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

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

Search for the Most Effective Ways to Protect Legal Order During the Civil War in Russia: Formation and Activity of Police Bodies of the Main State Formations

Abstract. Introduction. The legal order as the ordering of public relations on the basis of law is one of the main elements of the state. The problem of its provision was actualized during the Civil War. The presence of a firm legal order meant the stability of the government, and also directly influenced its support from the population, stability in the rear and success at the front. An important role in ensuring the protection of legal order, along with ordinary and emergency bodies, was played by the police. Methods and materials. With the help of historical-legal, systematic, formal-legal and comparative-legal methods, the analysis of written sources was carried out, among which the main attention was paid to legislation and other official acts of the authorities of state formations during the Civil War, works and memoirs of its participants, as well as scientific works devoted to the study of this period. Results. The article shows that the most radical changes in the organization of the police were carried out by the Soviet government. The flexibility of the leadership in matters of ideology (without affecting the foundations of Marxist doctrine and the construction of socialist statehood in the country) ensured the effectiveness of the activities of the Soviet law enforcement agencies and the significant contribution of the Soviet police to restoring elementary order and countering rampant crime on the territory of the RSFSR

Quantum integrability and nonintegrability in the spin-boson model

We study the spectral properties of a spin-boson Hamiltonian that depends on two continuous parameters $0\leq\Lambda<\infty$ (interaction strength) and $0\leq\alpha\leq\pi/2$ (integrability switch). In the classical limit this system has two distinct integrable regimes, $\alpha=0$ and $\alpha=\pi/2$. For each integrable regime we can express the quantum Hamiltonian as a function of two action operators. Their eigenvalues (multiples of $\hbar$) are the natural quantum numbers for the complete level spectrum. This functional dependence cannot be extended into the nonintegrable regime $(0<\alpha<\pi/2)$. Here level crossings are prohibited and the level spectrum is naturally described by a single (energy sorting) quantum number. In consequence, the tracking of individual eigenstates along closed paths through both regimes leads to conflicting assignments of quantum numbers. This effect is a useful and reliable indicator of quantum chaos -- a diagnostic tool that is independent of any level-statistical analysis

Integrability and level crossing manifolds in a quantum Hamiltonian system

We consider a two-spin model, represented classically by a nonlinear autonomous Hamiltonian system with two degrees of freedom and a nontrivial integrability condition, and quantum mechanically by a real symmetric Hamiltonian matrix with blocks of dimensionalities K=l(l+1)/2, l=1,2,... In the six-dimensional (6D) parameter space of this model, classical integrability is satisfied on a 5D hypersurface, and level crossings occur on 4D manifolds that are completely embedded in the integrability hypersurface except for some lower-D sub-manifolds. Under mild assumptions, the classical integrability condition can be reconstructed from a purely quantum mechanical study of level degeneracies in finite-dimensional invariant blocks of the Hamiltonian matrix. Our conclusions are based on rigorous results for K=3 and on numerical results for K=6,10.Comment: 8 pages, 3 figure

ОСОБЕННОСТИ ФОРМИРОВАНИЯ ТОНКИХ ПЛЕНОК КРЕМНИЯ, ОСАЖДАЕМЫХ МАГНЕТРОННЫМ РАСПЫЛЕНИЕМ

The surface morphology and optical properties of Si coatings formed by magnetron sputtering were studied using atomic force microscopy, scanning electron microscopy, and spectrophotometry methods. The possibility to influence the surface morphology of coating (filamentous structures and/or round holes) and the location of maxima and minima in reflectance and transmittance via a controllable variation of magnetron sputtering regimes (substrate temperature and bias potential) is shown. Методами атомно-силовой и сканирующей электронной микроскопии, а также спектрофотометрии исследованы морфология поверхности и оптические характеристики тонких Si-покрытий, сформированных методом магнетронного распыления. Показано, что при контролируемой вариации технологических параметров магнетронного распыления таких, как температура подложки и потенциал смещения, можно менять морфологию поверхности пленок Si. Для некоторых режимов осаждения обнаружено появление на поверхности нитевидных структур и/или круглых углублений, изменения положения минимумов и максимумов в оптических спектрах отражения и пропускания.

Triazoles and Strobilurin Mixture Affects Soil Microbial Community and Incidences of Wheat Diseases

Pesticides are widely used in agriculture as a pest control strategy. Despite the benefits of pesticides on crop yields, the persistence of chemical residues in soil has an unintended impact on non-targeted microorganisms. In the present study, we evaluated the potential adverse effects of a mixture of fungicides (difenoconazole, epoxiconazole, and kresoxim-methyl) on soil fungal and bacterial communities, as well as the manifestation of wheat diseases. In the fungicide-treated soil, the Shannon indices of both fungal and bacterial communities decreased, whereas the Chao1 indices did not differ compared to the control soil. Among bacterial taxa, the relative abundances of Arthrobacter and Sphingomonas increased in fungicide-treated soil due to their ability to utilize fungicides and other toxic compounds. Rhizopus and plant-beneficial Chaetomium were the dominant fungal genera, with their prevalence increasing by 2&ndash;4 times in the fungicide-treated soil. The genus Fusarium, which includes phytopathogenic species, which are notably responsible for root rot, was the most abundant taxon in each of the two conditions but its relative abundance was two times lower in fungicide-treated soils, consistent with a lower level of disease incidence in plants. The prediction of metabolic pathways revealed that the soil bacterial community had a high potential for degrading various pollutants, and the soil fungal community was in a state of recovery after the application of quinone outside inhibitor (QoI) fungicides. Fungicide-treated soil was characterized by an increase in soil microbial carbon, compared with the control soil. Collectively, the obtained results suggest that the application of difenoconazole, epoxiconazole, and kresoxim-methyl is an effective approach for pest control that does not pose a hazard for the soil ecosystem in the short term. However, it is necessary to carry out additional sampling to take into account the spatio-temporal impact of this fungicide mixture on the functional properties of the soil