Decay in a uniform field: an exactly solvable model

2003/07/31 by R. M. Cavalcanti, P. Giacconi, Paola Giacconi +2 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Cold Atom Physics and Bose-Einstein Condensates #Quantum Information and Cryptography #math-ph #math.MP #physics.atom-ph #quant-ph

paper · pdf · doi:10.1088/0305-4470/36/48/009

published as J. Phys. A: Math. Gen. 36, 12065 (2003) · 21 pages, 2 figures. v3: typos corrected

arxiv created 2003/11/18 · openalex publication_date 2003/11/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

We investigate the time evolution of the decay (or ionization) probability of a D -dimensional model atom ( D = 1, 2, 3) in the presence of a uniform (i.e., static and homogeneous) background field. The model atom consists in a non-relativistic point particle in the presence of a point-like attractive well. It is shown that the model exhibits infinitely many resonances leading to possible deviations from the naive exponential decay law of the non-decay (or survival) probability of the initial atomic quantum state. Almost stable states exist due to the presence of the attractive interaction, no matter how weak it is. Analytic estimates as well as numerical evaluation of the decay rates are explicitly given and discussed.

Citations

• Fate of the false vacuum: Semiclassical theory
• Continuum eigenfunction expansions and resonances: A simple model

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