Fermi's golden rule in the Wigner representation

Bilha Segev

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


When Fermi's golden rule (FGR) is studied in the Wigner representation, the transition rate from an initial pure state or from an initial thermal distribution into a quasicontinuum manifold of degenerate states is given by an overlap integral of Wigner functions in phase space. In the semiclassical limit the transition rate is obtained by integrating over the regions in phase space where the energy difference between the initial and final potential surfaces is equal to the available energy. The integral is weighted by the initial probability density to be at that phase-space region. The classical limit of FGR is thus both simple and intuitive. In one dimension a relation to the Landau-Zener-Stuckelberg formula is established. The multi-dimensional case is considered by induction, proving that for separable multi-dimensional systems deviations of the logarithm of the transition rate from its classical limit scale at worst linearly with the dimension.

Original languageEnglish
Pages (from-to)S381-S387
JournalJournal of Optics B: Quantum and Semiclassical Optics
Issue number3
StatePublished - 1 Jun 2003


  • Fermi's golden rule
  • Franck-Condon factors
  • Landau-Zener-Stuckelberg formula
  • Semiclassical limit
  • Wigner function

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Physics and Astronomy (miscellaneous)


Dive into the research topics of 'Fermi's golden rule in the Wigner representation'. Together they form a unique fingerprint.

Cite this