A Mathematical Aspect of A Tunnel-Junction for Spintronic Qubit

2013/06/12 by Masao Hirokawa, Hirokawa, Masao, Takuya Kosaka +1
Mathematics · Physics and Astronomy · #Quantum and electron transport phenomena #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #math-ph #math.MP #quant-ph

paper · pdf · doi:10.48550/arxiv.1306.2688

26 pages, 2 figures: We changed the title a little, and rewrote the paper based on some preceding works

arxiv created 2013/09/05 · arxiv updated 2013/09/06

Abstract

We consider the Dirac particle living in the 1-dimensional configuration space with a junction for a spintronic qubit. We give concrete formulae explicitly showing the one-to-one correspondence between every self-adjoint extension of the minimal Dirac operator and the boundary condition of the wave functions of the Dirac particle. We then show that the boundary conditions are classified into two types: one of them is characterized by two parameters and the other is by three parameters. Then, we show that Benvegnu and Dabrowski's four-parameter family can actually be characterized by three parameters, concerned with the reflection, penetration, and phase factor.

Related

• One-Dimensional Tunnel-Junction Formula for Schrodinger Particle
• Hearing the boundary conditions of the one-dimensional Dirac operator
• On the confinement of a quantum particle to a two-dimensional ring in systems described by the Dirac equation
• A Linear-confined Particle and the Dirac Equation
• Point-like Rashba interactions as singular self-adjoint extensions of the Schrödinger operator in one dimension