Abstract
We investigate the two-dimensional motion of relativistic cold electrons in the presence of `strictly’ spatially varying magnetic fields satisfying, however, no magnetic monopole condition. We find that the degeneracy of Landau levels, which arises in the case of the constant magnetic field, lifts out when the field is variable and the energy levels of spin-up and spin-down electrons align in an interesting way depending on the nature of change of field. Also, the varying magnetic field splits Landau levels of electrons with zero angular momentum from positive angular momentum, unlike the constant field which only can split the levels between positive and negative angular momenta. Exploring Landau quantization in non-uniform magnetic fields is a unique venture on its own and has interdisciplinary implications in the fields ranging from condensed matter to astrophysics to quantum information. As examples, we show magnetized white dwarfs, with varying magnetic fields, involved simultaneously with Lorentz force and Landau quantization affecting the underlying degenerate electron gas, exhibiting a significant violation of the Chandrasekhar mass-limit; and an increase in quantum speed of electrons in the presence of a spatially growing magnetic field.
Highlights
As the density is expected to be highest at the center and lowest at the surface, it is a reasonable assumption that the magnetic field too follows the same trend, as proposed earlier [27]. Such a field profile has been extensively used for neutron stars and white dwarfs with appropriate parameters, which may induce a sharp variation of the field in a short spatial scale, depending upon the parameters
As an application of non-uniform and growing magnetic field, we show its role in attaining higher quantum speed, i.e. transition speed from one energy level to other, of electrons as compared to uniform magnetic field
An immediate astrophysical implication of LQ is to the mass–radius relation of magnetized white dwarfs
Summary
The role of magnetic fields in controlling the natural – Earth based to astrophysical – systems from the microscopic to macroscopic scales is well established. As the density is expected to be highest at the center and lowest at the surface, it is a reasonable assumption that the magnetic field too follows the same trend, as proposed earlier [27] Such a field profile has been extensively used for neutron stars and white dwarfs with appropriate parameters (see, e.g., [24, 29]), which may induce a sharp variation of the field in a short spatial scale, depending upon the parameters. As an application of non-uniform and growing magnetic field, we show its role in attaining higher quantum speed, i.e. transition speed from one energy level to other, of electrons as compared to uniform magnetic field.
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call