Short-time behavior of quantum correlation functions in rate theory

Ran Qi, Zhe-Yu Shi, Hui Zhai

In this Letter we study how fast the energy density of a quantum gas can increase in time, when the interatomic interaction characterized by the s-wave scattering length a_{s} is increased from zero with arbitrary time dependence. We show that, at short time, the energy density can at most increase as sqrt[t], which can be achieved when the time dependence of a_{s} is also proportional to sqrt[t], and especially, a universal maximum energy growth rate can be reached when a_{s} varies as 2sqrt[ℏt/(πm)]. If a_{s} varies faster or slower than sqrt[t], it is, respectively, proximate to the quench process and the adiabatic process, and both result in a slower energy growth rate. These results are obtained by analyzing the short time dynamics of the short-range behavior of the many-body wave function characterized by the contact, and are also confirmed by numerically solving an example of interacting bosons with time-dependent Bogoliubov theory. These results can also be verified experimentally in ultracold atomic gases.

Dave Thirumalai, B. J. Berne

Claude Aslangul, No�lle Pottier, Daniel Saint-James

Libo Han, Cao Li, Yang Hong-Quan +1 more

By using the linear approximation method, the intensity correlation function is calculated for a single-mode laser modulated by a bias signal and driven by colored pump and quantum noises with colored cross-correlation. We found that, when the correlation time between the two noises is very short, the behavior of the intensity correlation function versus the time, in addition to decreasing monotonously, also exhibits several cases, such as one maximum, one minimum, and two extrema. When the correlation time between the two noises is very long, the behavior of the intensity correlation function exhibits oscillation and the envelope is similar to the case of short cross-correlation time.

CHRISTOF WETTERICH

Elizabeth Behrman, Gary A. Jongeward, Peter Guy Wolynes

We derive an optimized random phase approximation from an expansion of the free energy in terms of the generating functional. We apply the theory to a quantum mechanical tunneling system coupled to a Gaussian bath. The theory reproduces both short-time behavior and long-time averages of (real time) correlation functions, and compares favorably with both nonoptimized RPA and the cumulant expansion.