We study the quantum backflow problem in the noncommutative plane. In particular, we have considered a charged particle with and without an oscillator interaction with noncommuting momentum operators and examined angular momentum backflow in each case and how they differ from each other. We also propose a probability associated with the occurrence of angular momentum backflow and investigate whether or not the probability depends on a physical parameter, namely, the magnetic field.

The need for sustainable and long-term environmental monitoring has driven the development of energy-autonomous sensors, which either operate passively or integrate energy harvesting (EH) solutions. In many applications, the energy cost of data transmission is a critical factor in autonomous sensing systems. To address this challenge, optical passive sensors, which exploit changes in reflectivity to monitor physical parameters, offer self-sustained operation without requiring an external power source. Similarly, RF-based passive sensors, both chipless and with minimal circuitry, enable wireless monitoring with low power consumption. When more energy is available, EH techniques can be combined with active optical sensors. Infrared laser-based CO₂ sensors, as well as drone-mounted optical systems, demonstrate how EH can power precise environmental measurements. Beyond optics, other sensing modalities also benefit from EH, further expanding the range of self-powered environmental monitoring technologies. This review discusses the trade-offs between passive and EH-assisted sensing strategies, with a focus on optical implementations. The outlook highlights emerging solutions to enhance sensor autonomy while minimizing the energy cost of data transmission, paving the way for sustainable and scalable environmental monitoring.

We use ray-tracing techniques to determine the evolution of the event horizon of a large black hole that “gobbles” a tiny, traversable wormhole. This calculation has physical meaning in the extreme mass ratio limit. Two setups are considered; a single-mouth wormhole connecting two otherwise independent universes, and a double-mouth zero-length wormhole within the same universe. In the first setting it turns out that, at early times, there exist two disconnected horizons, one in each universe, which then merge as the wormhole falls into the large black hole. In the second setup, we observe the appearance of an “island,” a region of spacetime that is spatially disconnected from the exterior of the black hole, but in causal contact with future null infinity. The island shrinks as time evolves and eventually disappears after sufficient time has elapsed, as compared to the distance between the two mouths. This provides a communication channel with the interior of the large black hole for a certain time interval. We compute numerically the lifetime of the island and verify that it depends linearly on the intermouth distance. Extending the analysis to wormholes with finite length, we show that the achronal averaged null energy condition prevents the appearance of islands.

We study the quantum backflow problem of a relativistic charged Dirac fermion constrained to move on a ring of radius R . Using the relativistic current operator we compute the probability flux through a generic time interval to show emergence of quantum backflow. We also discuss the limiting case when the particle moves along a line.

We use ray-tracing techniques to determine the evolution of the event horizon of a large black hole that ``gobbles'' a tiny, traversable wormhole. This calculation has physical meaning in the extreme mass ratio limit. Two setups are considered: a single-mouth wormhole connecting two otherwise independent universes, and a double-mouth zero-length wormhole within the same universe. In the first setting it turns out that, at early times, there exist two disconnected horizons, one in each universe, which then merge as the wormhole falls into the large black hole. In the second setup, we observe the appearance of an `island', a region of spacetime that is spatially disconnected from the exterior of the black hole, but in causal contact with future null infinity. The island shrinks as time evolves and eventually disappears after sufficient time has elapsed, as compared to the distance between the two mouths. This provides a communication channel with the interior of the large black hole for a certain time interval. We compute numerically the lifetime of the island and verify that it depends linearly on the inter-mouth distance. Extending the analysis to wormholes with finite length, we show that the achronal averaged null energy condition prevents the appearance of islands.