Exact Ionization Amplitudes for a Delta-Function Well in an Arbitrary-Strength DC Electric Field
Abstract
We investigate finite-time field-induced ionization from a one-dimensional attractive delta-function well in a uniform dc electric field of arbitrary strength. Our aim is to determine the physical bound-state survival amplitude ab(t) at any observation time without constructing the complete time-dependent propagator or wavefunction. In the gauge-equivalent Kramers--Henneberger representation, the field appears as motion of the contact point, and the resulting dynamics reduces to a closed Volterra equation. Exact endpoint-phase factorization organizes the full chronological rescattering history into a relative-time convolution hierarchy and an exact resolvent. By introducing the accumulated bound-state amplitude and reorganizing its two-time domain in relative and complementary center times, the final contact contribution becomes an explicit boundary integral. All spatial integrations are carried out analytically. The field-driven contact-free term is obtained in closed form using the Faddeeva function, while the direct and repeated-rescattering terms are expressed as explicitly evaluable time integrals. The result applies at arbitrary dc-field strength and finite time, with no weak-field expansion, rescattering truncation, or asymptotic-time approximation. It is verified through the exact field-free limit and an independent numerical solution of the original physical Volterra equation. The formulation gives an exact nonperturbative solution of a fundamental ionization model and reveals otherwise hidden analytical structure in driven quantum dynamics.
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BibTeX
@misc{kim2026exact,
title = {{Exact Ionization Amplitudes for a Delta-Function Well in an Arbitrary-Strength DC Electric Field}},
author = {Ilki Kim and Gerald J. Iafrate},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.16507},
eprint = {2609.16507},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.16507},
}
RIS
TY - UNPB
TI - Exact Ionization Amplitudes for a Delta-Function Well in an Arbitrary-Strength DC Electric Field
AU - Ilki Kim
AU - Gerald J. Iafrate
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.16507
UR - https://arxiv.org/abs/2609.16507
AB - We investigate finite-time field-induced ionization from a one-dimensional attractive delta-function well in a uniform dc electric field of arbitrary strength. Our aim is to determine the physical bound-state survival amplitude a_b(t) at any observation time without constructing the complete time-dependent propagator or wavefunction. In the gauge-equivalent Kramers--Henneberger representation, the field appears as motion of the contact point, and the resulting dynamics reduces to a closed Volterra equation. Exact endpoint-phase factorization organizes the full chronological rescattering history into a relative-time convolution hierarchy and an exact resolvent. By introducing the accumulated bound-state amplitude and reorganizing its two-time domain in relative and complementary center times, the final contact contribution becomes an explicit boundary integral. All spatial integrations are carried out analytically. The field-driven contact-free term is obtained in closed form using the Faddeeva function, while the direct and repeated-rescattering terms are expressed as explicitly evaluable time integrals. The result applies at arbitrary dc-field strength and finite time, with no weak-field expansion, rescattering truncation, or asymptotic-time approximation. It is verified through the exact field-free limit and an independent numerical solution of the original physical Volterra equation. The formulation gives an exact nonperturbative solution of a fundamental ionization model and reveals otherwise hidden analytical structure in driven quantum dynamics.
ER -