Moments Of Particles Research Articles

Particle Spin Described by Quantum Hamilton Equations

AbstractThe anomalous Zeeman effect made it clear that charged particles like the electron possess a magnetic dipole moment. Classically, this could be understood if the charged particle possesses an eigenrotation, that is, spin. Within Nelson's stochastic mechanics, it was shown that the model of a rotating charged ball is able to reproduce the well‐known spin expectation values. This classically motivated model of intrinsic rotation described in terms of a stochastic process is revisited here within the formalism of stochastic optimal control theory. Quantum Hamilton equations (QHE) for spinning particles are derived, which reduce to their classical counterpart in the zero quantum noise limit. These equations enable the calculation of the common spin expectation values without the use of the wave function. They also offer information on the orientation dynamics of the magnetic moment of charged particles beyond the behavior of the spin averages.

Effect of the electronic pressure on the energy and magnetic moment of charged test particles in turbulent electromagnetic fields

In this work, we perform direct numerical simulations of three-dimensional magnetohydrodynamics with a background magnetic field, representing solar wind plasma, and introduce test particles to explore how a turbulent electromagnetic environment affects them. Our focus is on the terms of the electric field present in the generalized Ohm's law that is usually dismissed as unimportant. These are the Hall and the electronic pressure (EP) terms, but we concentrate primarily on the latter. We discover that the EP term generates an acceleration of the particles, which represent protons, in the direction parallel to the background magnetic field, in contrast to the known preferential perpendicular energization. By studying the electric field itself, we are able to detect the type of structures of the EP field that produce such parallel acceleration. These are thin and elongated structures placed on top of a monotonic and near-zero background. A statistical study to understand the real significance of the electronic pressure term is also performed.

Relativistic second-order dissipative spin hydrodynamics from the method of moments

We derive relativistic second-order dissipative fluid-dynamical equations of motion for massive spin-1/2 particles from kinetic theory using the method of moments. Besides the usual conservation laws for charge, energy, and momentum, such a theory of relativistic dissipative spin hydrodynamics features an equation of motion for the rank-3 spin tensor, which follows from the conservation of total angular momentum. Extending the conventional method of moments for spin-0 particles, we expand the spin-dependent distribution function near local equilibrium in terms of moments of the momentum and spin variables. We work to next-to-leading order in the Planck constant $\hbar$. As shown in previous work, at this order in $\hbar$ the Boltzmann equation for spin-1/2 particles features a nonlocal collision term. From the Boltzmann equation, we then obtain an infinite set of equations of motion for the irreducible moments of the deviation of the single-particle distribution function from local equilibrium. In order to close this system of moment equations, a truncation procedure is needed. We employ the "14+24-moment approximation", where "14" corresponds to the components of the charge current and the energy-momentum tensor and "24" to the components of the spin tensor, which completes the derivation of the equations of motion of second-order dissipative spin hydrodynamics. For applications to heavy-ion phenomenology, we also determine dissipative corrections to the Pauli-Lubanski vector.

Multiplicity distribution of backward shower particle in total disintegrated events revisited with Weibull distribution

The well-known statistical distribution function, Weibull distribution function, has been employed to study the multiplicity distribution and multiplicity moments for the backward shower particles produced in case of total disintegrated events of [Formula: see text]O–AgBr, [Formula: see text]Ne–AgBr and [Formula: see text]Si–AgBr interactions at (4.1–4.5) AGeV/c. Multiplicity fluctuation of backward shower particles in case of total disintegrated events by the method of scaled variance and the forward–backward asymmetry parameter had also been investigated.

Effects of rotation on a magnetic quadrupole moment system around a cylindrical cavity

We analyze the interaction of the magnetic quadrupole moment of a neutral particle with magnetic and electric fields around a cylindrical cavity in a rotating reference frame. In contrast to the energy levels yielded by a Coulomb-type potential that stems from the interaction of the magnetic quadrupole moment with a nonuniform magnetic field, we show that the effects of rotation break the degeneracy of the energy levels. Moreover, we show that the effects of rotation can gives rise to an Aharonov-Bohm-type effect. Further, we discuss the appearance of persistent currents and the revival time.

(g−2)μ and screened modified gravity

We show how light scalar fields can account for the discrepancy between the theoretical and observed values of the anomalous magnetic moment of the (anti)muon. When coupled to both matter and photons, light scalar fields induce a change of the anomalous magnetic moment of charged particles. This arises from two concurrent effects. Classically, light scalars induce a change of the cyclotron frequency, complementing the electromagnetic effects coming from the magnetic and electric fields used experimentally. Light scalars also contribute to the anomalous magnetic moment quantum mechanically at the one-loop level. For unscreened scalar fields coupling with a Yukawa interaction to matter, these contributions are negligible after applying the Cassini bound on deviations from Newtonian gravity. On the other hand, screened scalars such as chameleons or symmetrons can couple strongly to matter in the laboratory and decouple in the Solar System. This allows us to probe branches of their parameter spaces where the recently measured anomalous magnetic moment of the (anti)muon can be accounted for in the chameleon and symmetron cases. This might be a hint that modified gravity is at play in the laboratory.

Dual Relativistic Quantum Mechanics I

In \cite{2} it was shown that Einstein's special theory of relativity and Maxwell's field theory have mathematically equivalent dual versions. The dual versions arise from an identity relating observer time to proper time as a contact transformation on configuration space, which leaves phase space invariant. The special theory has a dual version in the sense that, for any set of $n$ particles, every observer has two unique sets of global variables $({\bf{X}}, t)$ and $({\bf{X}}, \tau)$ to describe the dynamics, where ${\bf{X}}$ is the (unique) canonical center of mass. In the $({\bf{X}}, t)$ variables, time is relative and the speed of light is unique, while in the $({\bf{X}}, \tau)$ variables, time is unique and the speed of light is relative with no upper bound. In the Maxwell case, the two sets of particle wave equations are not equivalent. The dual version contains an additional longitudinal (dissipative) radiation term that appears instantaneously with acceleration, leading to the prediction that radiation from a betatron (of any frequency) will not produce photoelectrons. A major outcome is the dual unification of Newtonian mechanics and classical electrodynamics with Einstein's special theory of relativity, without a self-energy divergency, or need of the problematic Lorentz-Dirac equation or any assumptions about the size or structure of a particle. The purpose of this paper is to introduce and develop the dual theory of relativistic quantum mechanics. We obtain three distinct dual relativistic wave equations that reduce to the Schr{\"o}dinger equation when minimal coupling is turned off. We show that the dual Dirac equation provides a new formula for the anomalous magnetic moment of a charged particle. We can obtain the exact value for the electron g-factor and phenomenological values for the muon and proton g-factors.

Evolution of microstructure and magnetic properties from amorphous Fe3O4/SiO2 nanocomposite

Amorphous Fe3O4/SiO2 composite particles have been synthesized by using a one-pot sol-gel route. The evolution of Fe3O4 nanoparticles from the amorphous matrix on annealing temperatures up to 600 °C is identified through structural and vibrational mode studies. Electron microscopy measurements confirm that particles of 2–4 nm are embedded in the SiO2 matrix. The detailed analysis of temperature and field dependent magnetization data shows that a weak magnetic ground state of the as-prepared sample develops into a single domain state on annealing at 600 °C. Annealed samples exhibit higher magnetization values of ∼27 emu/g and coercivity of ∼1927 Oe at temperature of 2.5 K yet negligible spontaneous magnetization, suggesting short range magnetic order. A suitable distribution model with single domain particle assemblies is employed to analyze the particle size and moment distribution. From the analysis of M-T and M-H data it is found that interacting and non-interacting SPM models explain the data in different tampretaure ranges. We show magnetic interactions and anisotropy can be effectively controlled by the size and interparticle interactions of Fe3O4 nanoparticles. These particles are useful for the design of thermal seeds for magnetic hyperthermia.

The effect of inter-particle hydrodynamic and magnetic interactions in a magnetorheological fluid

A magnetorheological fluid, which consists of magnetic particles suspended in a viscous fluid, flows freely with well-dispersed particles in the absence of a magnetic field, but particle aggregation results in flow cessation when a field is applied. The mechanism of dynamical arrest is examined by analysing interactions between magnetic particles in a magnetic field subject to a shear flow. An isolated spherical magnetic particle undergoes a transition between a rotating state at low magnetic field and a static orientation at high magnetic field. The effect of interactions for spherical dipolar and polarisable particles with static orientation is examined for an unbounded dilute viscous suspension. There are magnetic interactions due to the magnetic field disturbance at one particle caused by the dipole moment of another, hydrodynamic interactions due to the antisymmetric force moment of a non-rotating particle in a shear flow, and a modification of the magnetic field due to the particle magnetic moment density. When there is a concentration variation, the torque balance condition results in a disturbance to the orientation of the particle magnetic moment. The net force and the drift velocity due to these disturbances is calculated, and the collective motion generated is equivalent to an anisotropic diffusion process. When the magnetic field is in the flow plane, the diffusion coefficients in the two directions perpendicular to the field direction are negative, implying that concentration fluctuations are unstable in these directions. This instability could initiate field-induced dynamical arrest in a magnetorheological fluid.

Aggregation phenomena and regime change in a magnetic cubic particle suspension in an alternating magnetic field via quasi-two-dimensional Brownian dynamics

We have addressed the aggregation phenomena of a cubic haematite particle suspension in an alternating magnetic field in order to investigate the regime change in the aggregate structure. Brownian dynamics simulations have been performed for a quasi-two-dimensional system with an alternating magnetic field applied in the plane of the system. In a weak alternating field, the cubic particles aggregate to form closely-packed structures tending to an aligned face-to-face configuration with increasing magnetic particle-particle interaction strength. In a closely-packed cluster, the orientation of the magnetic moment of a constituent particle tends to be more strongly influenced by the magnetic interaction between neighbouring particles and less influenced by the direction of the alternating magnetic field. As the strength of the applied field is increased, the particle moments become more restricted to the direction of the alternating field and the closely-packed structures transform into elongated aggregates with an offset face-to-face configuration. As the direction of the alternating magnetic field switches from the positive to the negative x-direction, the elongated aggregates tend to collapse temporarily and when the orientation of the moments is again strongly restricted to the switched field direction, elongated aggregate structures with offset face-to-face contact are re-formed in the system. Highlights of the present paper We have investigated a regime change in the internal structure of cubic particle aggregates in an alternating magnetic field. As the magnetic field strength is increased, closely-packed aggregates with an aligned face-to-face configuration transform into elongated aggregates with an offset face-to-face configuration. We have clarified that the elongated aggregates collapse temporarily and then re-form when the direction of the alternating magnetic field switches. We have suggested that the frequency of the magnetic field may be used as a means for controlling the local internal structure of particle aggregates.

Comparative study of magnetic moment of leptons in hot and dense media

We study the magnetic moment of leptons in extremely hot universe and superdense media of stars at high temperatures. Anomalous magnetic moment of charged leptons is inversely proportional to its mass, whereas the induced dipole moment of neutral leptons is directly proportional to their mass. Neutral massive point particles exert nonzero magnetic moment as a higher order effect, which is smaller than the anomalous magnetic moment of a charged particle of their same flavor partner. All leptons acquire some extra mass due to their interaction with the medium and affect the magnetic moment accordingly. We compare the contribution to the magnetic moment of various leptons due to their temperature and chemical potential dependent masses. It is shown that the magnetic moment contributions are nonignorable for lighter leptons and heavy neutrinos. These calculations are very important to study the particle propagation in the early universe and in superdense stellar media.

Geometric phase effect study in electric dipole moment rings

Several proposals to measure a possible small electric dipole moment (EDM) of charged particles aligned with the spin and the well-known magnetic dipole moment (MDM) are based on the concept to circulate bunches with an initial polarization in the horizontal plane and to observe the buildup of a vertical spin component caused by the EDM. Most proposals aim at operating the ring with ``frozen spin,'' such that, with an MDM only, the spin remains aligned with the trajectory. The signature of a finite EDM is the buildup of a vertical spin component. Machine imperfections may lead as well to a vertical spin buildup, which can be misinterpreted as an EDM and thus limit the sensitivity of the experiment. For that reason, a good understanding of spin dynamics is mandatory to estimate and limit such systematic errors in the measurement. In this paper, a coordinate system attached to the trajectory is introduced to expand the spin. This is of particular interest for fully electric EDM rings operated at the ``magic energy'' to satisfy the frozen spin condition. The procedure is used for a straightforward analysis of geometric phase and other second order effects, which limit the possible sensitivity, i.e., the smallest EDM which can be detected in presence of systematic effects.

Muon electric dipole moment as a probe of flavor-diagonal CP violation

Electric dipole moments (EDMs) of elementary particles are powerful probes of new physics with flavor-diagonal CP violation. The reported discrepancy in the muon anomalous magnetic moment motivates us to explore to what extent new physics with flavor-diagonal CP violation to address the discrepancy is probed by searches for the muon EDM. As a benchmark, we focus on a CP-violating two-Higgs-doublet model to explain the muon g−2 anomaly where the muon exclusively couples to one Higgs doublet. Since contributions to flavor violating processes as well as the electron EDM are suppressed, the muon EDM becomes an essential probe of the model. Our result shows that some viable parameter space leads to the muon EDM of around dμ≃6×10−23e cm probed by the PSI experiment and most of the parameter space is covered by the proposed J-PARC experiment.

Evolution of energy and magnetic moment of a quantum charged particle in power-decaying magnetic fields

We consider a quantum spinless nonrelativistic charged particle moving in the xy plane under the action of a homogeneous time-dependent magnetic field B(t)=B0(1+t/t0)−1−g, directed along the z-axis and described by means of the vector potential A(t)=B(t)[−y,x]/2. Assuming that the particle was initially in the thermal equilibrium state with a negligible coupling to a reservoir, we obtain exact formulas for the time-dependent mean values of the energy and magnetic moment in terms of the Bessel functions. Different regimes of the evolution are discovered and illustrated in several figures. The energy goes asymptotically to a finite value if g>0 (“fast” decay), while it goes asymptotically to zero if g≤0 (“slow” decay). The dependence on parameter t0 practically disappears when 1+g is close to zero value (“superslow” decay). The mean magnetic moment goes to zero for g>1, while it grows unlimitedly if g<1.

Oxygen nonstoichiometry and magnetic properties of doped manganites La0.7Sr0.3Mn0.95Fe0.05O3-δ

In this work, solid solutions of La0.7Sr0.3Mn0.95Fe0.05O3-δ with different oxygen content were obtained by the solid-phase reactions technique. Based on the investigation of the dynamics of changes in the oxygen index (3 – δ) during heating of the samples, the formation of a stressed state in their grains as a result of annealing was established. This results in a decrease in the mobility of oxygen vacancies during the reduction of cations according to the Mn4+ + e– → Mn3+ scheme and explains the decrease of released oxygen amount with an increase of δ as well as the heating rate of the samples. When studying the magnetic properties of the obtained samples, it was found that the temperature dependence of the magnetization obeys the Curie–Weiss law and as the oxygen defficiency increases, the Curie temperature for solid solutions decreases. It was found that the particles are in a frozen ferromagnetic state when measured in the low-temperature region of the М(Т) dependence in “zero-field mode” at Т ˂ ТВ. The presence of ferromagnetism at Т ˃ ТВ leads to a magnetically ordered state, in which the resulting magnetic moment of the magnetic particle is influenced by thermal fluctuations. When considering the temperature values of the magnetization of lanthanum-strontium manganite samples, it was found that with an increase of temperature in the low-temperature region, magnetic ordering is disturbed due to the excitation of magnons with a quadratic dependence of the energy from the wave vector, the number of which increases in proportion to T3/2. This results in a decrease in the manganite magnetization. The observed temperature dependence of the magnetization measured in the “field-cooling mode” was approximated taking into account the quadratic and non-quadratic dispersion laws of the magnon spectrum.

One-loop matching for quark dipole operators in a gradient-flow scheme

The quark chromoelectric dipole (qCEDM) operator is a CP-violating operator describing, at hadronic energies, beyond-the-standard-model contributions to the electric dipole moment of particles with nonzero spin. In this paper we define renormalized dipole operators in a regularization-independent scheme using the gradient flow, and we perform the matching at one loop in perturbation theory to renormalized operators of the same and lower dimension in the more familiar MS scheme. We also determine the matching coefficients for the quark chromo-magnetic dipole operator (qCMDM), which contributes for example to matrix elements relevant to CP-violating and CP-conserving kaon decays. The calculation provides a basis for future lattice QCD computations of hadronic matrix elements of the qCEDM and qCMDM operators.

Missing He–McKellar–Wilkens geometric quantum phase

We discuss the appearance of a missing geometric quantum phase from the interaction of the permanent electric dipole moment of a neutral particle with the magnetic field produced by a uniform distribution of the magnetic charges inside an infinitely long non-conductor cylinder with an inner radius r a . This geometric quantum phase is associated with the missing magnetic charge per unit length in a region with a cylindrical shape of radius r a and gives rise to an analogue of the He–McKellar–Wilkens geometric quantum phase. By searching for bound state solutions, we show that an Aharonov–Bohm-type effect arises from the influence of the missing geometric quantum phase on the eigenvalues of energy.

Geometric quantum phase from the interaction of the permanent electric dipole moment of a neutral particle with an axial magnetic field

Geometric quantum phase from the interaction of the permanent electric dipole moment of a neutral particle with an axial magnetic field

Oscillating magnetized hybrid stars under the magnifying glass of multimessenger observations

ABSTRACTWe model neutron stars as magnetized hybrid stars with an abrupt hadron–quark phase transition in their cores, taking into account current constraints from nuclear experiments and multimessenger observations. We include magnetic field effects considering the Landau level quantization of charged particles and the anomalous magnetic moment of neutral particles. We construct the magnetized hybrid equation of state, and we compute the particle population, the matter magnetization and the transverse and parallel pressure components. We integrate the stable stellar models, considering the dynamical stability for rapid or slow hadron–quark phase conversion. Finally, we calculate the frequencies and damping times of the fundamental and g non-radial oscillation modes. The latter, a key mode to learn about phase transitions in compact objects, is only obtained for stars with slow conversions. For low magnetic fields, we find that one of the objects of the GW170817 binary system might be a hybrid star belonging to the slow extended stability branch. For magnetars, we find that a stronger magnetic field always softens the hadronic equation of state. Besides, only for some parameter combinations a stronger magnetic field implies a higher hybrid star maximum mass. Contrary to previous results, the incorporation of anomalous magnetic moment does not affect the studied astrophysical quantities. We discuss possible imprints of the microphysics of the equation of state that could be tested observationally in the future, and that might help infer the nature of dense matter and hybrid stars.

Role of the surface effects and interparticle magnetic interactions in the temperature evolution of magnetic resonance spectra of ferrihydrite nanoparticle ensembles

Ferrihydrite is characterized by the antiferromagnetic ordering and, in ferrihydrite nanoparticles, as in nanoparticles of any antiferromagnetic material, an uncompensated magnetic moment is formed. We report on the investigations of ferrihydrite powder systems with an average particle size of ∼ 2.5 nm obtained (i) as a product of the vital activity of bacteria (sample FH-bact) and (ii) by a chemical method (sample FH-chem). In the first approximation, these samples can be considered to be identical. However, in sample FH-chem, particles contact directly, while in sample FH-bact, they have organic shells; therefore, the interparticle magnetic interactions in these samples have different degrees. The main goal of this work has been to establish the effects of the interparticle magnetic interactions and individual characteristics of ferrihydrite nanoparticles on ferromagnetic resonance (FMR) spectra. The FMR spectra have been measured at different (9.4–75 GHz) frequencies in a wide temperature range. It has been found that, at low temperatures, the field-frequency dependence ν(HR) of the investigated systems has a gap ν/γ = HR + HA, where HR is the resonance field and HA is the induced anisotropy, which decreases with increasing temperature. To estimate a degree of the effect of interparticle interactions on the results obtained and to correctly determine the temperature range of the superparamagnetic (or blocked) state, the static magnetic measurement and Mössbauer spectroscopy data have been obtained and analyzed. It has been shown that the most striking feature of the FMR spectra - a gap in the field-frequency dependences - is a manifestation of individual characteristics of ferrihydrite nanoparticles. The induced anisotropy is caused by freezing of a subsystem of surface spins and its coupling with the particle core, which is observed in both samples at a temperature of ∼80 K. The temperature range (below 80 K) in which the gap exists corresponds to the blocked state in the FMR technique. In sample FH-bact, the ratio between the FMR parameters HA and linewidth ΔH obeys the standard expression HA ∼ (ΔH)3. In sample FH-chem, however, the interparticle magnetic interactions dramatically affect the behavior of parameters of the FMR spectra, which change nonmonotonically upon temperature variation. This fact is attributed to the collective freezing of the magnetic moments of particles under the conditions of sufficiently strong interactions, which follows from the temperature dependence of the particle magnetic moment relaxation time determined from the Mössbauer spectroscopy and static magnetometry data obtained in weak magnetic fields.