Work

Complex translation methods and its application to resonances for quantum walks

Year: 2024

Type: article

Abstract: In this paper, some properties of resonances for multi-dimensional quantum walks are studied. Resonances for quantum walks are defined as eigenvalues of complex translated time evolution operators in the pseudo momentum space. For some typical cases, we show some results of existence or nonexistence of resonances. One is a perturbation of an elastic scattering of a quantum walk which is an analogue of classical mechanics. Another one is a shape resonance model which is a perturbation of a quantum walk with a non-penetrable barrier.

Source: Reviews in Mathematical Physics

DOI: 10.1142/s0129055x24500181

Authors: Kenta Higuchi, Hisashi Morioka

Institution: Ehime University

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Japan Society for the Promotion of Science

Awards: G4122923635, Spectral theory for unitary operators and its applications to scattering theory, G7125832331, Semiclassical distribution of quantum resonances and graph structure of classical trapped trajectories