a guideline in nucleon pairing estimations

The ground state multiplet structure for nuclei over the wide range of mass number $A$ was calculated in $\delta$-approximation and different mass relations for pairing energy was analysed in this work. Correlation between the calculated multiplet structure and experimental data offer a guideline in deciding between mass relations for nucleon pairing.Comment: 6 pages, 2 fig., Proceedings of Intern. Session-Conference of the Section of Nuclear Physics of PSD RAS (April 12 - 15, 2016, JINR Dubna), to be published in Journal Physics of Elementary Particles and Atomic Nuclei (PEPAN

Signatures of quantum integrability and nonintegrability in the spectral properties of finite Hamiltonian matrices

For a two-spin model which is (classically) integrable on a five-dimensional hypersurface in six-dimensional parameter space and for which level degeneracies occur exclusively (with one known exception) on four-dimensional manifolds embedded in the integrability hypersurface, we investigate the relations between symmetry, integrability, and the assignment of quantum numbers to eigenstates. We calculate quantum invariants in the form of expectation values for selected operators and monitor their dependence on the Hamiltonian parameters along loops within, without, and across the integrability hypersurface in parameter space. We find clear-cut signatures of integrability and nonintegrability in the observed traces of quantum invariants evaluated in finite-dimensional invariant Hilbert subspaces, The results support the notion that quantum integrability depends on the existence of action operators as constituent elements of the Hamiltonian.Comment: 11 page

Semiclassical treatment of logarithmic perturbation theory

The explicit semiclassical treatment of logarithmic perturbation theory for the nonrelativistic bound states problem is developed. Based upon $\hbar$-expansions and suitable quantization conditions a new procedure for deriving perturbation expansions for the one-dimensional anharmonic oscillator is offered. Avoiding disadvantages of the standard approach, new handy recursion formulae with the same simple form both for ground and exited states have been obtained. As an example, the perturbation expansions for the energy eigenvalues of the harmonic oscillator perturbed by $\lambda x^{6}$ are considered.Comment: 6 pages, LATEX 2.09 using IOP style