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Fermi's Golden Rule and Exponential Decay as a RG Fixed Point
KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik.
KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik.
2009 (Engelska)Ingår i: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 134, nr 4, s. 749-768Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

We discuss the decay of unstable states into a quasicontinuum using Hamiltonian models. We show that exponential decay and the golden rule are exact in a suitable scaling limit, and that there is an associated renormalization group (RG) with these properties as a fixed point. The method is inspired by a limit theorem for infinitely divisible distributions in probability theory, where there is a RG with a Cauchy distribution, i.e. a Lorentz line shape, as a fixed point. Our method of solving for the spectrum is well known; it does not involve a perturbation expansion in the interaction, and needs no assumption of a weak interaction. Using random matrices for the interaction we show that the ensemble fluctuations vanish in the scaling limit. For non-random models we can use uniformity assumptions on the density of states and the interaction matrix elements to estimate the deviations from the decay rate defined by the golden rule.

Ort, förlag, år, upplaga, sidor
2009. Vol. 134, nr 4, s. 749-768
Nyckelord [en]
Fermi's golden rule, Renormalization group, Feshbach method, Random, matrix, Unstable states, Lorentz line shape, nuclear reactions, unified theory
Identifikatorer
URN: urn:nbn:se:kth:diva-18255DOI: 10.1007/s10955-009-9700-xISI: 000264326400006Scopus ID: 2-s2.0-62949202781OAI: oai:DiVA.org:kth-18255DiVA, id: diva2:336301
Anmärkning
QC 20100525Tillgänglig från: 2010-08-05 Skapad: 2010-08-05 Senast uppdaterad: 2017-12-12Bibliografiskt granskad

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Langmann, EdwinLindblad, Göran
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