Morita base change in Hopf-cyclic (co)homology

In this paper, we establish the invariance of cyclic (co)homology of left Hopf algebroids under the change of Morita equivalent base algebras. The classical result on Morita invariance for cyclic homology of associative algebras appears as a special example of this theory. In our main application we consider the Morita equivalence between the algebra of complex-valued smooth functions on the classical 2-torus and the coordinate algebra of the noncommutative 2-torus with rational parameter. We then construct a Morita base change left Hopf algebroid over this noncommutative 2-torus and show that its cyclic (co)homology can be computed by means of the homology of the Lie algebroid of vector fields on the classical 2-torus.Comment: Final version to appear in Lett. Math. Phy

The role of electromagnetic trapped modes in extraordinary transmission in nanostructured materials

We assert that the physics underlying the extraordinary light transmission (reflection) in nanostructured materials can be understood from rather general principles based on the formal scattering theory developed in quantum mechanics. The Maxwell equations in passive (dispersive and absorptive) linear media are written in the form of the Schr\"{o}dinger equation to which the quantum mechanical resonant scattering theory (the Lippmann-Schwinger formalism) is applied. It is demonstrated that the existence of long-lived quasistationary eigenstates of the effective Hamiltonian for the Maxwell theory naturally explains the extraordinary transmission properties observed in various nanostructured materials. Such states correspond to quasistationary electromagnetic modes trapped in the scattering structure. Our general approach is also illustrated with an example of the zero-order transmission of the TE-polarized light through a metal-dielectric grating structure. Here a direct on-the-grid solution of the time-dependent Maxwell equations demonstrates the significance of resonances (or trapped modes) for extraordinary light transmissioComment: 14 pages, 6 figures; Discussion in Section 4 expanded; typos corrected; a reference added; Figure 4 revise

Continuum corrections to the level density and its dependence on excitation energy, n-p asymmetry, and deformation

In the independent-particle model, the nuclear level density is determined from the neutron and proton single-particle level densities. The single-particle level density for the positive-energy continuum levels is important at high excitation energies for stable nuclei and at all excitation energies for nuclei near the drip lines. This single-particle level density is subdivided into compound-nucleus and gas components. Two methods were considered for this subdivision. First in the subtraction method, the single-particle level density is determined from the scattering phase shifts. In the Gamov method, only the narrow Gamov states or resonances are included. The level densities calculated with these two methods are similar, both can be approximated by the backshifted Fermi-gas expression with level-density parameters that are dependent on A, but with very little dependence on the neutron or proton richness of the nucleus. However, a small decrease in the level-density parameter was predicted for some nuclei very close to the drip lines. The largest difference between the calculations using the two methods was the deformation dependence on the level density. The Gamov method predicts a very strong peaking of the level density at sphericity for high excitation energies. This leads to a suppression of deformed configurations and, consequently, the fission rate predicted by the statistical model is reduced in the Gamov method.Comment: 18 pages 24 figure

Near-threshold boson pair production in the model of smeared-mass unstable particles

Near-threshold production of boson pairs is considered within the framework of the model of unstable particles with smeared mass. We describe the principal aspects of the model and consider the strategy of calculations including the radiative corrections. The results of calculations are in good agreement with LEP II data and Monte-Carlo simulations. Suggested approach significantly simplifies calculations with respect to the standard perturbative one.Comment: 15 pages, 6 figures, minor corrections, references adde

Entangled Quantum Clocks for Measuring Proper-Time Difference

We report that entangled pairs of quantum clocks (non-degenerate quantum bits) can be used as a specialized detector for precisely measuring difference of proper-times that each constituent quantum clock experiences. We describe why the proposed scheme would be more precise in the measurement of proper-time difference than a scheme of two-separate-quantum-clocks. We consider possibilities that the proposed scheme can be used in precision test of the relativity theory.Comment: no correction, 4 pages, RevTe

Isotope shift in the dielectronic recombination of three-electron ^{A}Nd^{57+}

Isotope shifts in dielectronic recombination spectra were studied for Li-like ^{A}Nd^{57+} ions with A=142 and A=150. From the displacement of resonance positions energy shifts \delta E^{142,150}(2s-2p_1/2)= 40.2(3)(6) meV (stat)(sys)) and \delta E^{142,150}(2s-2p_3/2) = 42.3(12)(20) meV of 2s-2p_j transitions were deduced. An evaluation of these values within a full QED treatment yields a change in the mean-square charge radius of ^{142,150}\delta = -1.36(1)(3) fm^2. The approach is conceptually new and combines the advantage of a simple atomic structure with high sensitivity to nuclear size.Comment: 10 pages, 3 figures, accepted for publication in Physical Review Letter

One and two-center processes in high-order harmonic generation in diatomic molecules: influence of the internuclear separation

We analyze the influence of different recombination scenarios, involving one or two centers, on high-order harmonic generation (HHG) in diatomic molecules, for different values of the internuclear separation. We work within the strong-field approximation, and employ modified saddle-point equations, in which the structure of the molecule is incorporated. We find that the two-center interference patterns, attributed to high-order harmonic emission at spatially separated centers, are formed by the quantum interference of the orbits starting at a center $C_{j}$ and finishing at a different center $C_{\nu }$ in the molecule with those starting and ending at a same center $C_{j}.$ Within our framework, we also show that contributions starting at different centers exhibit different orders of magnitude, due to the influence of additional potential-energy shifts. This holds even for small internuclear distances. Similar results can also be obtained by considering single-atom saddle-point equations and an adequate choice of molecular prefactors.Comment: 8 pages, 5 figure

The four weeks before lockdown during the COVID-19 pandemic in Germany: A weekly serial cross-sectional survey on risk perceptions, knowledge, public trust and behaviour, 3 to 25 March 2020

Background: During the COVID-19 pandemic, public perceptions and behaviours have had to adapt rapidly to new risk scenarios and radical behavioural restrictions. Aim: To identify major drivers of acceptance of protective behaviours during the 4-week transition from virtually no COVID-19 cases to the nationwide lockdown in Germany (3–25 March 2020). Methods: A serial cross-sectional online survey was administered weekly to ca 1,000 unique individuals for four data collection rounds in March 2020 using non-probability quota samples, representative of the German adult population between 18 and 74 years in terms of age × sex and federal state (n = 3,910). Acceptance of restrictions was regressed on sociodemographic variables, time and psychological variables, e.g. trust, risk perceptions, self-efficacy. Extraction of homogenous clusters was based on knowledge and behaviour. Results: Acceptance of restrictive policies increased with participants’ age and employment in the healthcare sector; cognitive and particularly affective risk perceptions were further significant predictors. Acceptance increased over time, as trust in institutions became more relevant and trust in media became less relevant. The cluster analysis further indicated that having a higher education increased the gap between knowledge and behaviour. Trust in institutions was related to conversion of knowledge into action. Conclusion: Identifying relevant principles that increase acceptance will remain crucial to the development of strategies that help adjust behaviour to control the pandemic, possibly for years to come. Based on our findings, we provide operational recommendations for health authorities regarding data collection, health communication and outreach

Self-interactions of the lightest MSSM Higgs boson in the large pseudoscalar-mass limit

We investigate the decoupling properties of the Higgs-sector-induced one-loop corrections in the lightest Higgs-boson self-couplings, in the framework of the Minimal Supersymmetric Standard Model (MSSM). The renormalized n-point vertex functions with external Higgs particles in the MSSM and in the SM are derived to the one-loop level and compared in the MA >> MZ limit. The computation has been done in a general R_{xi} gauge and the on-shell renormalization scheme is chosen. By a comparison of the renormalized lightest Higgs-boson h^0 vertex functions with respect to the corresponding SM ones, we find that the differences between the predictions of both models are summarized in the lightest Higgs-boson mass correction Delta Mh. Consequently, the radiative corrections are absorbed in the Higgs-boson mass, and the trilinear and quartic h^0 self-couplings acquire the same structure as the couplings of the SM Higgs-boson. Therefore, decoupling of the heavy MSSM Higgs bosons occurs and the MSSM h^0 self-interactions converge to the SM ones in the MA >> MZ limit.Comment: LaTeX, 26 pages, 1 figure. Sections 4 and 5 summarized in one section. Some references added. Published version in Phys. Rev.