Even after decades of research, the problem of first passage time statistics for quantum dynamics remains a challenging topic of fundamental and practical importance. Using a projective measurement approach, with a sampling time τ, we obtain the statistics of first detection events for quantum dynamics on a lattice, with the detector located at the origin. A quantum renewal equation for a first detection wave function, in terms of which the first detection probability can be calculated, is derived. This formula gives the relation between first detection statistics and the solution of the corresponding Schrödinger equation in the absence of measurement. We illustrate our results with tight-binding quantum walk models. We examine a closed system, i.e., a ring, and reveal the intricate influence of the sampling time τ on the statistics of detection, discussing the quantum Zeno effect, half dark states, revivals, and optimal detection. The initial condition modifies the statistics of a quantum walk on a finite ring in surprising ways. In some cases, the average detection time is independent of the sampling time while in others the average exhibits multiple divergences as the sampling time is modified. For an unbounded one-dimensional quantum walk, the probability of first detection decays like (time)^{(-3)} with superimposed oscillations, with exceptional behavior when the sampling period τ times the tunneling rate γ is a multiple of π/2. The amplitude of the power-law decay is suppressed as τ→0 due to the Zeno effect. Our work, an extended version of our previously published paper, predicts rich physical behaviors compared with classical Brownian motion, for which the first passage probability density decays monotonically like (time)^{-3/2}, as elucidated by Schrödinger in 1915.

Low-energy visible light (LEVL) has been shown to stimulate cell functions. This is called "photobiostimulation" and has been used successfully over the last three decades for treating a range of conditions, including soft tissue injuries, severe wounds, chronic pain, and more. Nevertheless, the mechanism of photobiostimulative processes is still being debated. It is obvious that, in order to interact with the living cell, light has to be absorbed by intracellular chromophores. In a search for chromophores responsible for photobiostimulation, endogenous porphyrins, mitochondrial and membranal cytochromes, and flavoproteins were found to be suitable candidates. The above-mentioned chromophores are photosensitizers that generate reactive oxygen species (ROS) following irradiation. As the cellular redox state has a key role in maintaining the viability of the cell, changes in ROS may play a significant role in cell activation. In the present review, we summarize evidence demonstrating that various ROS and antioxidants are produced following LEVL illumination. We found that very little evidence for NO formation in illuminated non-vascular smooth muscle cells exists in the literature. We suggest that the change in the cellular redox state which plays a pivotal role in maintaining cellular activities leads to photobiostimulative processes.

We investigate the statistics of the first detected passage time of a quantum walk. The postulates of quantum theory, in particular the collapse of the wave function upon measurement, reveal an intimate connection between the wave function of a process free of measurements, i.e. the solution of the Schrödinger equation, and the statistics of first detection events on a site. For stroboscopic measurements a quantum renewal equation yields basic properties of quantum walks. For example, for a tight binding model on a ring we discover critical sampling times, diverging quantities such as the mean time for first detection, and an optimal detection rate. For a quantum walk on an infinite line the probability of first detection decays like (time) −3 with a superimposed oscillation, critical behavior for a specific choice of sampling time, and vanishing amplitude when the sampling time approaches zero due to the quantum Zeno effect.

Light induces NO formation in endothelial and sperm cells. In endothelial cells, NO formation may explain previous results demonstrating enhanced wound healing and pain relief following illumination. In illuminated sperm cells, NO formation may account for the enhanced fertilization rate.

No abstract