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- Title
Resonance expansion for quantum walks and its applications to the long-time behavior.
- Authors
Kenta Higuchi; Hisashi Morioka; Etsuo Segawa
- Abstract
In this paper, resonances are introduced to a class of quantum walks on Z. Resonances are defined as poles of the meromorphically extended resolvent of the unitary time evolution operator. In particular, they appear inside the unit circle. Some analogous properties to those of quantum resonances for Schrödinger operators are shown. Especially, the resonance expansion, an analogue of the eigenfunction expansion, indicates the long-time behavior of quantum walks. The decaying rate, the asymptotic probability distribution, and the weak limit of the probability density are described by resonances and associated (generalized) resonant states. The generic simplicity of resonances is also investigated.
- Subjects
RESONANT states; RESONANCE; DISTRIBUTION (Probability theory); SCHRODINGER operator; RESOLVENTS (Mathematics); EIGENFUNCTION expansions
- Publication
Journal of Spectral Theory, 2024, Vol 14, Issue 1, p207
- ISSN
1664-039X
- Publication type
Article
- DOI
10.4171/JST/494