Note on “Exponential Decay with a Memory”

R. T. Robiscoe, John C. Hermanson

We examine the exponential decay law for an excited quantum system in the case where the state amplitude has a “memory,” that is, where the rate at which the amplitude is decaying at a particular time depends to some extent on values of the amplitude at previous times. For a particular choice of memory, characterized by a memory time τ, the amplitude obeys the differential equation of a damped harmonic oscillator. When τ is greater than a certain critical memory time τc, comparable to the natural lifetime of the state, the amplitude becomes an exponentially damped oscillation in time. When τ is less than τc, the decay is nearly exponential with a decay rate somewhat greater than that calculated from standard theory. By comparing theory with experiment, we can place an upper limit on the memory time for the radiative decay of atoms.

David P. Vasholz

Dmitrii Kouznetsov

Hiromichi Nakazato

The time ranges of the three typical decay forms in quantum mechanics, i.e., the Gaussian, exponential and power-law decays, are investigated on the basis of the Friedrichs model. The analysis yields a deeper understanding of the decay dynamics of quantum systems.

Alexander Rudol'fovich Its, Anatoli G. Izergin, V. E. Korepin +1 more

This is a historical note. In 1993 we calculated space, time and temperature dependent correlation function in isotropic version of one dimensional XY spin chain. The correlation function decays exponentially with time and space separation. The rate of exponential decay was evaluated explicitly. Since that time similar results were obtained in other models: Bose gas with delta interaction, Ising model and strongly correlated electrons.

Frank T. Avignone III