We study a relativistic charged Dirac particle moving in a rotating magnetic field. By using a time-dependent unitary transformation, the Dirac equation with the time-dependent Hamiltonian can be reduced to a Dirac-like equation with a time-independent effective Hamiltonian. Eigenstates of the effective Hamiltonian correspond to cyclic solutions of the original Dirac equation. The nonadiabatic geometric phase of a cyclic solution can be expressed in terms of the expectation value of the component of the total angular momentum along the rotating axis, regardless of whether the solution is explictly available. For a slowly rotating magnetic field, the eigenvalue problem of the effective Hamiltonian is solved approximately and the geometric phases are calculated. The same problem for a charged or neutral Dirac particle with an anomalous magnetic moment is discussed briefly.
The Dirac equation is invariant under rotations with a constant frequency and invariable cylindrical radius. 3D transformation for rotating frames is found with help of this invariance. Exact localized solutions of the Dirac equation in the field of a traveling circularly polarized electromagnetic wave and constant magnetic field exist and possess unusual properties. Temporal changes of spin pertaining to the solutions are studied.
In this contribution, we study the Dirac oscillator under the influence of noninertial effects of a rotating frame in the cosmic string spacetime. We show that both noninertial effects and the topology of the cosmic string spacetime restrict the physical region of the spacetime where the quantum particle can be placed, and discuss two different cases of bound states solutions of the Dirac equation by analysing the behaviour of the Dirac oscillator frequency.
By considering a spacetime with a spiral dislocation, we analyse the behaviour of the Dirac field subject to a hard-wall confining potential. In search of relativistic bound states solutions, we discuss the influence of the topology of the spiral dislocation spacetime on the energy levels. Further, we analyse the effects of rotation on the Dirac field in the spiral dislocation spacetime. We show that both rotation and the topology of the spacetime impose a restriction on the values of the radial coordinate. Thus, we analyse the effects of rotation and the topology of the spiral dislocation spa…
Parameters of localization are defined in the lab and rotating frame for solutions of the Dirac equation in the field of a traveling circularly polarized electromagnetic wave and constant magnetic field. The radius of localization is of the order of the electromagnetic wavelength and lesser.
There are many stars that are rotating spheroids in the Universe, and studying them is of very important significance. Since the times of Newton, many astronomers and physicists have researched gravitational properties of stars by considering the moment equations derived from Eulerian hydrodynamic equations. In this paper we study the scattering of spinors of the Dirac equation, and in particular investigate the scattering issue in the limit case of rotating Maclaurin spheroids. Firstly we give the metric of a rotating ellipsoid star, then write the Dirac equation under this metric, and finall…
The aim of this paper is to investigate the separability of a spin-1/2 spinor field in a five-dimensional rotating, charged black hole constructed by Cvetic and Youm in string theory, in the case when three U(1) charges are set equal. This black hole solution represents a natural generalization of the famous four-dimensional Kerr-Newman solution to five dimensions with the inclusion of a Chern-Simons term to the Maxwell equation. It is shown that the usual Dirac equation can not be separated by variables in this general spacetime with two independent angular momenta. However if one supplements…
The problem of Dirac's equation in a rotating electromagnetic field can be reduced to the stationary by using a transformation for point rotating reference frames. The general form of the non-Galilean transformation is deduced in the paper. For the non-Galilean transformation time is different in the rotating and resting frame. This transformation contains a constant, with the dimension of time. The constant is assumed to be fundamental. The transformation forms the necessary condition for the existence of periodic, bounded and square integrable solutions in both the rotating and resting frame…
We discuss results obtained recently for a quantum-mechanical model given by a neutral particle with a magnetic quadrupole moment in a radial electric field and a scalar potential proportional to the radial variable in cylindrical coordinates that also includes the noninertial effects of a rotating reference frame. We show that the conjectured allowed values of the cyclotron frequency are a mere artifact of the truncation of the power series used to solve the radial eigenvalue equation. Our analysis proves that the analytical expression for the eigenvalues are far from correct.
Approximate analytic solutions of the Dirac equation with Tietz-Hua (TH) potential are obtained for arbitrary spin-orbit quantum number using the Pekeris approximation scheme to deal with the spin-orbit coupling terms In the presence of exact spin and pseudo-spin (pspin) symmetric limitation, the bound state energy eigenvalues and associated two-component wave functions of the Dirac particle moving in the field of attractive and repulsive TH potential are obtained using the parametric generalization of the Nikiforov-Uvarov (NU) method. The cases of the Morse potential, the generalized Morse po…
A precessing spin observed in a rotating frame of reference appears frequency-shifted, an effect analogous to the precession of a Foucault pendulum observed on the rotating Earth. This frequency shift can be understood as arising from a magnetic pseudo-field in the rotating frame that nevertheless has physically significant consequences, such as the Barnett effect. Detecting these pseudo-fields is experimentally challenging, as a rotating-frame sensor is required. Previous work has realised classical rotating-frame detectors. Here we use quantum sensors, nitrogen-vacancy (NV) centres, in a rap…
We find solutions of the Dirac equation in curved spacetime. In particular, we consider 1+1 dimensional sections of several exotic metrics: the Alcubierre metric, which describes a scenario that allows faster-than-light (FTL) velocity; the Gödel metric, that describes a universe containing closed timelike curves (CTC); and the Kerr metric, which corresponds to the spacetime of a rotating black hole. Moreover, we also show that the techniques that we use in these cases can be extended to nonstatic metrics.
It was argued by Mashhoon that a spin-rotation coupling term should add to the Hamiltonian operator in a rotating frame, as compared with the one in an inertial frame. For a Dirac particle, the Hamiltonian and energy operators H and E were recently proved to depend on the tetrad field. We argue that this non-uniqueness of H and E really is a physical problem. We compute the energy operator in the inertial and the rotating frame, using three tetrad fields: one for each of two frameworks proposed to select the tetrad field so as to solve this non-uniqueness problem, and one proposed by Ryder. We…
We construct a Darboux transformation for a class of two-dimensional Dirac systems at zero energy. Our starting equation features a position-dependent mass, a matrix potential, and an additional degree of freedom that can be interpreted either as a magnetic field perpendicular to the plane or a generalized Dirac oscillator interaction. We obtain a number of Darbouxtransformed Dirac equations for which the zero energy solutions are exactly known.
We show that 2+1 dimensional Dirac oscillators in an external magnetic field is mapped onto the same with reduced angular frequency in absence of magnetic field. This can be used to study the atomic transitions in a radiation field. Relativistic Landau levels are constructed explicitly. Several interesting features of this system are discussed.
We present a novel perspective to characterize the chiral magnetic and related effects in terms of angular decomposed modes. We find that the vector current and the chirality density are connected through a surprisingly simple relation for all the modes and any mass, which defines the mode decomposed chiral magnetic effect in such a way free from the chiral chemical potential. The mode decomposed formulation is useful also to investigate properties of rotating fermions. For demonstration we give an intuitive account for a nonzero density emerging from a combination of rotation and magnetic fie…
Based on the single particle approximation [V. F. Dmitriev {\it et al}, Phys. Rev. C {\bf50}, 2358 (1994), C.-C. Chen, Phys. Rev. A {\bf51}, 2611 (1995)], the Landau quantization associated with an atom with a magnetic quadrupole moment is introduced, and then, rotating effects on this analogue of the Landau quantization is investigated. It is shown that rotating effects can modify the cyclotron frequency and breaks the degeneracy of the analogue of the Landau levels.
We investigate torsion and noninertial effects on a spin-$1/2$ quantum particle in the nonrelativistic limit of the Dirac equation. We consider the cosmic dislocation spacetime as a background and show that a rotating system of reference can be used out to distances which depend on the parameter related to the torsion of the defect. Therefore, we analyse torsion effects on the spectrum of energy of a nonrelativistic Dirac particle confined to a hard-wall potential in a Fermi-Walker reference frame.
We consider Pauli--Dirac fermion submitted to an inhomogeneous magnetic field. It is showed that the propagator of the neutral Dirac particle with an anomalous magnetic moment in an external linear magnetic field is the causal Green function $S^{c}(x_{b},x_{a})$ of the Pauli--Dirac equation. The corresponding Green function is calculated via path integral method in global projection, giving rise to the exact eigenspinors expressions. The neutral particle creation probability corresponding to our system is analyzed, which is obtained as function of the introduced field $B'$ and the additional s…
Structure of spinning particle based on the rotating black hole solution is considered. It has gyromagnetic ratio $g=2$ and a nontrivial twistorial and stringy systems. The mass and spin appear from excitations of the Kerr circular string, while the Dirac equation describes excitations of an {\it axial} stringy system which is responsible for scattering. Complex Kerr geometry contains an open twistor-string, target space of which is equivalent to the Witten's `diagonal' of the $ CP^3\times CP^{*3}$.
It is shown that a spin-1/2 fermion coupled to the axially symmetric electromagnetic vector potential has the same matrix structure as that one for the planar Dirac oscillator. In particular, the planar Dirac oscillator can be interpreted as a charged particle minimally coupled to a transverse homogeneous magnetic field.
