Double-Barrier Resonances and Time Decay of the Survival Probability: A Toy Model

  • Andrea SacchettiEmail author
Part of the Springer INdAM Series book series (SINDAMS, volume 18)


In this talk we consider the time evolution of a one-dimensional quantum system with a double barrier given by a couple of repulsive Dirac’s deltas. In such a pedagogical model we give, by means of the theory of quantum resonances, the asymptotic behavior of 〈ψ, e itH ϕ〉 for large times, where H is the double-barrier Hamiltonian operator and where ψ and ϕ are two test functions. In particular, when ψ is close to a resonant state then explicit expression of the dominant terms of the survival probability defined as | 〈ψ, e itH ψ〉 |2 is given.


Lambert special functions Quantum resonances Quantum survival probability Singular barrier potential 



I’m very grateful to Sandro Teta for fruitful discussions. I thank very much Gian Michele Graf and Kenji Yajima for useful comments to my talk. This work is partially supported by Gruppo Nazionale per la Fisica Matematica (GNFM-INdAM).


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Authors and Affiliations

  1. 1.Dipartimento di Scienze Fisiche, Informatiche e MatematicheUniversitá degli Studi di Modena e Reggio EmiliaModenaItaly

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