Radiation-induced fermion resonance

The Dirac equation is solved for two novel terms which describe the interaction energy between the half-integral spin of a fermion and the classical, circularly polarized, electromagnetic field. A simple experiment is suggested to test the new terms and the existence of radiation-induced fermion resonance.     

自旋-轨道耦合对磁性绝缘体磁光Kerr效应的影响

采用单原子能级跃迁模型,导出在同时考虑自旋交换劈裂和自旋轨道耦合时磁光Kerr旋转的微观表达式,并就四能级跃迁情况,研究了磁光效应随原子基态及激发态能级自旋轨道耦合常数的变化规律.结果表明:磁光Kerr旋转角与自旋轨道耦合劈裂能量不成正比;单原子能级自旋轨道耦合常数为正或中间激发态自旋轨道耦合常数为负时,有利于提高磁光Kerr旋转. 关键词： 磁光Kerr效应 自旋轨道耦合 线性响应核 劈裂     

Supersymmetrization of Quaternion Dirac Equation for Generalized Fields of Dyons

The quaternion Dirac equation in presence of generalized electromagnetic field has been discussed in terms of two gauge potentials of dyons. Accordingly, the supersymmetry has been established consistently and thereafter the one, two and component Dirac Spinors of generalized quaternion Dirac equation of dyons for various energy and spin values are obtained for different cases in order to understand the duality invariance between the electric and magnetic constituents of dyons.     

Phenomenological description of relativistic-quark interaction on the basis of the Dirac equation with the Cornell potential

Relativistic-quark interaction is described phenomenologically on the basis of the Dirac equation with the Cornell potential. A general form of the initial equation involving the vector and scalar components of the Cornell potential is used for the case of an arbitrary relation between them. The Hamiltonian in the Foldy–Wouthuysen representation is derived in a general form with allowance for electromagnetic interaction. In contrast to earlier investigations, it is relativistic and exact for the zeroth- and first-order terms in the Planck constant and also for those second-order terms that describe contact interactions. General quantum-mechanical equations of motion for the momentum and spin are derived, and the classical limit of the Hamiltonian and for the equations of motion is found for the first time. A relation between the angular velocity of quark spin precession and the force acting on the quark is obtained. The energy of spin–orbit interaction is rather high (on the order of 100 MeV). Terms that describe spin–orbit and contact interactions have opposite signs for the vector and scalar components of the Cornell potential. The evolution of the quark helicity and the spin–spin interaction of the quarks are also calculated.     

Pseudospin and spin symmetry in the Dirac equation with Woods-Saxon potential and tensor potential

The Dirac equation is solved approximately for the Woods-Saxon potential and a tensor potential with the arbitrary spin-orbit coupling quantum number k \kappa under pseudospin and spin symmetry. The energy eigenvalues and the Dirac spinors are obtained in terms of hypergeometric functions. The energy eigenvalues are calculated numerically.     

Relativistic symmetries in the Hulthn scalar-vector-tensor interactions

In the presence of spin and pseudospin (p-spin) symmetries, the approximate analytical bound states of the Dirac equation for scalar-vector-tensor Hulthn potentials are obtained with any arbitrary spin-orbit coupling number κ using the Pekeris approximation. The Hulthn tensor interaction is studied instead of the commonly used Coulomb or linear terms. The generalized parametric Nikiforov-Uvarov (NU) method is used to obtain energy eigenvalues and corresponding wave functions in their closed forms. It is shown that tensor interaction removes degeneracy between spin and p-spin doublets. Some numerical results are also given.     

Spin polarization effects and their time evolutions

The time evolution of the density corresponding to the polarization operator, originally constructed to commute with the Dirac Hamiltonian in the absence of an external electromagnetic field, is investigated in terms of the time-dependent Dirac equation taking the presence of an external electromagnetic field into account. It is found that this time evolution leads to ‘tensorial’ and ‘vectorial’ particle current densities and to the interaction of the spin density with the external electromagnetic field. As the time evolution of the spin density does not refer to a constant of motion (continuity condition) it only serves as auxiliary density. By taking the non-relativistic limit, it is shown that the polarization, spin and magnetization densities are independent of electric field effects and, in addition, no preferred directions can be defined.     

球对称动态黑洞的量子能层效应

用Newman-Penrose形式,研究了球对称动态时空中的引力、电磁、标量和Dirac场,表明量子能层会影响动态黑洞的辐射机制.与Kerr能层和电磁势产生的经典效应不同,这个效应的特征是辐射机制明显依赖于自旋态. 关键词：     

The electromagnetic coupling in Kemmer-Duffin-Petiau theory

We analyze the electromagnetic coupling in the Kemmer-Duffin-Petiau (KDP) equation. Since the KDP equation which describes spin-0 and spin-1 bosons is of Dirac type, we examine some analogies with and differences from the Dirac equation. The main difference with the Dirac equation is that the KDP equation contains redundant components. We will show that as a result certain interaction terms in the Hamilton form of the KDP equation do not have a physical meaning and will not affect the calculation of physical observables. We point out that a second order KDP equation derived by Kemmer as an analogy to the second order Dirac equation is of limited physical applicability as (i) it belongs to a class of second order equations which can be derived from the original KDP equation and (ii) it lacks a back-transformation which would allow one to obtain solutions of the KDP equation out of solutions of the second order equation.     

Relativistic Symmetries in the Hulthén-like Potential and Tensor Interaction

In the presence of spin and pseudospin (p-spin) symmetries, the approximate analytical bound states of the Dirac equation for Hulthén-like potential including a Coulomb-like tensor interaction are obtained with any arbitrary spin–orbit coupling number κ using the Pekeris approximation. The generalized parametric Nikiforov–Uvarov (NU) method is used to obtain the energy eigenvalues and the corresponding wave functions in their closed forms. We show that tensor interaction removes degeneracies between spin and p-spin doublets. Some numerical results are also given.     

Spontaneous creation of massive spin half particles by a rotating block hole

The techniques of second quantization in Kerr metric for the scalar and neutrino (massless) fields are extended to the massive spin half case. The normal modes of Dirac field in Kerr metric are obtained in Chandrasekhar’s representation and the field is quantized as usual by imposing equal-time anti-commutation relations. The vacuum expectation value of energy-momentum tensor is evaluated asymptotically, leading to the result that a Kerr black hole spontaneously creates, in addition to scalar and neutrino quanta, massive Dirac particles in the classical superradiant modes.     

Quaternion Dirac Equation and Supersymmetry

Quaternion Dirac equation has been analyzed and its supersymmetrization has been discussed consistently. It has been shown that the quaternion Dirac equation automatically describes the spin structure with its spin up and spin down components of two component quaternion Dirac spinors associated with positive and negative energies. It has also been shown that the supersymmetrization of quaternion Dirac equation works well for different cases associated with zero mass, nonzero mass, scalar potential and generalized electromagnetic potentials. Accordingly we have discussed the splitting of supersymmetrized Dirac equation in terms of electric and magnetic fields.     

Introduction to Topological Phases and Electronic Interactions in (2+1) Dimensions

A brief introduction to topological phases is provided, considering several two-band Hamiltonians in one and two dimensions. Relevant concepts of the topological insulator theory, such as: Berry phase, Chern number, and the quantum adiabatic theorem, are reviewed in a basic framework, which is meant to be accessible to non-specialists. We discuss the Kitaev chain, SSH, and BHZ models. The role of the electromagnetic interaction in the topological insulator theory is addressed in the light of the pseudo-quantum electrodynamics (PQED). The well-known parity anomaly for massless Dirac particle is reviewed in terms of the Chern number. Within the continuum limit, a half-quantized Hall conductivity is obtained. Thereafter, by considering the lattice regularization of the Dirac theory, we show how one may obtain the well-known quantum Hall conductivity for a single Dirac cone. The renormalization of the electron energy spectrum, for both small and large coupling regime, is derived. In particular, it is shown that massless Dirac particles may, only in the strong correlated limit, break either chiral or parity symmetries. For graphene, this implies the generation of Landau-like energy levels and the quantum valley Hall effect.     

Hawking radiation of scalar and Dirac quanta from a Kerr black hole

Unruh’s technique of replacing collapse by boundary conditions on the past horizon (theξ-quantisation scheme) for the derivation of the well-known Hawking radiation is extended to the Kerr black hole for the scalar and especially for the spin half field. The expectation value of the energy momentum tensor is evaluated asymptotically in theξ-vacuum state yielding explicitly the net Hawking flux of scalar and spin half quanta. The appropriate statistical distribution that emerges naturally for Dirac quanta validates the ξ-scheme for fermions and confirms the association of temperature with a Kerr black hole.     

Particle-like solutions of the Einstein–Dirac–Maxwell equations

We consider the coupled Einstein–Dirac–Maxwell equations for a static, spherically symmetric system of two fermions in a singlet spinor state. Soliton-like solutions are constructed numerically. The stability and the properties of the ground state solutions are discussed for different values of the electromagnetic coupling constant. We find solutions even when the electromagnetic coupling is so strong that the total interaction is repulsive in the Newtonian limit. Our solutions are regular and well-behaved; this shows that the combined electromagnetic and gravitational self-interaction of the Dirac particles is finite.     

Spin force and torque in non-relativistic Dirac oscillator on a sphere

The spin force operator on a non-relativistic Dirac oscillator (in the non-relativistic limit the Dirac oscillator is a spin one-half 3D harmonic oscillator with strong spin–orbit interaction) is derived using the Heisenberg equations of motion and is seen to be formally similar to the force by the electromagnetic field on a moving charged particle. When confined to a sphere of radius R, it is shown that the Hamiltonian of this non-relativistic oscillator can be expressed as a mere kinetic energy operator with an anomalous part. As a result, the power by the spin force and torque operators in this case are seen to vanish. The spin force operator on the sphere is calculated explicitly and its torque is shown to be equal to the rate of change of the kinetic orbital angular momentum operator, again with an anomalous part. This, along with the conservation of the total angular momentum, suggests that the spin force exerts a spin-dependent torque on the kinetic orbital angular momentum operator in order to conserve total angular momentum. The presence of an anomalous spin part in the kinetic orbital angular momentum operator gives rise to an oscillatory behavior similar to the Zitterbewegung. It is suggested that the underlying physics that gives rise to the spin force and the Zitterbewegung is one and the same in NRDO and in systems that manifest spin Hall effect.     

Relativistic New Yukawa-Like Potential and Tensor Coupling

We approximately solve the Dirac equation for a new suggested generalized inversely quadratic Yukawa potential including a Coulomb-like tensor interaction with arbitrary spin-orbit coupling quantum number ${\kappa}$ . In the framework of the spin and pseudospin (p-spin) symmetry, we obtain the energy eigenvalue equation and the corresponding eigenfunctions, in closed form, by using the parametric Nikiforov–Uvarov method. The numerical results show that the Coulomb-like tensor interaction, ?T/r, removes degeneracies between spin and p-spin state doublets. The Dirac solutions in the presence of exact spin symmetry are reduced to Schr?dinger solutions for Yukawa and inversely quadratic Yukawa potentials.     

Relativistic Morse Potential and Tensor Interaction

In this paper, by applying the Pekeris approximation, we present solutions of the Dirac equation for the Morse potential including a Coulomb-like tensor potential with arbitrary spin-orbit coupling number κ under spin and pseudospin symmetry limits. The generalized parametric Nikiforov–Uvarov method is used to obtain energy eigenvalues and corresponding eigenfunctions in their closed forms. We show that tensor interaction removes degeneracies between spin and pseudospin doublets. Some numerical results are given, too.     

Relativistic symmetries with the trigonometric Pschl-Teller potential plus Coulomb-like tensor interaction

The Dirac equation is solved to obtain its approximate bound states for a spin-1/2 particle in the presence of trigonometric Pschl-Teller(tPT) potential including a Coulomb-like tensor interaction with arbitrary spin-orbit quantum number κ using an approximation scheme to substitute the centrifugal terms κ(κ± 1)r-2.In view of spin and pseudo-spin(p-spin) symmetries,the relativistic energy eigenvalues and the corresponding two-component wave functions of a particle moving in the field of attractive and repulsive tPT potentials are obtained using the asymptotic iteration method(AIM).We present numerical results in the absence and presence of tensor coupling A and for various values of spin and p-spin constants and quantum numbers n and κ.The non-relativistic limit is also obtained.     

Coupled perpendicular magnetization in Fe/Cu/Fe trilayers

Ultrathin epitaxial Fe films on Cu(1 0 0) with perpendicular magnetization have been used as templates for the preparation of FCC Fe/Cu/Fe trilayers. The magnetic anisotropy and the coupling of these films have been studied by in-situ magneto optical Kerr effect measurements and Kerr microscopy. The magnetic coupling of both Fe layers is found to be dominated by magnetostatic interaction. Adsorbate-induced spin reorientation in the top layer also causes spin reorientation in the bottom layer. The governing role of the Fe-vacuum interface for the magnetism of the whole trilayer is demonstrated.