On the definition of the resonance

T. Kohmoto, Yukio Fukuda, Masakazu Kunitomo +3 more

Summary form only given. According to the conventional expression the group velocity of optical pulses in resonantly absorbing media can exceed the light velocity in the vacuum and even become negative. Recently a new definition of group velocity has been proposed by means of the saddle point method. We observed the propagation of femtosecond optical pulses in a dye solution and experimentally tested the new definition of the group velocity.

Richard Henry Dalitz

Shachar Klaiman, Ido Gilary

Arturo Cisneros, Harold V. McIntosh

Abstract The widely cited definition of quantization in terms of square‐integrable wave functions does not apply to continuum wave functions, to such phenomena as metastable states, or many‐body resonances. A better philosophical foundation for quantum mechanics separates the probabilistic aspects based on square integrable Hilbert space functions from the dynamical aspects based upon the solutions of Shroedinger's (or Dirac's) equation. A Hilbert space may have a non‐Hilbert space basis, which may be described by Stieltjes integrals and a spectrum measure. This viewpoint is expounded by reference to a very detailed analysis of a simple model, through which a precise definition of a Bohr–Feshbach resonance can be given. We propose a definition of a “metastable state,” showing that it is consistent with accepted usage, and that it overcomes a series of objections which have been catalogued by Simon. Its rate of decay is given by the Fourier–Stieltjes transform of the spectral density function; it is moreover the longest‐lived initially localized state which can be formed from a small span of energy eigenfunctions near its mean energy.

Augustin Gille

Mao-Fa Fang, Peng Zhou, S. Swain

The usual definition of squeezing, based on the Heisenberg uncertainty principle, measures uncertainty in terms of the standard deviation. It can run into difficulties when applied to squeezing in the two-level atom. An alternative definition of squeezing is presented for this system, based on information entropy theory, which overcomes the disadvantages of the definition based on the Heisenberg uncertainty relation. The utility of this definition is illustrated by examining squeezing in the information entropy of a two-level atom in the Jaynes-Cummings model, and in resonance fluorescence.