Magnetic Field Of Arbitrary Strength Research Articles

Classical Stark and Zeeman Effects of Axially-symmetric Circular Rydberg States of He and He-like Ions

Background: Circular Rydberg States (CRS) were studied theoretically and experimentally in numerous works. In particular, in the previous paper by one of us, there were derived analytical expressions for the energy of classical CRS in collinear electric (F) and magnetic (B) fields of arbitrary strengths imposed on a hydrogenic system (atom or ion). For the magnetic field B of any strength, the author of that study gave formulas for the dependency of the classical ionization threshold Fc(B) and the energy at this threshold Ec(B). He also analyzed the stability of the motion by going beyond the CRS. In addition, for two important particular cases previously studied in the literature – classical CRS in a magnetic field only and classical CRS in an electric field only – some new results were also presented in that paper, especially concerning the Stark effect. Objective: In the present paper, we study analytically axially-symmetric CRS of a heliumic system (He atom or He-like ion) subjected to an electric or magnetic field of arbitrary strength. Methods: In this investigation, analytical techniques were applied Results: We showed that in the case of the Stark effect, the difference in the unperturbed structure of the heliumic systems (compared to hydrogenic systems), i.e., the non-negligible size, causes the decrease of the classical ionization threshold, as well as increases the energy and the orbit radius of the outer electron at the ionization threshold. Also, the allowance for the non-negligible size of the internal subsystem increases the maximum possible absolute value of the induced electric dipole moment. In the case of the Zeeman effect, we demonstrated that the non-negligible size of the inner system increases the energy and the orbit radius of the outer electron. Conclusion: The allowance for the non-negligible size of the internal subsystem can strongly affect the properties of the axially symmetric circular states. We believe that our results are of fundamental importance.

COLMAR1d: A Web Server for Automated, Quantitative One-Dimensional Nuclear Magnetic Resonance-Based Metabolomics at Arbitrary Magnetic Fields.

The field of metabolomics, which is quintessential in today's omics research, involves the large-scale detection, identification, and quantification of small-molecule metabolites in a wide range of biological samples. Nuclear magnetic resonance spectroscopy (NMR) has emerged as a powerful tool for metabolomics due to its high resolution, reproducibility, and exceptional quantitative nature. One of the key bottlenecks of metabolomics studies, however, remains the accurate and automated analysis of the resulting NMR spectra with good accuracy and minimal human intervention. Here, we present the COLMAR1d platform, consisting of a public web server and an optimized database, for one-dimensional (1D) NMR-based metabolomics analysis to address these challenges. The COLMAR1d database comprises more than 480 metabolites from GISSMO enabling a database query of spectra measured at arbitrary magnetic field strengths, as is demonstrated for spectra acquired between 1H resonance frequencies of 80 MHz and 1.2 GHz of mouse serum, DMEM cell growth medium, and wine. COLMAR1d combines the GISSMO metabolomics database concept with the latest tools for automated processing, spectral deconvolution, database querying, and globally optimized mixture analysis for improved accuracy and efficiency. By leveraging advanced computational algorithms, COLMAR1d offers a user-friendly, automated platform for quantitative 1D NMR-based metabolomics analysis allowing a wide range of applications, including biomarker discovery, metabolic pathway elucidation, and integration with multiomics strategies.

Modeling the scattering polarization in the solar Ca I 4227Å line with angle-dependent PRD effects and bulk velocities

Context. Modeling the scattering polarization signals of strong chromospheric lines requires solving the radiative transfer problem for polarized radiation, out of local thermodynamic equilibrium, taking partial frequency redistribution (PRD) effects into account. This problem is extremely challenging from a computational standpoint and, so far, most studies have been carried out by either modeling PRD effects under the angle-average approximation or by considering academic models of the solar atmosphere. Thanks to a new solution strategy, applicable to atomic systems that allow for a linearization of the problem, accurate solutions can now be routinely obtained in realistic 1D models, taking angle-dependent (AD) PRD effects into account. Aims. This work is aimed at assessing the suitability and performance of this new approach to handling dynamic scenarios. At the same time, it aims to explore the joint impact of magnetic fields and bulk velocities on the scattering polarization profiles of strong resonance lines, accounting for AD PRD effects and considering more realistic atmospheric models than in previous investigations. Methods. By using a two-level atomic model for neutral calcium, we synthesized the intensity and polarization profiles of the Ca I 4227 Å line. Our calculations were performed in 1D atmospheric models, both semi-empirical and extracted from 3D magnetohydrodynamic simulations, including vertical bulk velocities and magnetic fields of arbitrary strength and orientation, both constant and varying with height. Results. We obtained accurate solutions after only a few iterations across all considered scenarios. Even when formulating the problem in the observer’s reference frame, the frequency and angular grids required for accurate results were easily manageable. The calculated profiles showed the expected signatures of bulk velocities: wavelength shifts, enhancement of the line-core polarization amplitude, and prominent asymmetries in the wing signals. The results obtained in atmospheric models with complex thermal, dynamic, and magnetic structures unveiled the broad diversity of features in the emergent radiation that can be expected from realistic scenarios. Conclusions. The presented results assess the suitability of the proposed solution strategy and its parallel implementation, thus supporting its generalization to the 3D case. Our applications in increasingly realistic atmospheric models showed the difficulty related to precisely establishing the individual weight of bulk velocities and magnetic fields in the shape of the emergent profiles. This highlights the need to account for both these physical ingredients to perform reliable inversions of observed scattering polarization profiles.

Quantum torque on a non-reciprocal body out of thermal equilibrium and induced by a magnetic field of arbitrary strength

AbstractA stationary body that is out of thermal equilibrium with its environment, and for which the electric susceptibility is non-reciprocal, experiences a quantum torque. This arises from the spatially non-symmetric electrical response of the body to its interaction with the non-equilibrium thermal fluctuations of the electromagnetic field: the non-equilibrium nature of the thermal field fluctuations results in a net energy flow through the body, and the spatially non-symmetric nature of the electrical response of the body to its interaction with these field fluctuations causes that energy flow to be transformed into a rotational motion. We establish an exact, closed-form, analytical expression for this torque in the case that the environment is the vacuum and the material of the body is described by a damped oscillator model, where the non-reciprocal nature of the electric susceptibility is induced by an external magnetic field, as for magneto-optical media. We also generalise this expression to the context in which the body is slowly rotating. By exploring the high-temperature expansion of the torque, we are able to identify the separate contributions from the continuous spectral distribution of the non-reciprocal electric susceptibility, and from the resonance modes. In particular, we find that the torque persists in the limiting case of zero damping parameter, due to the contribution of the resonance modes. We also consider the low-temperature expansion of the torque. This work extends our previous consideration of this model to an external magnetic field of arbitrary strength, thereby including non-linear magnetic field effects.

Remarks on propagating waves in non-linear vacuum electrodynamics

Using the quadratic expansion in the photon fields of Euler–Heisenberg (EH) non-linear electrodynamics (NLED) Lagrangian model we study relevant vacuum properties in a scenario involving the propagation of a photon probe in the presence of a background constant and static magnetic field, mathbf{B_e}. We compute the gauge invariant, symmetric and conserved energy–momentum tensor (EMT) and angular momentum tensor (AMT) for arbitrary magnetic field strength using the Hilbert method under the soft-photon approximation. We discuss how the presence of magneto-electric terms in the EH Lagrangian is a source of anisotropy, induce the non-zero trace in the EMT and leads to differences between EMT calculated by the Hilbert or Noether method. From the Hilbert EMT we analyze some quantities of interest such as the energy density, pressures, Poynting vector, and angular momentum vector, comparing and discussing the differences with respect to the improved Noether method. The magnetized vacuum properties are also studied showing that a photon effective magnetic moment can be defined for different polarization modes. The calculations are done in terms of derivatives of the two scalar invariants of electrodynamics, hence, extension to other NLED Lagrangian is straightforward. We discuss further physical implications and experimental strategies to test magnetization, photon pressure, and effective magnetic moment.

Zeeman-Stark problem in a two-dimensional disk

Under a perpendicular magnetic field, electrons in two-dimensional disks occupy quantum-confined Landau levels. By analyzing the electric polarizability of such states, we reveal an extreme sensitivity to confinement. Hence, an exponential increase with magnetic field or disk size is found and ascribed to the linear Zeeman effect. In contrast, if the balance between linear and quadratic Zeeman terms is slightly reduced, due to, e.g., addition of a nonmagnetic parabolic potential, the polarizability varies nonmonotonically with field strength and eventually vanishes. The analysis is based on a compact exact expression for the polarizability valid for arbitrary magnetic field, disk size, and linear Zeeman strength.

The polarization signals of the solar K I D lines and their magnetic sensitivity

Aims. This work aims to identify the relevant physical processes in shaping the intensity and polarization patterns of the solar K I D lines through spectral syntheses, placing particular emphasis on the D2 line. Methods. The theoretical Stokes profiles were obtained by numerically solving the radiative transfer problem for polarized radiation considering one-dimensional semi-empirical models of the solar atmosphere. The calculations account for scattering polarization, partial frequency redistribution (PRD) effects, hyperfine structure (HFS), J- and F-state interference, multiple isotopes, and magnetic fields of arbitrary strength and orientation. Results. The intensity and circular polarization profiles of both D lines can be suitably modeled while neglecting both J-state interference and HFS. The magnetograph formula can be applied to both lines, without including HFS, to estimate weak longitudinal magnetic fields in the lower chromosphere. By contrast, modeling the scattering polarization signal of the D lines requires the inclusion of HFS. The amplitude of the D2 scattering polarization signal is strongly depolarized by HFS, but it remains measurable. A small yet appreciable error is incurred in the scattering polarization profile if PRD effects are not taken into account. Collisions during scattering processes have a clear depolarizing effect, although a quantitative analysis is left for a forthcoming publication. Finally, the D2 scattering polarization signal is particularly sensitive to magnetic fields with strengths around 10 G and it strongly depends on their orientation. Despite this, its center-to-limb variation relative to the amplitude at the limb is largely insensitive to the field strength and orientation. Conclusions. These findings highlight the value of the K I D2 line polarization for diagnostics of the solar magnetism, and show that the linear and circular polarization signals of this line are primarily sensitive to magnetic fields in the lower chromosphere and upper photosphere, respectively.

Toward a magnetic warm inflation scenario

In this work we explore the effects that a possible primordial magnetic field can have on the inflaton effective potential, taking as the underlying model a warm inflation scenario, based on global supersymmetry with a new-inflation-type potential. The decay scheme for the inflaton field is a two-step process of radiation production, where the inflaton couples to heavy intermediate superfields, which in turn interact with light particles. In this context, we consider that both sectors, heavy and light, are charged and work in the strong magnetic field approximation for the light fields. We find an analytical expression for the one-loop effective potential, for an arbitrary magnetic field strength, and show that the trend of the magnetic contribution is to make the potential flatter in the origin's vicinity, preserving the conditions for a successful inflationary process. This result is backed up by the behavior of slow-roll parameter $\ensuremath{\epsilon}$. The viability of this magnetic warm inflation scenario is also supported by the estimation of the effect of the magnetic field on the heavy particles decay width.

Onset of Electron Captures and Shallow Heating in Magnetars

The loss of magnetic pressure accompanying the decay of the magnetic field in a magnetar may trigger exothermic electron captures by nuclei in the shallow layers of the stellar crust. Very accurate analytical formulas are obtained for the threshold density and pressure, as well as for the maximum amount of heat that can be possibly released, taking into account the Landau–Rabi quantization of electron motion. These formulas are valid for arbitrary magnetic field strengths, from the weakly quantizing regime to the most extreme situation in which electrons are all confined to the lowest level. Numerical results are also presented based on experimental nuclear data supplemented with predictions from the Brussels-Montreal model HFB-24. This same nuclear model has been already employed to calculate the equation of state in all regions of magnetars.

Redshift of light emitted by particles orbiting a black hole immersed in a strong magnetic field

In this paper we analyze the frequency shifts of the light emitted by particles describing stable circular geodesics around a static black hole immersed in an external magnetic field of arbitrary strength. This system is represented by the Ernst solution of the Einstein-Maxwell equations. The presence of the magnetic field and its magnitude affects both the geodesics and the red-blueshifts of the light emitted by neutral or charged particles orbiting the black hole. When the magnetic field is turned off we recover the characteristic redshifts coming from particles orbiting a Schwarzschild black hole.

Magnetic-field-dependent intervalley relaxation time in Weyl semimetals

The zeroth Landau levels in Weyl semimetals (WSMs) are singular, which result in the anomalous nonsaturated positive longitudinal magnetoconductivity (LMC). The LMC exhibits periodic-in-$1/B$ quantum oscillations attributable to the the oscillating electron density of states in a magnetic field. The intervalley relaxation time ${\ensuremath{\tau}}^{a}$ is a key material parameter determining the magnitude of the LMC directly. In existing theories of the LMC, the magnetic field dependence of ${\ensuremath{\tau}}^{a}$ is usually neglected. Based upon the Boltzmann equation, we derive analytical expression for the intervalley relaxation time for short-range impurity scattering potential and arbitrary magnetic field strength. Taking the magnetic field dependence of ${\ensuremath{\tau}}^{a}$ into consideration, we find that the quantum oscillations of the LMC are enhanced. Numerical calculations are also carried out to verify the analytical derivations. Moreover, we provide an explanation for the anomalous behavior of the LMC observed in WSMs that the amplitude of LMC first increases and then decreases with increasing temperature.

Nonlinear high-frequency magnetic response of magnetoferritin metacrystals governed by spin thermodynamics

A theory is developed of the time-dependent magnetization of the metacrystal composed of magnetoferritin macromolecules. Such superstructures, comprising up to several millions of superparamagnetic nanoparticles encapsulated in protein shells, can be created artificially using biochemical assembling technologies. They have been also shown to occur naturally in sensitive cells of the inner ear of birds, which suggests their possible involvement in the detection of the geomagnetic field for orientation and navigation of migratory animals. The dynamics of the magnetic system of the magnetoferritin metacrystal, comprising a very large number of magnetic moments coupled by long-range dipole forces, is exceedingly complex. In order to find the response of the metacrystal to high-frequency magnetic fields, we used a thermodynamic approach borrowed from the theory of nuclear spin systems of solids. The resulted theory yields the time-dependent superspin temperature and magnetization induced by oscillating magnetic fields of arbitrary strength. The predicted dependence of the high-frequency response on the static magnetic field can be used for experimental detection and characterization of magnetoferritin metacrystals in biological tissues.

The role of the Debye screening of circular Rydberg states of hydrogenic systems in collinear electric and magnetic fields of arbitrary strengths

We consider classical circular Rydberg states of a hydrogenic atom/ion under collinear electric and magnetic fields of arbitrary strengths, the entire system being immersed into a plasma with the Debye screening. In this way we add a “new dimension” to the results of the previous paper of one of us, where the screening was not taken into account. We show in detail how the screening decreases the value of the critical electric field required for the ionization at different values of the magnetic field. Our results should have a fundamental importance because hydrogenic atoms/ions under external fields remain a test-bench for atomic physics. Also our results could motivate experiments on the magnetic control of the “continuum lowering” in cold Rydberg plasmas, this being of practical importance.

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field

We calculate the neutral pion mass in the presence of an external magnetic field of arbitrary strength in the framework of the linear sigma model coupled to quarks at zero temperature. We find nonmonotonic behavior of the pion mass as a function of magnetic field. We are also able to reproduce existing results for the weak-field approximation.

The Magnetic Sensitivity of the Resonance and Subordinate Lines of Mg II in the Solar Chromosphere

Abstract We carry out a theoretical study of the polarization of the solar Mg ii h–k doublet (including its extended wings) and the subordinate ultraviolet (UV) triplet around 280 nm. These lines are of great diagnostic interest, as they encode information on the physical properties of the solar atmosphere from the upper photosphere to the chromosphere–corona transition region. We base our study on radiative transfer calculations of spectral line polarization in one-dimensional models of quiet and plage regions of the solar atmosphere. Our calculations take into account the combined action of atomic polarization, quantum level interference, frequency redistribution, and magnetic fields of arbitrary strength. In particular, we study the sensitivity of the emergent Stokes profiles to changes in the magnetic field through the Zeeman and Hanle effects. We also study the impact of the chromospheric plasma dynamics on the emergent Stokes profiles, taking into account the angle-dependent frequency redistribution in the h–k resonance transitions. The results presented here are of interest for the interpretation of spectropolarimetric observations in this important region of the solar UV spectrum.

General structure of the neutral ρ meson self-energy and its spectral properties in a hot and dense magnetized medium

The one loop self energy of the neutral $\rho$ meson is obtained for the effective $\rho\pi\pi$ and $\rho NN$ interaction at finite temperature and density in the presence of a constant background magnetic field of arbitrary strength. In our approach, the eB-dependent vacuum part of the self energy is extracted by means of dimensional regularization where the ultraviolet divergences corresponding to the pure vacuum self energy manifest as the pole singularities of gamma as well as Hurwitz zeta functions. This improved regularization procedure consistently reproduces the expected results in the vanishing magnetic field limit and can be used quite generally in other self energy calculations dealing with arbitrary magnetic field strength. In presence of the external magnetic field, the general Lorentz structure for the in-medium vector boson self energy is derived which can also be implemented in case of the gauge bosons such as photons and gluons. It has been shown that with vanishing perpendicular momentum of the external particle, essentially two form factors are sufficient to describe the self energy completely. Consequently, two distinct modes are observed in the study of the effective mass, dispersion relations and the spectral function of $\rho^0$ where one of the modes possesses two fold degeneracy. For large baryonic chemical potential, it is observed that the critical magnetic field required to block the $\rho^0\rightarrow\pi^+\pi^-$ decay channel increases significantly with temperature. However, in case of smaller values reaching down to vanishing chemical potential, the critical field follows the opposite trend.

Magnetoresistance of semimetals: The case of antimony

Large unsaturated magnetoresistance has been recently reported in numerous semi-metals. Many of them have a topologically non-trivial band dispersion, such as Weyl nodes or lines. Here, we show that elemental antimony displays the largest high-field magnetoresistance among all known semi-metals. We present a detailed study of the angle-dependent magnetoresistance and use a semi-classical framework invoking an anisotropic mobility tensor to fit the data. A slight deviation from perfect compensation and a modest variation with magnetic field of the components of the mobility tensor are required to attain perfect fits at arbitrary strength and orientation of magnetic field in the entire temperature window of study. Our results demonstrate that large orbital magnetoresistance is an unavoidable consequence of low carrier concentration and the sub-quadratic magnetoresistance seen in many semi-metals can be attributed to field-dependent mobility, expected whenever the disorder length-scale exceeds the Fermi wavelength.

Solar Spectral Lines with Special Polarization Properties for the Calibration of Instrument Polarization

Abstract We investigate atomic transitions that have previously been identified as having zero polarization from the Zeeman effect. Our goal is to identify spectral lines that can be used for the calibration of instrumental polarization of large astronomical and solar telescopes, such as the Daniel K. Inouye Solar Telescope, which is currently under construction on Haleakala. We use a numerical model that takes into account the generation of scattering polarization and its modification by the presence of a magnetic field of arbitrary strength. We adopt values for the Landé factors from spectroscopic measurements or semi-empirical results, thus relaxing the common assumption of LS-coupling previously used in the literature. The mechanisms dominating the polarization of particular transitions are identified, and we summarize groups of various spectral lines useful for the calibration of spectropolarimetric instruments, classified according to their polarization properties.

Efficient Calculation of Molecular Integrals over London Atomic Orbitals.

The use of London atomic orbitals (LAOs) in a nonperturbative manner enables the determination of gauge-origin invariant energies and properties for molecular species in arbitrarily strong magnetic fields. Central to the efficient implementation of such calculations for molecular systems is the evaluation of molecular integrals, particularly the electron repulsion integrals (ERIs). We present an implementation of several different algorithms for the evaluation of ERIs over Gaussian-type LAOs at arbitrary magnetic field strengths. The efficiencies of generalized McMurchie-Davidson (MD), Head-Gordon-Pople (HGP), and Rys quadrature schemes are compared. For the Rys quadrature implementation, we avoid the use of high precision arithmetic and interpolation schemes in the computation of the quadrature roots and weights, enabling the application of this algorithm seamlessly to a wide range of magnetic fields. The efficiency of each generalized algorithm is compared by numerical application, classifying the ERIs according to their total angular momenta and evaluating their performance for primitive and contracted basis sets. In common with zero-field integral evaluation, no single algorithm is optimal for all angular momenta; thus, a simple mixed scheme is put forward that selects the most efficient approach to calculate the ERIs for each shell quartet. The mixed approach is significantly more efficient than the exclusive use of any individual algorithm.

Polarized Line Formation in Arbitrary Strength Magnetic Fields Angle-averaged and Angle-dependent Partial Frequency Redistribution

Abstract Magnetic fields in the solar atmosphere leave their fingerprints in the polarized spectrum of the Sun via the Hanle and Zeeman effects. While the Hanle and Zeeman effects dominate, respectively, in the weak and strong field regimes, both these effects jointly operate in the intermediate field strength regime. Therefore, it is necessary to solve the polarized line transfer equation, including the combined influence of Hanle and Zeeman effects. Furthermore, it is required to take into account the effects of partial frequency redistribution (PRD) in scattering when dealing with strong chromospheric lines with broad damping wings. In this paper, we present a numerical method to solve the problem of polarized PRD line formation in magnetic fields of arbitrary strength and orientation. This numerical method is based on the concept of operator perturbation. For our studies, we consider a two-level atom model without hyperfine structure and lower-level polarization. We compare the PRD idealization of angle-averaged Hanle–Zeeman redistribution matrices with the full treatment of angle-dependent PRD, to indicate when the idealized treatment is inadequate and what kind of polarization effects are specific to angle-dependent PRD. Because the angle-dependent treatment is presently computationally prohibitive when applied to realistic model atmospheres, we present the computed emergent Stokes profiles for a range of magnetic fields, with the assumption of an isothermal one-dimensional medium.