A non-relativistic model of two-particle decay

Dittrich, J.; Exner, Pavel

doi:10.1007/bf01599956

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Exponential Decay At Intermediate Times1

Introduction1

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2004

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Cited by 24 publications

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“…The way to prove that is inspired by [3]. We employ the fact that the continued resolvent is for any fixed x a meromorphic function and show that for a sufficiently weak coupling the time evolution is dominated by the contribution from the residue term in (4.5).…”

Section: Exponential Decay At Intermediate Timesmentioning

confidence: 99%

See 1 more Smart Citation

A model of interband radiative transition

Dittrich¹,

Exner²,

Hirokawa³

2004

J. Math. Soc. Japan

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We consider a simple model which is a caricature of a crystal interacting with a radiation field. The model has two bands of continuous spectrum and the particle can pass from the upper one to the lower by radiating a photon, the coupling between the excited and deexcited states being of a Friedrichs type. Under suitable regularity and analyticity assumptions we find the continued resolvent and show that for weak enough coupling it has a curve-type singularity in the lower halfplane which is a deformation of the upper-band spectral cut. We then find a formula for the decay amplitude and show that for a fixed energy it is approximately exponential at intermediate times, while the tail has a power-like behaviour.

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Section: Exponential Decay At Intermediate Timesmentioning

confidence: 99%

“…A rigorous description of decay and resonance processes in quantum theory has a long history starting from the Friedrichs model presented in [1] and discussed later in numerous papers -see, e.g. [2], [3]. A systematic study of the problem started in the seventies.…”

Section: Introductionmentioning

confidence: 99%