Strong Field Case Research Articles

Evolution of the Angular Momentum of Molecular Cloud Cores in Magnetized Molecular Filaments

The angular momentum of molecular cloud cores plays a key role in the star formation process. However, the evolution of the angular momentum of molecular cloud cores formed in magnetized molecular filaments is still unclear. In this paper, we perform 3D magnetohydrodynamics simulations to reveal the effect of the magnetic field on the evolution of the angular momentum of molecular cloud cores formed through filament fragmentation. As a result, we find that the angular momentum decreases by 30% and 50% at the mass scale of 1 M ⊙ in the case of weak and strong magnetic field, respectively. By analyzing the torques exerted on fluid elements, we identify the magnetic tension as the dominant process for angular momentum transfer for mass scales ≲3 M ⊙ for the strong magnetic field case. This critical mass scale can be understood semianalytically as the timescale of magnetic braking. We show that the anisotropy of the angular momentum transfer due to the presence of a strong magnetic field changes the resultant angular momentum of the core only by a factor of 2. We also find that the distribution of the angle between the rotation axis and the magnetic field does not show strong alignment even just before the first core formation. Our results also indicate that the variety of the angular momentum of the cores is inherited from the difference in the phase of the initial turbulent velocity field. The variety could contribute to the diversity in size and other properties of protoplanetary disks recently reported by observations.

A novel density functional study on the freezing mechanism of a nanodroplet under an external electric field

An electric field is one of the most favorable means to control the microscopic behavior of a nanodroplet/nanocluster, but the mechanisms to do so are still not very clear. In this work, we proposed dynamic density functional theory (DDFT) to mimic the freezing process of a nanodroplet under an external electric field (EEF). The molecular interaction is modeled by a Lennard–Jones potential plus a dipole–dipole interaction that is induced by the EEF. We found that the electric field could induce a series of structural transitions and that the droplet could form into a layered structure or a discrete lattice depending on the intensity of the EEF. Compared to molecular simulation, the transition EEF predicted from DDFT agrees more with reality. The time-dependent density profile indicates that the freezing process is nonlinear and irreversible, especially for the strong electric field case. These findings may provide insights into the control of nanodroplets and the preparation of nanoclusters.

Closing of the astrotail

Context. The structure of astrospheres depends on the interaction between the host star and the surrounding interstellar medium (ISM). Observations of astrospheres offer new opportunities to learn about the details of this interaction. Aims. The aim of this work is to study the global structure of astrospheres, concentrating on the case of strong interstellar magnetic field and low relative velocity between the star and the ISM. Methods. We used a simple magnetohydrodynamical numerical code to simulate the interaction between the stellar wind and the ISM, using different assumptions about the interstellar magnetic field strength, the velocity of the star, and the parameters of the interstellar medium. From the resulting time-stationary solutions, we derived the mass flux distribution of the stellar plasma inside the astrosphere, with particular attention to the flow topology. Results. We find that the tube-like topology of the astrosphere can occur for an interstellar magnetic field strength of 7 µG (a realistic value in the Galactic disk region), provided that the velocity of the star relative to the ISM is low enough (0.5 km s−1 ). The two-stream structure of the stellar wind mass flow appears to some extent in all our models.

Foldy-Wouthuysen transformation in strong magnetic fields and relativistic corrections for quantum cyclotron energy levels

We carry out a direct, iterative Foldy--Wouthuysen transformation of a general Dirac Hamiltonian coupled to an electromagnetic field, including the anomalous magnetic moment. The transformation is carried out through an iterative disentangling of the particle and antiparticle Hamiltonians, in the expansion for higher orders of the momenta. The time-derivative term from the unitary transformation is found to be crucial in supplementing the transverse component of the electric field in higher orders. Final expressions are obtained for general combined electric and magnetic fields, including strong magnetic fields. The time-derivative of the electric field is shown to enter only in the seventh order of the fine-structure constant if the transformation is carried out in the standard fashion. We put special emphasis on the case of strong fields, which are important for a number of applications, such as electrons bound in Penning traps.

A comparison of 2D Magnetohydrodynamic supernova simulations with the CoCoNuT-FMT and Aenus-Alcar codes

ABSTRACT Code comparisons are a valuable tool for the verification of supernova simulation codes and the quantification of model uncertainties. Here, we present a first comparison of axisymmetric magnetohydrodynamic (MHD) supernova simulations with the CoCoNuT-FMT and Aenus-Alcar codes, which use distinct methods for treating the MHD induction equation and the neutrino transport. We run two sets of simulations of a rapidly rotating 35M⊙ gamma-ray burst progenitor model with different choices for the initial field strength, namely $10^{12}\, \mathrm{G}$ for the maximum poloidal and toroidal field in the strong-field case and $10^{10}\, \mathrm{G}$ in the weak-field case. We also investigate the influence of the Riemann solver and the resolution in CoCoNuT-FMT. The dynamics is qualitatively similar for both codes and robust with respect to these numerical details, with a rapid magnetorotational explosion in the strong-field case and a delayed neutrino-driven explosion in the weak-field case. Despite relatively similar shock trajectories, we find sizeable differences in many other global metrics of the dynamics, like the explosion energy and the magnetic energy of the proto-neutron star. Further differences emerge upon closer inspection, for example, the disc-like surface structure of the proto-neutron star proves high sensitivity to numerical details. The electron fraction distribution in the ejecta as a crucial determinant for the nucleosynthesis is qualitatively robust, but the extent of neutron- or proton-rich tails is sensitive to numerical details. Due to the complexity of the dynamics, the ultimate cause of model differences can rarely be uniquely identified, but our comparison helps gauge uncertainties inherent in current MHD supernova simulations.

Scalar lumps with a horizon

We study a self-interacting scalar field theory coupled to gravity and are interested in spherically symmetric solutions with a regular origin surrounded by a horizon. For a scalar potential containing a barrier, and using the most general spherically symmetric ansatz, we show that in addition to the known static, oscillating solutions discussed earlier in the literature there exist new classes of solutions which appear in the strong field case. For these solutions the spatial sphere shrinks either beyond the horizon, implying a collapsing universe outside of the cosmological horizon, or it shrinks already inside of the horizon, implying the existence of a black hole surrounding the scalar lump in all directions. Crucial for the existence of all such solutions is the presence of a scalar field potential with a barrier that satisfies the swampland conjectures.

Magnetic field dependence of the neutral pion mass in the linear sigma model with quarks: The strong field case

We use the linear sigma model with quarks to find the magnetic field-induced modifications to the neutral pion mass at one-loop level. The magnetic field effects are introduced by using charged particle propagators in the presence of a magnetic background in the strong field regime. We show that when accounting for the effects of the magnetic field on the model couplings, the vacuum sigma field and the neutral pion self-energy, the neutral pion mass decreases monotonically as a function of the field strength. We find an excellent qualitative and quantitative agreement with recent lattice QCD calculations, reproducing the monotonically decreasing trend with the field strength as well as the decrease when lattice data approaches the physical vacuum pion mass from larger values.

Error Estimates of Some Splitting Schemes for Charged-Particle Dynamics under Strong Magnetic Field

In this work, we consider the error estimates of some splitting schemes for the charged-particle dynamics under a strong magnetic field. We first propose a novel energy-preserving splitting scheme with computational cost per step independent of the strength of the magnetic field. Then under the maximal ordering scaling case, we establish for the scheme and in fact for a class of Lie--Trotter-type splitting schemes a uniform (in the strength of the magnetic field) and optimal error bound in the position and in the velocity parallel to the magnetic field. For the general strong magnetic field case, the modulated Fourier expansions of the exact and the numerical solutions are constructed to obtain a favorable dependence of the error on the strength of the magnetic field. Numerical experiments are presented to illustrate the error and energy behavior of the splitting schemes.

Magnetic phase diagram of a spin S = 1/2 antiferromagnetic two-leg ladder with modulated along legs Dzyaloshinskii-Moriya interaction

We study the ground-state magnetic phase diagram of a spin S=1/2 antiferromagnetic two-leg ladder in the presence of period two lattice units modulated, Dzyaloshinskii-Moriya (DM) interaction along the legs. We consider the case of collinear DM vectors and strong rung exchange and magnetic field. In this limit we map the initial ladder model onto the effective spin $\sigma=1/2$ XXZ chain and study the latter using the continuum-limit bosonization approach. We identified four quantum phase transitions and corresponding critical magnetic fields, which mark transitions from the spin gapped regimes into the gapless quantum spin-liquid regimes. In the gapped phases the magnetization curve of the system shows plateaus at magnetisation M=0 and to its saturation value per rung M=1. We have shown that the very presence of alternating DM interaction leads to opening of a gap in the excitation spectrum at magnetization M=0.5. The width of the magnetization plateau at M=0.5, is determined by the associated with the dynamical generation of a gap in the spectrum is calculated and is shown that its length scales as $(D_{0}D_{1}/J^{2})^{\alpha}$ where $D_{0},D_{1}$ are uniform and staggered components of the DM term, $J$ is the intraleg exchange and $\alpha \leq 3/4$ and weakly depends on the DM couplings.

Gravitational collapse in Einstein dilaton-Gauss–Bonnet gravity

We present results from a numerical study of spherical gravitational collapse in shift symmetric Einstein dilaton Gauss–Bonnet (EdGB) gravity. This modified gravity theory has a single coupling parameter that when zero reduces to general relativity (GR) minimally coupled to a massless scalar field. We first show results from the weak EdGB coupling limit, where we obtain solutions that smoothly approach those of the Einstein–Klein–Gordon system of GR. Here, in the strong field case, though our code does not utilize horizon penetrating coordinates, we nevertheless find tentative evidence that approaching black hole formation the EdGB modifications cause the growth of scalar field ‘hair’, consistent with known static black hole solutions in EdGB gravity. For the strong EdGB coupling regime, in a companion paper we first showed results that even in the weak field (i.e. far from black hole formation), the EdGB equations are of mixed type: evolution of the initially hyperbolic system of partial differential equations lead to formation of a region where their character changes to elliptic. Here, we present more details about this regime. In particular, we show that an effective energy density based on the Misner–Sharp mass is negative near these elliptic regions, and similarly the null convergence condition is violated then.

Metal-insulator transition in 8−Pmmn borophene under normal incidence of electromagnetic radiation

The energy spectrum for the problem of 8-Pmmn borophene's electronic carriers under perpendicular incidence of electromagnetic waves is studied without the use of any perturbative technique. This allows to study the effects of very strong fields. To obtain the spectrum and wavefunctions, the time-dependent Dirac equation is solved by using a frame moving with the space-time cone of the wave, i.e., by transforming the equation into an ordinary differential equation in terms of the wave-phase, leading to an electron-wave quasiparticle. The limiting case of strong fields is thus analyzed.The resulting eigenfunctions obey a generalized Mathieu equation,i.e., of a classical parametric pendulum. The energy spectrum presents bands, and a gap at the Fermi energy. The gaps are due to the space-time diffraction of electrons in phase with the electromagnetic field, i.e., electrons in borophene acquire an effective mass under strong electromagnetic radiation

Role of Interaction between Magnetic Rossby Waves and Tachocline Differential Rotation in Producing Solar Seasons

Abstract We present a nonlinear magnetohydrodynamic shallow-water model for the solar tachocline (MHD-SWT) that generates quasi-periodic tachocline nonlinear oscillations (TNOs) that can be identified with the recently discovered solar “seasons.” We discuss the properties of the hydrodynamic and magnetohydrodynamic Rossby waves that interact with the differential rotation and toroidal fields to sustain these oscillations, which occur due to back-and-forth energy exchanges among potential, kinetic, and magnetic energies. We perform model simulations for a few years, for selected example cases, in both hydrodynamic and magnetohydrodynamic regimes and show that the TNOs are robust features of the MHD-SWT model, occurring with periods of 2–20 months. We find that in certain cases multiple unstable shallow-water modes govern the dynamics, and TNO periods vary with time. In hydrodynamically governed TNOs, the energy exchange mechanism is simple, occurring between the Rossby waves and differential rotation. But in MHD cases, energy exchange becomes much more complex, involving energy flow among six energy reservoirs by means of eight different energy conversion processes. For toroidal magnetic bands of 5 and 35 kG peak amplitudes, both placed at 45° latitude and oppositely directed in north and south hemispheres, we show that the energy transfers responsible for TNO, as well as westward phase propagation, are evident in synoptic maps of the flow, magnetic field, and tachocline top-surface deformations. Nonlinear mode–mode interaction is particularly dramatic in the strong-field case. We also find that the TNO period increases with a decrease in rotation rate, implying that the younger Sun had more frequent seasons.

New Possibilities of Probe Detection of Anisotropic Charged-Particle Distribution Functions in an Arbitrary-Symmetry Plasma

We have analyzed the precision and systematic errors of the familiar method of a plane single-ended probe for measuring the anisotropic distribution functions for electrons and ions in plasma. Analytic relations that connect the plasma parameters and the required number of terms in a series are obtained under the conditions when anisotropy is due to the presence of an electric field in the plasma. It has been shown that ten terms of the series are usually sufficient to adequately describe the ion distribution function, except for the case of strong fields. For strongly anisotropic charged particle distribution functions, the spline interpolation technique for experimental data is proposed and tested, which substantially reduces the systematic error for a preset number of terms in the series. It has been shown for abundant actual plasma objects with the mirror symmetry that the number of required orientations of a plane probe for the experimental distribution function can be reduced by half compared to the most general case of the absence of any symmetry for a fixed number of terms in the Legendre series, while for the same number of orientations, the number of terms in the series, which are determined from these measurements, doubled accordingly.

Effects of magnetic field on plasma evolution in relativistic heavy-ion collisions

Very strong magnetic fields can arise in non-central heavy-ion collisions at ultrarelativistic energies, which may not decay quickly in a conducting plasma. We carry out relativistic magnetohydrodynamics (RMHD) simulations to study the effects of this magnetic field on the evolution of the plasma and on resulting flow fluctuations in the ideal RMHD limit. Our results show that magnetic field leads to enhancement in elliptic flow for small impact parameters while it suppresses it for large impact parameters (which may provide a signal for initial stage magnetic field). Interestingly, we find that magnetic field in localized regions can temporarily increase in time as evolving plasma energy density fluctuations lead to reorganization of magnetic flux. This can have important effects on chiral magnetic effect. Magnetic field has non-trivial effects on the power spectrum of flow fluctuations. For very strong magnetic field case one sees a pattern of even-odd difference in the power spectrum of flow coefficients arising from reflection symmetry about the magnetic field direction if initial state fluctuations are not dominant. We discuss the situation of nontrivial magnetic field configurations arising from collision of deformed nuclei and show that it can lead to anomalous elliptic flow. Special (crossed body-body) configurations of deformed nuclei collision can lead to presence of quadrupolar magnetic field which can have very important effects on the rapidity dependence of transverse expansion (similar to {\it beam focusing} from quadrupole fields in accelerators).

Coulomb-interaction-dependent effect of high-order sideband generation in an optomechanical system

High-order sideband generation in an optomechanical system coupled to a charged object is discussed, and the features of Coulomb-interaction-dependent effect are identified. We show that the Coulomb-interaction-dependent effect of high-order sideband generation exhibits essential difference between the case of weak control field and strong control field. In the weak control field case, the output spectra are in the perturbative regime and there is hardly any Coulomb-interaction-dependent effect in an optomechanical system coupling to an object with a small amount of charge. In the strong control field case, the output spectra are in the nonperturbative regime and robust Coulomb-interaction-dependent effect arises even if there are few charges. The amplitudes of specific sidebands are also discussed, and it is shown that Coulomb interaction plays an important role in achieving optomechanical control. Due to the extremely sensitive charge number, the Coulomb-interaction-dependent effect of high-order sideband generation is remarkable in many aspects and may be used to precision measurement of electrical charges beyond the linearized optomechanical interaction.

Order–disorder phase transitions in thin films described by transverse Ising model

Abstract The order–disorder phase transition in thin films at finite temperature and zero temperature (quantum phase transition) is discussed within the transverse Ising model using molecular field approximation. Experimentally, it is shown that the Curie temperature TC of perovskite PbTiO3 ultra-thin film decreases with decreasing film thickness. We obtain an equation for TC of thin film in external magnetic and transverse fields. Our equation explains well for the case of strong transverse strain field this behaviour.

Magnetohydrodynamical simulation of the formation of clumps and filaments in quiescent diffuse medium by thermal instability

We have used the AMR hydrodynamic code, MG, to perform idealised 3D MHD simulations of the formation of clumpy and filamentary structure in a thermally unstable medium without turbulence. A stationary thermally unstable spherical diffuse atomic cloud with uniform density in pressure equilibrium with low density surroundings was seeded with random density variations and allowed to evolve. A range of magnetic field strengths threading the cloud have been explored, from beta=0.1 to beta=1.0 to the zero magnetic field case (beta=infinity), where beta is the ratio of thermal pressure to magnetic pressure. Once the density inhomogeneities had developed to the point where gravity started to become important, self-gravity was introduced to the simulation. With no magnetic field, clouds and clumps form within the cloud with aspect ratios of around unity, whereas in the presence of a relatively strong field (beta=0.1) these become filaments, then evolve into interconnected corrugated sheets that are predominantly perpendicular to the magnetic field. With magnetic and thermal pressure equality (beta=1.0), filaments, clouds and clumps are formed. At any particular instant, the projection of the 3D structure onto a plane parallel to the magnetic field, i.e. a line of sight perpendicular to the magnetic field, resembles the appearance of filamentary molecular clouds. The filament densities, widths, velocity dispersions and temperatures resemble those observed in molecular clouds. In contrast, in the strong field case beta=0.1, projection of the 3D structure along a line of sight parallel to the magnetic field reveals a remarkably uniform structure.

強磁場下における磁性微粒子の薄膜形成に関するブラウン動力学シミュレーション

強磁場下における磁性微粒子の薄膜形成に関するブラウン動力学シミュレーション

Nonlinear dynamics of an optomechanical system with a coherent mechanical pump: Second-order sideband generation

Second-order sideband generation in a coherent-mechanical pumped optomechanical system is discussed, and the features of the coherent mechanical pump induced enhancement of second-order sideband generation are identified. We show that the coherent mechanical pump induced enhancement of second-order sideband generation exhibits an essential difference between the case of a weak control field and a strong control field. In the weak control field case, the efficiency of second-order sideband generation increases as the amplitude of the mechanical pump increases. In the strong control field case, the effect of optomechanically induced transparency occurs and increasing the amplitude of the mechanical pump does not always bring an enhancement of second-order sideband generation. The phase-dependent effect of the second-order sideband generation with a coherent mechanical pump is also discussed, and it is shown that the phase difference ϕ plays an important role in the process of second-order sideband generation.

Holographic model for the paramagnetism/antiferromagnetism phase transition

In this paper we build a holographic model of paramagnetism/antiferromagnetism phase transition, which is realized by introducing two real antisymmetric tensor fields coupling to the background gauge field strength and interacting with each other in a dyonic black brane background. In the case without external magnetic field and in low temperatures, the magnetic moments condense spontaneously in antiparallel manner with the same magnitude and the time reversal symmetry is also broken spontaneously (if boundary spatial dimension is more than 2, spatial rotational symmetry is broken spontaneously as well), which leads to an antiferromagnetic phase. In the case with weak external magnetic field, the magnetic susceptibility density has a peak at the critical temperature and satisfies the Curie-Weiss law in the paramagnetic phase of antiferromagnetism. In the strong external magnetic field case, there is a critical magnetic field $B_c$ in antiferromagnetic phase: when magnetic field reaches $B_c$, the system will return into the paramagnetic phase by a second order phase transition.