The Hanle Effect in 1D, 2D and 3D

This paper addresses the problem of scattering line polarization and the Hanle effect in one-dimensional (1D), two-dimensional (2D) and three-dimensional (3D) media for the case of a two-level model atom without lower-level polarization and assuming complete frequency redistribution. The theoretical framework chosen for its formulation is the QED theory of Landi Degl'Innocenti (1983), which specifies the excitation state of the atoms in terms of the irreducible tensor components of the atomic density matrix. The self-consistent values of these density-matrix elements is to be determined by solving jointly the kinetic and radiative transfer equations for the Stokes parameters. We show how to achieve this by generalizing to Non-LTE polarization transfer the Jacobi-based ALI method of Olson et al. (1986) and the iterative schemes based on Gauss-Seidel iteration of Trujillo Bueno and Fabiani Bendicho (1995). These methods essentially maintain the simplicity of the Lambda-iteration method, but their convergence rate is extremely high. Finally, some 1D and 2D model calculations are presented that illustrate the effect of horizontal atmospheric inhomogeneities on magnetic and non-magnetic resonance line polarization signals.Comment: 14 pages and 5 figure

Mixed Quantum/Classical Calculations of Total and Differential Elastic and Rotationally Inelastic Scattering Cross Sections for Light and Heavy Reduced Masses in a Broad Range of Collision Energies

The mixed quantum/classical theory (MQCT) for rotationally inelastic scattering developed recently [A. Semenov and D. Babikov, J. Chem. Phys.139, 174108 (2013)] is benchmarked against the full quantum calculations for two molecular systems: He + H2 and Na + N2. This allows testing new method in the cases of light and reasonably heavy reduced masses, for small and large rotational quanta, in a broad range of collision energies and rotational excitations. The resultant collision cross sections vary through ten-orders of magnitude range of values. Both inelastic and elastic channels are considered, as well as differential (over scattering angle) cross sections. In many cases results of the mixed quantum/classical method are hard to distinguish from the full quantum results. In less favorable cases (light masses, larger quanta, and small collision energies) some deviations are observed but, even in the worst cases, they are within 25% or so. The method is computationally cheap and particularly accurate at higher energies, heavier masses, and larger densities of states. At these conditions MQCT represents a useful alternative to the standard full-quantum scattering theory

Tax evasion on a social network

We relate tax evasion behavior to a substantial literature on social comparison in judgements. Taxpayers engage in tax evasion as a means to boost their expected consumption relative to others in their social network. The unique Nash equilibrium of the model relates optimal evasion to a (Bonacich) measure of network centrality: more central taxpayers evade more. Given that tax authorities are now investing heavily in big-data tools that aim to construct social networks, we investigate the value of acquiring network information. We do this using networks that allow for celebrity taxpayers, whose consumption is widely seen, and who are systematically of higher wealth. We show that there are pronounced returns to the initial acquisition of network information, albeit targeting audits with highly incomplete knowledge of social networks may be counterproductive

Marketed tax avoidance schemes : an economic analysis

Recent years have witnessed the growth of mass-marketed tax avoidance schemes aimed at the middle (not top) of the income distribution, with significant implications for tax revenue. We examine the consequences, for the structure of income tax, and for tax authority anti-avoidance efforts, of tax avoidance of this type. In a model that allows for both demand- and supply-side considerations, we find that (1) there is an endogenous threshold income below which taxpayers do not avoid, and above which they avoid maximally; (2) the per-dollar price of tax avoidance is decreasing in income under progressive taxation; (3) endogenous adjustments in the price of avoidance make supply less responsive to anti-avoidance activity than thought previously; and (4) that avoidance may drive a non-monotone (Laffer) relationship between tax rates and tax revenue. The findings suggest that new approaches to anti-avoidance, beyond legal enforcement, may be needed

Restrictions on dilatonic brane-world models

We consider dilatonic brane-world models with a non-minimal coupling between a dilaton and usual matter on a brane. We demonstrate that variation of the fundamental constants on the brane due to such interaction leads to strong restrictions on parameters of models. In particular, the experimental bounds on variation of the fine structure constant rule out non-minimal dilatonic models with a Liouville-type coupling potential f(varphi) = exp (b varphi) where b is order of 1.Comment: MiKTeX2-LaTeX2e, 10 pages, minor changes, improved references, to appear in IJMP

Magnetic Field Measurement with Ground State Alignment

Observational studies of magnetic fields are crucial. We introduce a process "ground state alignment" as a new way to determine the magnetic field direction in diffuse medium. The alignment is due to anisotropic radiation impinging on the atom/ion. The consequence of the process is the polarization of spectral lines resulting from scattering and absorption from aligned atomic/ionic species with fine or hyperfine structure. The magnetic field induces precession and realign the atom/ion and therefore the polarization of the emitted or absorbed radiation reflects the direction of the magnetic field. The atoms get aligned at their low levels and, as the life-time of the atoms/ions we deal with is long, the alignment induced by anisotropic radiation is susceptible to extremely weak magnetic fields ($1{\rm G}\gtrsim B\gtrsim 10^{-15}$G). In fact, the effects of atomic/ionic alignment were studied in the laboratory decades ago, mostly in relation to the maser research. Recently, the atomic effect has been already detected in observations from circumstellar medium and this is a harbinger of future extensive magnetic field studies. A unique feature of the atomic realignment is that they can reveal the 3D orientation of magnetic field. In this article, we shall review the basic physical processes involved in atomic realignment. We shall also discuss its applications to interplanetary, circumstellar and interstellar magnetic fields. In addition, our research reveals that the polarization of the radiation arising from the transitions between fine and hyperfine states of the ground level can provide a unique diagnostics of magnetic fields in the Epoch of Reionization.Comment: 30 pages, 12 figures, chapter in Lecture Notes in Physics "Magnetic Fields in Diffuse Media". arXiv admin note: substantial text overlap with arXiv:1203.557

Fusion rate enhancement due to energy spread of colliding nuclei

Experimental results for sub-barrier nuclear fusion reactions show cross section enhancements with respect to bare nuclei which are generally larger than those expected according to electron screening calculations. We point out that energy spread of target or projectile nuclei is a mechanism which generally provides fusion enhancement. We present a general formula for calculating the enhancement factor and we provide quantitative estimate for effects due to thermal motion, vibrations inside atomic, molecular or crystal system, and due to finite beam energy width. All these effects are marginal at the energies which are presently measurable, however they have to be considered in future experiments at still lower energies. This study allows to exclude several effects as possible explanation of the observed anomalous fusion enhancements, which remain a mistery.Comment: 17 pages with 3 ps figure included. Revtex styl

Cosmological Challenges in Theories with Extra Dimensions and Remarks on the Horizon Problem

We consider the cosmology that results if our observable universe is a 3-brane in a higher dimensional universe. In particular, we focus on the case where our 3-brane is located at the $Z_2$ symmetry fixed plane of a $Z_2$ symmetric five-dimensional spacetime, as in the Ho\v{r}ava-Witten model compactified on a Calabi-Yau manifold. As our first result, we find that there can be substantial modifications to the standard Friedmann-Robertson-Walker (FRW) cosmology; as a consequence, a large class of such models is observationally inconsistent. In particular, any relationship between the Hubble constant and the energy density on our brane is possible, including (but not only) FRW. Generically, due to the existence of the bulk and the boundary conditions on the orbifold fixed plane, the relationship is not FRW, and hence cosmological constraints coming from big bang nucleosynthesis, structure formation, and the age of the universe difficult to satisfy. We do wish to point out, however, that some specific choices for the bulk stress-energy tensor components do reproduce normal FRW cosmology on our brane, and we have constructed an explicit example. As our second result, for a broad class of models, we find a somewhat surprising fact: the stabilization of the radius of the extra dimension and hence the four dimensional Planck mass requires unrealistic fine-tuning of the equation of state on our 3-brane. In the last third of the paper, we make remarks about causality and the horizon problem that apply to {\it any} theory in which the volume of the extra dimension determines the four-dimensional gravitational coupling. We point out that some of the assumptions that lead to the usual inflationary requirements are modified.Comment: 15 page REVTeX file; to appear in Phys. Rev. D; clarified the statement of being able to obtain any power dependence of the Hubble expansion rate on the energy density; added reference

Zero-Field Dichroism in the Solar Chromosphere

We explain the linear polarization of the Ca II infrared triplet observed close to the edge of the solar disk. In particular, we demonstrate that the physical origin of the enigmatic polarizations of the 866.2 nm and 854.2 nm lines lies in the existence of atomic polarization in their metastable lower levels, which produces differential absorption of polarization components (dichroism). To this end, we have solved the problem of the generation and transfer of polarized radiation by taking fully into account all the relevant optical pumping mechanisms in multilevel atomic models. We argue that `zero-field' dichroism may be of great diagnostic value in astrophysics.Comment: 10 pages, 3 figure