The Inverse Decay Problem

Anthony Sudbery

Badri Berrabah, Baya Bentag, Ahmida Bendjoudi

The problem of a spineless charged particle with a time-dependent decaying mass interacting with a Coulomb and an inverse quadratic potentials is considered. The Green’s function is explicitly evaluated. The energy levels as well as the wave functions for the bound states are exactly determined.

А. В. Солдатов, JOSIP SEKE, Nikolay N. Bogolubov +1 more

An alternative way of reconstructing a function from its Laplace transform \nusing the Widder inversion method was shown to be useful in treating some \nproblems of nonequilibrium statistical mechanics. As an example of a successful application of the method, a decay was investigated of the excited \natomic state in a simple, but nonetheless physically relevant, model featuring a two-level atom interacting with a continuum of field modes.

Edward J. Robinson

A calculation is presented of population trapping by an infinite sequence of bound states and continua, with results that differ from both the pure exponential decay exhibited by a single bound state, and from the combination of exponential decay and no decay that is obtained when there are two bound states coupled to a single continuum. Instead of either of these, the theory predicts a rule for the decay that becomes, for time t large (but not so large that events are unobservable), an inverse power law in t 1 2/. Possible experimental realizations of this problem are discussed, which also indicate that the Floquet form of the wavefunction does not apply.