### Abstract

We consider the Dirac particle that lives in the 1-dimensional configuration space consisting of two quantum wires and a junction between the two. We regard the spin of a Dirac particle as spintronic qubit. We give concrete formulae explicitly expressing the one-to-one correspondence between every self-adjoint extension of the minimal Dirac operator and its corresponding boundary condition of the wave functions of the Dirac particle. We then show that all the boundary conditions can be classified into just two types. The two types are characterized by whether the electron passes through the junction or not. We also show how the tunneling produces its own phase factor and what is the relation between the phase factor and the spintronic qubit in the tunneling boundary condition.

Original language | English |
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Pages (from-to) | 856-872 |

Number of pages | 17 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 417 |

Issue number | 2 |

DOIs | |

Publication status | Published - Sep 15 2014 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics

### Cite this

*Journal of Mathematical Analysis and Applications*,

*417*(2), 856-872. https://doi.org/10.1016/j.jmaa.2014.03.061

**A mathematical aspect of a tunnel-junction for spintronic qubit.** / Hirokawa, Masao; Kosaka, Takuya.

Research output: Contribution to journal › Article

*Journal of Mathematical Analysis and Applications*, vol. 417, no. 2, pp. 856-872. https://doi.org/10.1016/j.jmaa.2014.03.061

}

TY - JOUR

T1 - A mathematical aspect of a tunnel-junction for spintronic qubit

AU - Hirokawa, Masao

AU - Kosaka, Takuya

PY - 2014/9/15

Y1 - 2014/9/15

N2 - We consider the Dirac particle that lives in the 1-dimensional configuration space consisting of two quantum wires and a junction between the two. We regard the spin of a Dirac particle as spintronic qubit. We give concrete formulae explicitly expressing the one-to-one correspondence between every self-adjoint extension of the minimal Dirac operator and its corresponding boundary condition of the wave functions of the Dirac particle. We then show that all the boundary conditions can be classified into just two types. The two types are characterized by whether the electron passes through the junction or not. We also show how the tunneling produces its own phase factor and what is the relation between the phase factor and the spintronic qubit in the tunneling boundary condition.

AB - We consider the Dirac particle that lives in the 1-dimensional configuration space consisting of two quantum wires and a junction between the two. We regard the spin of a Dirac particle as spintronic qubit. We give concrete formulae explicitly expressing the one-to-one correspondence between every self-adjoint extension of the minimal Dirac operator and its corresponding boundary condition of the wave functions of the Dirac particle. We then show that all the boundary conditions can be classified into just two types. The two types are characterized by whether the electron passes through the junction or not. We also show how the tunneling produces its own phase factor and what is the relation between the phase factor and the spintronic qubit in the tunneling boundary condition.

UR - http://www.scopus.com/inward/record.url?scp=84899111043&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84899111043&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2014.03.061

DO - 10.1016/j.jmaa.2014.03.061

M3 - Article

VL - 417

SP - 856

EP - 872

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -