Majorana Fermions in a Box

Abstract

Majorana fermion dynamics may arise at the edge of Kitaev wires or superconductors. Alternatively, it can be engineered by using trapped ions or ultracold atoms in an optical lattice as quantum simulators. This motivates the theoretical study of Majorana fermions confined to a finite volume, whose boundary conditions are characterized by self-adjoint extension parameters. While the boundary conditions for Dirac fermions in $(1+1)$-d are characterized by a 1-parameter family, $\lambda =-{\lambda }^{\ast }$, of self-adjoint extensions, for Majorana fermions $\lambda$ is restricted to $\pm i$. Based on this result, we compute the frequency spectrum of Majorana fermions confined to a 1-d interval. The boundary conditions for Dirac fermions confined to a 3-d region of space are characterized by a 4-parameter family of self-adjoint extensions, which is reduced to two distinct 1-parameter families for Majorana fermions. We also consider the problems related to the quantum mechanical interpretation of the Majorana equation as a single-particle equation. Furthermore, the equation is related to a relativistic Schrödinger equation that does not suffer from these problems.

arXiv comment23 pages, 2 figures

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Cited by in corpus (7)

• Chiral oscillations in the non-relativistic regime
• On real solutions of the Dirac equation for a one-dimensional Majorana particle
• Effects of chiral MIT boundary conditions for a Dirac particle in a box
• Dynamics of Majorana fermions in two-dimensions
• Axial momentum for the relativistic Majorana particle
• On wave equations for the Majorana particle in (3+1) and (1+1) dimensions
• Relativistic quantum mechanics of the Majorana particle: quaternions, paired plane waves, and orthogonal representations of the Poincaré group