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Accidental paths

Physicists describe random routes of light and animals

A complex device equipped with small glass boxes and a super sensitive camera allowed French researchers – one of whom lives in the State of Paraíba – to describe how light behaves under very special conditions. When a photon – a particle of light – hits a rubidium atom – and then another one and still another one – the atom travels distances that follow a pattern named Lévy flight. The result, published at the end of May on the Nature Physics journal website, is the first statistical description of this physical phenomenon based on experimental observations; it can help predict the propagation of photons in certain situations.

“Many researchers have looked for natural events that follow Lévy flights”, says physicist Martine Chevrollier, from the Federal University of Paraíba/UFPB. The random movements are characterized by a series of small steps interspersed with rare longer displacements. This is exactly what happened in the experiment where photons were launched into atomic steam at 47 degrees Celsius, whose rubidium atoms float at a certain distance one from the other. Under this low density, the photons bump into a single atom each time and the researchers can measure these interactions in detail.

The work of the French researcher who lives in Paraíba shows an interaction in these encounters in which an atom absorbs a photon and re-emits it into another direction, in the manner of a player who gets the ball and kicks it over to the other side. The interaction between photons and atoms has a particular characteristic: if the frequency of the vibration is similar between the two particles, which happens most of the time, the photon is launched at a short distance – 5 millimeters on average. “However, there is a tiny probability that the frequency of the atom might be too far from the photon”, says Martine. When this happens, the photon is re-emitted with a different frequency from the previous one, in an effect known as the Doppler effect and this is why it travels much longer distances, of up to 50 millimeters. However, this change in frequency only happens at very low temperatures, is only obtained in a laboratory environment.

Researchers already imagined that this could happen in theory. “The difficult thing is to observe this interaction”, says the researcher. She had unsuccessfully attempted to try the experiment in her lab. It was necessary to control precisely the conditions to photograph the trajectory of the photons and the distance traveled by each photon with an ultra sensitive camera. This is why the experimental part was conducted at the University of Nice, in France. Martine participated during the calculations and analyses results phase. “The special conditions of the experiments we conducted were merely imposed by a technique created to measure the photons’ individual steps”, explains the physicist. But the Lévy flight is very common in phenomena that involve the spreading of light and happens, for example, in stars, fluorescent lamps and part of the suns rays that are propagated in the atmosphere and in the sea.

Animal world
The Lévy flight also accurately describes some ecological phenomena, explains physicist Marcos da Luz, from the Federal University of Paraná/UFPR. Until some time ago, the general belief was that everything followed normal distributions, where average events are very common and the very small ones or the very big ones are rare. Recently, however, convincing data has indicated that many animals – such as jackals, bees, penguins and others – follow Lévy flights. Together with his colleagues Gandhi Mohan Viswanathan, from the Federal University of Alagoas, and Ernesto Raposo, from the Federal University of Pernambuco, the physicist from UFPR has used Lévy flights to understand how these animals search for food.

The Lévy flight is an advantage, for example, when a source of food is distributed randomly and sparsely. The most advantageous strategy for an animal searching for food is, in these cases, to make small movements for some time to search the surroundings. If the animal doesn’t find any food, then it’s better for it to move on to a distant place, where the probability of finding food might be higher. Several research studies have shown that this pattern is very common in nature, as is discussed in the review published in 2008 in Physics of Life Reviews, by Viswanathan, Raposo and Luz. They show that a wide variety of animals, from amoebas to whales, seem to adopt Lévy flights for their displacements.

In an on-going collaboration, the three physicists from Paraná, Alagoas, and Pernambuco are now working on detailed analyses to formalize the theory of Lévy flights in a strict mathematical context. By doing so, they hope to describe, by using mathematical formulas, not only what happens with individual movements – the more commonly observed situations so far – but also what happens during collective search procedures, such as groups of monkeys that follow internal rules to coordinate the routes in order to increase the chances of finding food. To encourage scientific discussion on this topic, the three researchers are organizing a special issue of the Journal of Physics A, with review articles and original papers on random search movements. The issue is scheduled for publication in October this year.

Scientific articles
MERCADIER, N. et al. Lévy flights of photons in hot atomic vapours. Nature Physics. 2009.
VISWANATHAN, G. M. et al. Lévy flights and superdiffusion in the context of biological encounters and random searches. Physics of Life Reviews. v. 5, n. 3, p. 133-150. set. 2008.