Arbitrary External Magnetic Field Research Articles

Wavelength-division multiplexing optical Ising simulator enabling fully programmable spin couplings and external magnetic fields.

Recently various physical systems have been proposed for modeling Ising spin Hamiltonians appealing to solve combinatorial optimization problems with remarkable performance. However, how to implement arbitrary spin-spin interactions is a critical and challenging problem in unconventional Ising machines. Here, we propose a general gauge transformation scheme to enable arbitrary spin-spin interactions and external magnetic fields as well, by decomposing an Ising Hamiltonian into multiple Mattis-type interactions. With this scheme, a wavelength-division multiplexing spatial photonic Ising machine (SPIM) is developed to show the programmable capability of general spin coupling interactions. We exploit the wavelength-division multiplexing SPIM to simulate three spin systems: ±J models, Sherrington-Kirkpatrick models, and only locally connected J1-J2 models and observe the phase transitions. We also demonstrate the ground-state search for solving Max-Cut problem with the wavelength-division multiplexing SPIM. These results promise the realization of ultrafast-speed and high-power efficiency Boltzmann sampling to a generalized large-scale Ising model.

Decomposition of the induced magnetism degaussing problem for fast determination of currents in demagnetization coils wrapped outside an object under arbitrary external field conditions

Safe passage of ships in the presence of sea mines can be ensured by limiting or reducing the ship’s magnetic footprint. For vessels with plastic hulls, the main component that requires magnetic damping is the engine. Demagnetization of such an object can be achieved by wrapping it with coils and setting the direct current appropriately. For each specific geographic location, the currents in the coils can be determined iteratively from measurements of the magnetic signature in the cardinal directions. In this paper the magnetic signatures are calculated using decomposition-based approach for each coil and each component of the external field separately. Hence the overall magnetic signature of the object can be reproduced in arbitrary external magnetic field (i.e. anywhere on the Earth). Knowing the influence of each coil, it is possible to formulate the optimization task (signature minimization) and determine the currents. The presented method is verified in FEM software with the use of engine models of both symmetrical and asymmetrical shapes. Since the determination of the currents takes place as a result of solving the optimization problem, the effectiveness of obtaining the results, the speed of convergence and the dependence on initial conditions is under investigation. The effect of the model mesh size on the quality of object signature reduction is also analyzed. The developed method can be used for a real object. In that case acquiring the data then requires the measurements of the object placed inside the Helmholtz coils.

Phase diagrams of Kitaev models for arbitrary magnetic field orientations

The Kitaev model is an exactly solvable quantum spin model within the language of constrained real fermions. In spite of numerous studies for magnetic fields along special orientations, there is a limited amount of knowledge on the complete field-angle characterization, which can provide valuable information on the existence of fractionalized excitations. For this purpose, we first study the pure ferromagnetic and antiferromagnetic Kitaev models for arbitrary external magnetic field directions via a mean-field theory, showing that there are many topological phases with different (or zero) Chern numbers, depending on the magnetic field strength and orientations. However, a realistic description of the candidate Kitaev materials, within the edge-sharing octahedra paradigm, requires additional coupling terms, including a large off-diagonal term $\mathrm{\ensuremath{\Gamma}}$ along with possible anisotropic corrections ${\mathrm{\ensuremath{\Gamma}}}_{p}$. It is therefore not sufficient to rely on the topological properties of the bare Kitaev model as the basis for the observed thermal Hall-conductivity signals, and an understanding of these extended Kitaev models with a complete field response is demanded. Starting from the zero-field phase diagram of $\mathrm{K}\text{\ensuremath{-}}\mathrm{\ensuremath{\Gamma}}\text{\ensuremath{-}}{\mathrm{\ensuremath{\Gamma}}}_{p}$ models, we identify, besides the Kitaev spin liquid phase, antiferromagnetic zigzag, ferromagnetic phases, as well as an unusual Kitaev(-$\mathrm{\ensuremath{\Gamma}}$) spin liquid phase. The magnetic field response of these phases for arbitrary field orientations provides a remarkably rich phase diagram. For an extended parameter range and just above the critical field where the zigzag phase is suppressed, there is an intermediate phase region with suppressed energy gaps and substantial spin fractionalization. To comply our findings with experiments, we also reproduce a large asymmetry in the extent of this intermediate phases specifically for the two different field directions $\ensuremath{\theta}=\ifmmode\pm\else\textpm\fi{}{60}^{o}$ with respect to the normal to the plane of the honeycomb lattice.

The Generalized Lipkin-Meshkov-Glick Model and the Modified Algebraic Bethe Ansatz

We show that the Lipkin-Meshkov-Glick 2N-fermion model is a particular case of one-spin Gaudin-type model in an external magnetic field corresponding to a limiting case of non-skew-symmetric elliptic r-matrix and to an external magnetic field directed along one axis. We propose an exactly-solvable generalization of the Lipkin-Meshkov-Glick fermion model based on the Gaudin-type model corresponding to the same r-matrix but arbitrary external magnetic field. This model coincides with the quantization of the classical Zhukovsky-Volterra gyrostat. We diagonalize the corresponding quantum Hamiltonian by means of the modified algebraic Bethe ansatz. We explicitly solve the corresponding Bethe-type equations for the case of small fermion number N=1,2.

Lepton pair production from a hot and dense QCD medium in the presence of an arbitrary magnetic field

In this article, we have explored the very important quantity of lepton pair production from a hot and dense QCD medium in presence of an arbitrary external magnetic field for simultaneous nonzero values of both the parallel (along the direction of the external field) and perpendicular (lying on the transverse plane to the external field) components of the dilepton momentum. As opposed to the zero magnetic field case (the so-called Born rate) or the lowest Landau level approximated rate, where only the annihilation process contributes, here we observe contributions also arising out of the quark and antiquark decay processes. We found the encouraging result of considerable enhancement of lepton pair production in presence of an arbitrary magnetic field. We decompose the total rate into different physical processes and discuss their behaviors for both zero and nonzero baryon density. The whole analysis is then subjected to an effective model treatment, where we have incorporated the magnetic field induced novel effects of magnetic catalysis (MC) and inverse MC (IMC) through a medium dependent scalar coupling, which leads to some further interesting observations.

Thermomagnetic modification of the anomalous magnetic moment of quarks using the NJL model

The effective photon-quark-antiquark ($\gamma q \overline{q}$) vertex function is evaluated at finite temperature in the presence of an arbitrary external magnetic field using the two-flavor gauged Nambu--Jona-Lasinio (NJL) model in the mean field approximation. The lowest order diagram contributing to the magnetic form factor and the anomalous magnetic moment (AMM) of the quarks is calculated at finite temperature and external magnetic field using the imaginary time formalism of finite temperature field theory and the Schwinger proper time formalism. The Schwinger propagator including all the Landau levels with non-zero AMM of the dressed quarks is considered while calculating the loop diagram. Using sharp as well as smooth three momentum cutoff, we regularize the UV divergences arising from the vertex function and the parameters of our model are chosen to reproduce the well known phenomenological quantities at zero temperature and zero magnetic field, such as pion-decay constant ($f_\pi$), vacuum quark condensate, vacuum pion mass ($m_\pi$) as well as the magnetic moments of proton and neutron. We then study the temperature and magnetic field dependence of the AMM and constituent mass of the quark. We found that, the AMM as well as the constituent quark mass are large at the chiral symmetry broken phase in the low temperature region. Around the pseudo-chiral phase transition they decrease rapidly and at high temperatures both of them approach vanishingly small values in the symmetry restored phase.

One-loop Kubo estimations of the shear and bulk viscous coefficients for hot and magnetized bosonic and fermionic systems

The expressions of the shear viscosity and the bulk viscosity components in the presence of an arbitrary external magnetic field for a system of hot charged scalar bosons (spin 0) as well as for a system of hot charged Dirac fermions (spin $\frac{1}{2}$) have been derived by employing the one-loop Kubo formalism. This is done by explicitly evaluating the thermomagnetic spectral functions of the energy-momentum tensors using the real time formalism of finite temperature field theory and the Schwinger proper time formalism. In the present work, a rich quantum field theoretical structure in the expressions of the viscous coefficients in nonzero magnetic field are found, which are different from their respective expressions obtained earlier via kinetic-theory-based calculations; though, in the absence of a magnetic field, the one-loop Kubo and the kinetic-theory-based expressions for the viscosities are known to be identical. We have identified that Kubo and kinetic-theory-based results of viscosity components follow a similar kind of temperature and magnetic field dependency. The relaxation time and the synchrotron frequency in the kinetic theory formalism are realized to be connected, respectively, with the thermal width of propagator and the transitions among the Landau levels of the charged particles in the Kubo formalism. We believe that the connection of the latter quantities is quite new and probably the present work is the first time addressing this interpretation along with the new expressions of viscosity components, not seen in existing works.

Noncommutativity of the static and homogeneous limit of the axial chemical potential in the chiral magnetic effect

We study the noncommutativity of different orders of zero energy-momentum limit pertaining to the axial chemical potential in the chiral magnetic effect. While this noncommutativity issue originates from the pinching singularity at one-loop order, it cannot be removed by introducing a damping term to the fermion propagators. The physical reason is that modifying the propagator alone would violate the axial-vector Ward identity and as a result a modification of the longitudinal component of the axial-vector vertex is required, which contributes to chiral magnetic effect (CME). The pinching singularity with free fermion propagators was then taken over by the singularity stemming from the dressed axial-vector vertex. We show this mechanism by a concrete example. Moreover, we proved, in general, the vanishing CME in the limit order that the static limit was taken prior to the homogeneous limit in the light of Coleman-Hill theorem for a static external magnetic field. For the opposite limit that the homogeneous limit is taken first, we show that the nonvanishing CME was a consequence of the nonrenormalization of chiral anomaly for an arbitrary external magnetic field.

Effects of the anomalous magnetic moment of quarks on the dilepton production from hot and dense magnetized quark matter using the NJL model

Dilepton production rate (DPR) from hot and dense quark matter is studied in the presence of an arbitrary external magnetic field using the 2-flavour Nambu--Jona-Lasinio (NJL) model. The anomalous magnetic moment (AMM) of the quarks is taken into consideration while calculating the constituent quark mass as well as the DPR from the thermo-magnetic medium. An infinite number of quark Landau levels is incorporated so that no approximations are made on the strength of the background magnetic field. The analytic structure of the two point vector current correlation function in the complex energy plane reveals that, in addition to the usual Unitary cut, a non-trival Landau cut appears in the physical kinematic domains solely due to the external magnetic field. Moreover, these kinematic domains of the Unitary and Landau cuts are found to be significantly modified due to the AMM of the quarks. With finite AMM of the quarks, for certain values of the external magnetic field, the kinematically forbidden gap between the Unitary and Landau cuts are shown to vanish leading to the generation of a continuous spectrum of dilepton emission over the whole invariant mass region not observed earlier.

Effect of the anomalous magnetic moment of quarks on the phase structure and mesonic properties in the NJL model

Employing a field dependent three-momentum cut-off regularization technique, we study the phase structure and mesonic masses using the $2$-flavour Nambu-Jona Lasinio model at finite temperature and density in presence of arbitrary external magnetic field. This approach is then applied to incorporate the effects of the anomalous magnetic moment(AMM) of quarks on constituent quark mass and thermodynamic observables as a function of temperature/baryonic density. The critical temperature for transition from chiral symmetry broken to the restored phase is observed to decrease with the external magnetic field, which can be classified as inverse magnetic catalysis, while an opposite behaviour is realized in the case of a vanishing magnetic moment, implying magnetic catalysis. These essential features are also reflected in the phase diagram. Furthermore, the properties of the low lying scalar and neutral pseudoscalar mesons are also studied in presence of a hot and dense magnetized medium including AMM of the quarks using random phase approximation. For non-zero values of magnetic field, we notice a sudden jump in the mass of the Goldstone mode at and above the Mott transition temperature which is found to decrease substantially with the increase in magnetic field when the AMM of the quarks are taken into consideration.

A New Approach to Calculate the Shielding Factor of Magnetic Shields Comprising Nonlinear Ferromagnetic Materials under Arbitrary Disturbances

To enable the realization of ultra-low magnetic fields for scientific and technological research, magnetic shielding is required to create a space with low residual magnetic field and high shielding factors. The shielding factors of magnetic shields are due to nonlinear material properties, the geometry and structure of the shields, and the external magnetic fields. Magnetic shielding is used in environments full of random realistic disturbances, resulting in an arbitrary and random external magnetic field, and in this case, the shielding effect is hard to define simply by the shielding factors. A new method to simulate and predict a dynamic internal space magnetic field wave is proposed based on the Finite Element method (FEM) combined with the Jiles-Atherton (JA) model. By simulating the hysteresis behavior of the magnetic shields and establishing a dynamic model, the new method can simulate dynamic magnetic field changes inside magnetic shields as long as the external disturbances are known. The shielding factors under an AC external field with a sine wave and certain frequencies are calculated to validate the feasibility of the new method. A real-time wave of internal magnetic flux density under an AC triangular wave external field is simulated directly with the new method versus a method that splits the triangular wave into several sine waves by a Fourier transform, divides the shielding factors, and then adds the quotients together. Moreover, real-time internal waves under some arbitrary fields are measured. Experimental internal magnetic flux density waves of a 4-layer magnetically shielded room (MSR) at the Harbin Institute of Technology (HIT) fit the simulated results well, taking experimental errors into account.

Electromagnetic spectral function and dilepton rate in a hot magnetized QCD medium

The dilepton production rate in hot QCD medium is studied within a effective description of the medium in the presence of magnetic field. This could be done by obtaining the one-loop self energy of photon due to the effective (quasi-) quark loop at finite temperature under an arbitrary external magnetic field while employing the real time formalism of Thermal Field Theory. The effective quarks and gluons encode hot QCD medium effective in terms of their respective effective fugacities. The magnetic field enters in the form of landau level quantization, in the matter sector (quarks, antiquarks). The full Schwinger proper time propagator including all the Landau levels is considered for the quasi quarks while calculating the photon self energy. The electromagnetic Debye screening (in terms of the self-energy) has seen to be influenced both by the hot QCD medium effects and magnetic field. Analogous results are also obtained from the semi classical transport theory. The imaginary part of the photon self energy function is obtained from the discontinuities of the self energy across the Unitary cuts which are also present at zero magnetic field and the Landau cuts which are purely due to the magnetic field. The dilepton production rate is then obtained in terms of the product of electromagnetic spectral functions due to quark loop and lepton loop. The modifications of both the quarks/antiquarks as well as leptons in presence of an arbitrary external magnetic field have been considered in the formalism. Significant enhancement of the low invariant mass dileptons due the appearance of the Landau cuts in the electromagnetic spectral function at finite external magnetic field has been observed. A substantial enhancement of dilepton rate is also found when the EOS effects are considered through the effective quarks/antiquraks.

Thermodynamic model of a solid with RKKY interaction and magnetoelastic coupling

Thermodynamic description of a model system with magnetoelastic coupling is presented. The elastic, vibrational, electronic and magnetic energy contributions are taken into account. The long-range RKKY interaction is considered together with the nearest-neighbour direct exchange. The generalized Gibbs potential and the set of equations of state are derived, from which all thermodynamic functions are self-consistently obtained. Thermodynamic properties are calculated numerically for FCC structure for arbitrary external pressure, magnetic field and temperature, and widely discussed. In particular, for some parameters of interaction potential and electron concentration corresponding to antiferromagnetic phase, the existence of negative thermal expansion coefficient is predicted.

Magnetically-driven medical robots: An analytical magnetic model for endoscopic capsules design

Magnetic-based approaches are highly promising to provide innovative solutions for the design of medical devices for diagnostic and therapeutic procedures, such as in the endoluminal districts. Due to the intrinsic magnetic properties (no current needed) and the high strength-to-size ratio compared with electromagnetic solutions, permanent magnets are usually embedded in medical devices. In this paper, a set of analytical formulas have been derived to model the magnetic forces and torques which are exerted by an arbitrary external magnetic field on a permanent magnetic source embedded in a medical robot. In particular, the authors modelled cylindrical permanent magnets as general solution often used and embedded in magnetically-driven medical devices. The analytical model can be applied to axially and diametrically magnetized, solid and annular cylindrical permanent magnets in the absence of the severe calculation complexity. Using a cylindrical permanent magnet as a selected solution, the model has been applied to a robotic endoscopic capsule as a pilot study in the design of magnetically-driven robots.

An immersed‐boundary finite‐volume method for direct simulation of flows with suspended paramagnetic particles

AbstractIn the present study, we have proposed an immersed‐boundary finite‐volume method for the direct numerical simulation of flows with inertialess paramagnetic particles suspended in a nonmagnetic fluid under an external magnetic field without the need for any model such as the dipole–dipole interaction. In the proposed method, the magnetic field (or force) is described by the numerical solution of the Maxwell equation without current, where the smoothed representation technique is employed to tackle the discontinuity of magnetic permeability across the particle–fluid interface. The flow field, on the other hand, is described by the solution of the continuity and momentum equations, where the discrete‐forcing‐based immersed‐boundary method is employed to satisfy the no‐slip condition at the interface. To validate the method, we performed numerical simulations on the two‐dimensional motion of two and three paramagnetic particles in a nonmagnetic fluid subjected to an external uniform magnetic field and then compared the results with the existing finite‐element and semi‐analytical solutions. Comparison shows that the proposed method is robust in the direct simulation of such magnetic particulate flows. This method can be extended to more general flows without difficulty: three‐dimensional particulate flows, flows with a great number of particles, or flows under an arbitrary external magnetic field. Copyright © 2010 John Wiley & Sons, Ltd.

Non-equilibrium reversible dynamics of work production in four-spin system in a magnetic field

A closed system of the equations for the local Bloch vectors and spin correlation functions is obtained by decomplexification of the Liouville-von Neumann equation for 4 magnetic particles with the exchange interaction that takes place in an arbitrary time-dependent external magnetic field. The analytical and numerical analysis of the quantum thermodynamic variables is carried out depending on separable mixed initial state and the magnetic field modulation. Under unitary evolution, non-equilibrium reversible dynamics of power production in the finite environment is investigated.

On the First Critical Field in Ginzburg–Landau Theory for Thin Shells and Manifolds

In this article, we investigate the response of a thin superconducting shell to an arbitrary external magnetic field. We identify the intensity of the applied field that forces the emergence of vortices in minimizers, the so-called first critical field Hc1 in Ginzburg–Landau theory, for closed simply connected manifolds and arbitrary fields. In the case of a simply connected surface of revolution and vertical and constant field, we further determine the exact number of vortices in the sample as the intensity of the applied field is raised just above Hc1. Finally, we derive via Γ-convergence similar statements for three-dimensional domains of small thickness, where in this setting point vortices are replaced by vortex lines.

Computation of electron cloud diagnostics and mitigation in the main injector

High-performance computations on Blue Gene/P at Argonne's Leadership Computing Facility have been used to determine phase shifts induced in injected RF diagnostics as a function of electron cloud density in the Main Injector. Inversion of the relationship between electron cloud parameters and induced phase shifts allows us to predict electron cloud density and evolution over many bunch periods. Long time-scale simulations using Blue Gene have allowed us to measure cloud evolution patterns under the influence of beam propagation with realistic physical parameterizations, such as elliptical beam pipe geometry, self-consistent electromagnetic fields, space charge, secondary electron emission, and the application of arbitrary external magnetic fields. Simultaneously, we are able to simulate the use of injected microwave diagnostic signals to measure electron cloud density, and the effectiveness of various mitigation techniques such as surface coating and the application of confining magnetic fields. These simulations provide a baseline for both RF electron cloud diagnostic design and accelerator fabrication in order to measure electron clouds and mitigate the adverse effects of such clouds on beam propagation.

Fisher zeros of the Ising antiferromagnet in an arbitrary nonzero magnetic field

From the exact partition functions of the Ising model on L x L square lattices (up to L = 14) in an arbitrary nonzero external magnetic field H, the precise distributions of the Fisher zeros in the complex temperature (a = e(2betaJ)) plane are obtained. Our results indicate that in the limit L-->infinity the Fisher zeros for H not = 0 do cut the positive real axis at the antiferromagnetic critical point ac(H); these values are compared with the results of closed-form approximations for the antiferromagnetic critical line. From the Fisher zeros the thermal scaling exponent yt = 1 is also obtained along the critical line, indicating the logarithmic singularity of the specific heat for the antiferromagnetic Ising model even in a strong uniform magnetic field.

Density of Yang–Lee zeros and Yang–Lee edge singularity for the antiferromagnetic Ising model

The microcanonical transfer matrix is used to evaluate the exact partition function of the antiferromagnetic (AF) Ising model on L × L square lattices in an arbitrary nonzero external magnetic field at arbitrary temperature. The precise distribution of the Yang–Lee zeros in the complex x = e − 2 β H plane for the AF Ising model is determined as a function of temperature. Some of the Yang–Lee zeros for the AF Ising model lie on the negative real x axis, and the number of the zeros on the negative real axis is increased as temperature increases. The zeros on the negative real axis accumulate at their right end x e . In the thermodynamic limit ( L → ∞ ), the density of the zeros g ( x ) on the negative real axis of the AF Ising model diverges at x e for all temperatures. Therefore, the AF Ising model has the Yang–Lee edge singularity x e whose existence has been known in the ferromagnetic models only for T > T c . For the AF Ising model the density of zeros near x e is given by g ( x ) ∼ ( x − x e ) − 1 / 6 , in the same way for the ferromagnetic models.