Ionization for Three Dimensional Timedependent Point Interactions

Michele Correggi, Centro Linceo Interdisciplinare Roma, Rodolfo Figari, Andrea Mantile

Published Jan 1, 2004• 23 citations

Abstract

We study the time evolution of a three dimensional quantum particle under the action of a time-dependent point interaction fixed at the origin. We assume that the “strength ” of the interaction α(t) is a periodic function with an arbitrary mean. Under very weak conditions on the Fourier coefficients of α(t), we prove that there is complete ionization as t → ∞, starting from a bound state at time t = 0. Moreover we prove also that, under the same conditions, all the states of the system are scattering states. 1

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Ionization for Three Dimensional Timedependent Point Interactions

Michele Correggi, Centro Linceo Interdisciplinare Roma, Rodolfo Figari, Andrea Mantile

Published Jan 1, 2004• 23 citations

OpenAlex

Abstract

Related papers

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N

-body Hamiltonian,

N\gg 1

, we formally derive a system of coupled, nonlinear evolution equations in

3+1

dimensions for the following quantities: (i) the wave function of the macroscopically occupied state; and (ii) the single-particle wave functions of thermally excited states. For stationary (bound) states and a scattering length with {\em periodic microstructure} of subscale

ε

, we heuristically extract effective equations of motion via periodic homogenization up to second order in

ε

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.