Geometric phases in a scattering process

Abstract

The study of geometric phase in quantum mechanics has so far be confined to discrete (or continuous) spectra and trace preserving evolutions. Consider only the transmission channel, a scattering process with internal degrees of freedom is neither a discrete spectrum problem nor a trace preserving process. We explore the geometric phase in a scattering process taking only the transmission process into account. We find that the geometric phase can be calculated by the some method as in an unitary evolution. The interference visibility depends on the transmission amplitude. The dependence of the geometric phase on the barrier strength and the spin-spin coupling constant is also presented and discussed.

4 pages, 5 figures

References in corpus (6)

• Geometric phase with nonunitary evolution in presence of a quantum critical bath
• Entanglement Controlled Single-Electron Transmittivity
• Electron Fabry-Perot interferometer with two entangled magnetic impurities
• Implementing quantum gates through scattering between a static and a flying qubit
• Generalized Geometrical Phase in the Case of Continuous Spectra
• Entanglement-induced electron coherence in a mesoscopic ring with two magnetic impurities

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• Honing in on a topological zero-bias conductance peak
• Surface induced odd-frequency spin-triplet superconductivity as a veritable signature of Majorana bound states
• Yu-Shiba-Rusinov bound states boost odd-frequency superconductivity
• Characterizing a high spin magnetic impurity via Andreev reflection spectroscopy
• Stability of Majorana bound states in the presence of spin-flip scattering