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math.SP2023
Complex translation methods and its application to resonances for quantum walks
Kenta Higuchi, Hisashi Morioka
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 evo…
math-ph2023
Local scattering matrix for a degenerate avoided-crossing in the non-coupled regime
Kenta Higuchi
A Landau-Zener type formula for a degenerate avoided-crossing is studied in the non-coupled regime. More precisely, a system of first order -differential operator wit…
math-ph2023
Resonance expansion for quantum walks and its applications to the long-time behavior
Kenta Higuchi, Hisashi Morioka, Etsuo Segawa
In this paper, resonances are introduced to a class of quantum walks on . Resonances are defined as poles of the meromorphically extended resolvent of the unitary time…