Spectral random walk of a single molecule

V. Palm, K. -S. K. Rebane

J. P. Mbelek

It is shown, by considering the case of the harmonic oscillator, that quantum fluctuations may be the most significant contribution to the random walk of a single molecule. From this point, the controversy on the existence of a standard quantum limit (SQL) is addressed and settled on the experimental ground. Comparisons to the experimental data yet avalaible in the literature provide a new estimate of the reduced Planck constant yielding \hbar = (1.1 \pm 0.2) ~ 10^{-34} J.s.

Taras Plakhotnik

František Šanda

We revisit the line-shape theory of a single molecule with anomalous stochastic spectral diffusion. Waiting time profiles for bath induced spectral jumps in the ground and excited states become different when a molecule, probed by continuous-wave laser field, reaches the steady state. This effect is studied for the stationary dichotomic continuous-time-random-walk spectral diffusion of a single two-level chromophore with power-law distributions of waiting times. Correlated waiting time distributions, line shapes, two-point fluorescence correlation function, and Mandel Q parameter are calculated for arbitrary magnitude of laser field. We extended previous weak field results and examined the breakdown of the central limit theorem in photon statistics, indicated by asymptotic power-law growth of Mandel Q parameter. Frequency profile of the Mandel Q parameter identifies the peaks of spectrum, which are related to anomalous spectral diffusion dynamics.

Jirô Akahori, Yusuke Ide, Tomoki Kato +3 more

In this paper, we introduce hierarchical random walks at first. In this model, we use two types of random walkers, global and local walkers. The global walker chooses a local walker at every step, then the chosen local walker moves a single step. After that we construct the corresponding continuous-time quantum walks and discuss their spectral structures. Then we define multi-dimensional continuous-time quantum walks by taking a marginal distribution with respect to the global walker.

Yuliy M. Baryshnikov, Wil Brady, Andrew Bressler +1 more