A Toy Model for Scalars in Transient Magnetic Fields

Abstract

We consider a special magnetic field, as for example the one in the crust of a magnetar, and solve the Klein–Gordon equation describing scalars evolving in such a configuration. For the wave number inside some computable ranges, the amplitude function of the charged boson is very sensitive to the magnetic field induction, turning from oscillatory to exponentially growing modes along Oz. One can recover the periodic behavior characterized by stationary amplitudes, by adding a self-interaction contribution to the spontaneously broken Lagrangian.

The one-dimensional thermal properties for the relativistic harmonic oscillators

“…Both objectives can be achieved by using a method based on the zeta function [12,13]. This method has been used by [14] with the aim of calculating the partition function in the case of the graphene. We note here that the zeta function has been applied successfully in different areas of physics, and the examples vary from ordinary quantum and statistical mechanics to quantum field theory (see for example [15]).…”

Approximative analytic study of fermions in magnetar’s crust; ultra-relativistic plane waves, Heun and Mathieu solutions and beyond

“…As in our previous works, [ Dariescu et al, 2011a;Dariescu and Dariescu, 2011b], we have considered that the periodic magnetic field proposed by Wareing and Hollerbach [Wareing and Hollerbach, 2006] is likely to exist in magnetar's crust and we have analyzed how the time and spatial distribution of the external fields ( 6) have an influence on the wave function, solutions to the corresponding Dirac equation. In a perturbative approach, for ultra-relativistic particles, we have derived the current density components and the charge density (22).…”

“…The present paper is following some previous investigations on spinless particles, described by the Klein-Gordon equation, moving in strong magnetic induction periodic along Oz [Dariescu et al, 2011a;Dariescu and Dariescu, 2011b].…”

Fermions in Magnetar's Crust in Terms of Heun Double Confluent Functions

“…With high densities and ultra-strong magnetism, this class of neutron stars is far from being composed of only neutrons and, once other particles are added to the normal matter, 10 they are expected to play a significant contribution to the stars' parameters. 11 The present paper is extending some of our previous investigations in the following directions: first, instead of using the Klein-Gordon equation, as in the toy model of scalars in transient magnetic fields, 12,13 we are dealing now with the Dirac equation, which is more suitable for describing the relativistic particles in magnetar's crust. Second, for a frozen periodic magnetic induction, similar to the one proposed by Wareing and Hollerbach, 14,15 we do not neglect any of the contributing terms, as we did in Ref.…”

“…Similarly to our previous investigations, 12,13 we are employing the following expressions for the electromagnetic field components…”