Stochastic processes applied to classical physics and quantum mechanics

Abstract

The dynamics in physical systems when subject to environmental fluctuations is usually described by ensemble averages, providing information on the probability of the described system to reside in a possible state. Classical description differs from quantum mechanical, since the latter includes state superpositions. However, the progression among both remains a subject of current research, and the investigation beyond averages, concerning the distributions upon which they are calculated, can unveil the features involved in quantum-to-classical descriptions. Without loosing sight on the optics-matter interaction involved in photosynthetic membranes, the quantum realm is studied with use of stochastic realizations for the description of photon time traces from fluorescent quantum multilevel systems, consistent with continous monitoring of the quantized surrounding electromagnetic field. We study non-renewal statistics, happening when a fluorescent system maintains information of its state after photon detection occurs. When a process is renewal, the distribution of consecutive inter-photon times factors out, and allows quantification of memory after photon detection, relying in the moments of inter-photon distributions. We study the feasibility to experimental verify this measure. Finally, physical realizations show that quantum systems are vulnerable to ensemble averaging. In particular, it is shown that entanglement is modeled on equal footing in very different systems at the level of a density operator due to the averaging effect, and that at such resolution, a prediction of quantum correlations is in general, misleading. Continuous environmental observation is shown to lift this ambiguity, while opens the possibility to witness entanglement on situations where the ensemble averaged state predict none. It is shown that entanglement can be experimentally verified there when none is expected from mixed state available measure, or enhanced by ?decoherent? mechanisms and witnessed through observables when pure dephasing is involved.The quantum-classical middle realm investigated in photosynthesis will provide insight on this progression and on the consequences of quantum properties at macroscopic scale