Relativistic Landau quantization in non-uniform magnetic field and its applications to white dwarfs and quantum information

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.

Non-uniform magnetic field as a booster for quantum speed limit: faster quantum information processing

“…such that the antiparticle wavefunction φ = −χ [58]. We solve equation (36) for our proposed power law variation of the magnetic field [45], given by…”

“…such that σ z R ± = ±R ± , equation (42) becomes ), is the square of dimensionless energy and acts as an eigenvalue of the problem [45]. Therefore, energy of level ν becomes…”

“…For uniform magnetic field, i.e. n = 0, from the solution of equation (45), the eigenvalue of level ν is given by…”

Spin-1/2 Particles under the Influence of a Uniform Magnetic Field in the Interior Schwarzschild Solution

“…For the former case, one needs to use again numerical methods (as in Ref. [45]) to solve the resulting equation, whereas for the latter case, one needs to consider, instead of the Dirac equation, the Gross-Pitaevskii equation coupled to the magnetic field inside the interior Schwarzschild solution.…”

Non-uniform magnetic field as a booster for quantum speed: faster quantum information processing

“…in cylindrical coordinates (ρ, φ, z), where 'n' is the magnetic non-uniformity index. Note that n > −1 so that effective potential is always attractive [33]. In this work, we take ρ in pm (picometer) and magnetic field B in G.…”