Quantum twinkling: statistics, coherence and the high order moments of probability amplitudes for systems coupled to quantum baths Original Research Article

We generalize the path integral influence functional technique to the study of a quantum system with interferences between different histories of paths, in contact with a quantum bath. We examine high moments of squared wavefunctions and find that “quantum twinkling”, or the existence of nontrivial moments of the subsystem density matrix, depends strongly on interference between the paths and can not be completely characterized by the usual influence functional which treats environments as effective average bath through spectral density alone. One striking result is that the statistics depend on the number of harmonic oscillators in the bath. Thus for higher moments, one faces directly the question of the exact nature of the bath when using an effective harmonic description. Possible connections of our results to single molecule experiments are discussed.