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• W3129014719 abstract "The transfer matrix M of a short-range potential may be expressed in terms of the time-evolution operator for an effective two-level quantum system with a time-dependent non-Hermitian Hamiltonian. This leads to a dynamical formulation of stationary scattering. We explore the utility of this formulation in the study of the low-energy behavior of the scattering data. In particular, for the exponentially decaying potentials, we devise a simple iterative scheme for computing terms of arbitrary order in the series expansion of M in powers of the wavenumber. The coefficients of this series are determined in terms of a pair of solutions of the zero-energy stationary Schrödinger equation. We introduce a transfer matrix for the latter equation, express it in terms of the time-evolution operator for an effective two-level quantum system, and use it to obtain a perturbative series expansion for the solutions of the zero-energy stationary Schrödinger equation. Our approach allows for identifying the zero-energy resonances for scattering potentials in both full line and half-line with zeros of the entries of the zero-energy transfer matrix of the potential or its trivial extension to the full line." @default.
• W3129014719 created "2021-02-15" @default.
• W3129014719 creator A5032645613 @default.
• W3129014719 creator A5063828115 @default.
• W3129014719 date "2021-04-01" @default.
• W3129014719 modified "2023-09-26" @default.
• W3129014719 title "Dynamical formulation of low-energy scattering in one dimension" @default.
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• W3129014719 doi "https://doi.org/10.1063/5.0050990" @default.
• W3129014719 hasPublicationYear "2021" @default.
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