Particles, waves and ants

November 26, 2014
Ants and waves -- are there similarities? Even in biology, this phenomenon can be observed: the path of ants crawling across a surface can be described as a random walk. A large ant will traverse an area with a smaller number of steps than a small ant that will change its direction more often. But regardless of their size, the time they spend on a given area is always the same. Credit: TU Wien / ant picture: Bild:Fir0002/Flagstaffotos, GNU Free Documentation Licence 1.2

Animals looking for food or light waves moving through turbid media – astonishing similarities have now been found between completely different phenomena.

A drunken sailor staggers onto a square with lots of streetlamps on it. Sometimes he will run into one of the lamps, change his direction and keep moving. Does the time he spends on this square depend on the number of streetlamps? The surprising answer is: no.

No matter whether there is a streetlamp on every square meter or whether the distance between the lamps is large: on average, the drunken sailor will always spend the same amount of time on the square. Calculations at the Vienna University of Technology (TU Wien) have now shown that this invariance of the dwell time is a universal phenomenon. It can be observed in completely different systems - from crawling ants to light waves in disordered media.

The research on this project was carried out with collaborators Romain Pierrat, Rémi Carminati, and Sylvain Gigan from Paris (Institut Langevin and Laboratoire Kastler-Brossel), the results have now been published in the journal PNAS.

Travelling Through Imperfect Materials

Professor Stefan Rotter's team (TU Wien) analyses the propagation of waves in disordered media, such as light waves in turbid glass or quantum particles moving as a quantum wave through a material with impurities.

"Usually, such transport phenomena are characterized by the so-called mean free path", says Stefan Rotter. It is the length of the path a particle or a wave can typically travel freely until it hits the next obstacle. In the case of the drunken sailor, the mean free path would be the average distance between the street lamps. In turbid glass, it would be the distance between two microscopic impurities at which the light wave is scattered.

Complicated paths of particles which are scattered many times.

The Length of the Path Stays the Same

Many important physical quantities depend on the mean free path - for instance the fraction of the light, which passes through semi-transparent glass. "We can calculate how much time the transmitted part and the reflected part of the spend inside the glass, respectively. These quantities, the transmission time and the reflection time, heavily depend on the mean free path", says Phillip Ambichl, PhD-student in Stefan Rotter's team and co-author of the paper.

But when those two quantities are combined to calculate the overall time the average particle or wave spends inside the medium, then the mean free path drops out of the result entirely. Quite surprisingly, light spends as much time in a turbid glass plate as in a transparent one.

It is the same with the drunken sailor: If his erratic path is blocked by an increasing number of streetlamps, there is a higher probability of the sailor hitting one of lamps right at the beginning, so that he will turn around and never venture far into the square - the time he spends on the square would thus be reduced. If, however, he happens to enter deep into the forest of streetlamps, he will be trapped there for a long time. Paths leading to the opposite side of the square thus become much longer when the number of streetlamps increases. As it turns out these two opposing effects fully compensate each other, so that the total average dwell time remains the same when changing the number of streeplamps.

Fewer scattering events - but the average length of the path stays the same. Fewer scattering events - but the average length of the path stays the same.

"It is quite a surprise to see that this effect shows up in completely different systems", says Philipp Ambichl. "Our findings apply to rubber balls rolling across a wooden plank, hitting randomly distributed nails, as well as to electron waves travelling through a disordered system, in which the electron can be scattered at individual atoms."

Even in biology, this phenomenon can be observed: the path of ants crawling across a surface can be described as a random walk too. A large ant will traverse an area with a smaller number of steps than a small ant that will change its direction more often. But regardless of their size, the time they spend on a given area is always the same.

"With the average dwell time in an area or in a specific medium we have identified a quantity which is completely independent of the mean free path. This remarkable result will help us to better understand quite different transport phenomena appearing also in everyday applications such as in solar cells", says Stefan Rotter. Whether it is particles, waves or ants - by studying one system, one can also learn much about others, even if at first glance they may seem completely unrelated.

Explore further: The paths of photons are random, but coordinated

More information: PNAS:

Related Stories

The paths of photons are random, but coordinated

December 20, 2012

(—Researchers at the Niels Bohr Institute have demonstrated that photons (light particles) emitted from light sources embedded in a complex and disordered structure are able to mutually coordinate their paths through ...

Absorption straightens the drunken stagger of light

July 1, 2014

( —In a study partly funded by the FOM Foundation, physicists from the University of Twente and Yale University have discovered that light travelling through an opaque material follows a straighter path, if the ...

Laser physics upside down

July 15, 2014

At the Vienna University of Technology a system of coupled lasers has been created which exhibits truly paradoxical behaviour: An increase in energy supply switches the lasers off, reducing the energy can switch them on.

Nanoparticles break the symmetry of light

October 6, 2014

How can a beam of light tell the difference between left and right? At the Vienna University of Technology (TU Wien) tiny particles have been coupled to a glass fibre. The particles emit light into the fibre in such a way ...

Two photons strongly coupled by glass fiber

November 2, 2014

Usually, light waves do not interact with each other. Coupling of photons with other photons is only possible with the help of special materials and very intense light. Scientists in Vienna have now created the strongest ...

Creating bright X-ray pulses in the laser lab

November 11, 2014

To create X-rays—short wave radiation—scientists at TU Vienna start out with very long wavelengths—infrared laser. Long wavelength laser pulses rip atoms out of metal and accelerate them, which leads to emission of ...

Recommended for you

Measuring tiny forces with light

August 25, 2016

Photons are bizarre: They have no mass, but they do have momentum. And that allows researchers to do counterintuitive things with photons, such as using light to push matter around.

DNA chip offers big possibilities in cell studies

August 25, 2016

A UT Dallas physicist has developed a novel technology that not only sheds light on basic cell biology, but also could aid in the development of more effective cancer treatments or early diagnosis of disease.

Spherical tokamak as model for next steps in fusion energy

August 24, 2016

Among the top puzzles in the development of fusion energy is the best shape for the magnetic facility—or "bottle"—that will provide the next steps in the development of fusion reactors. Leading candidates include spherical ...

Feeling the force between sand grains

August 24, 2016

For the first time, Lawrence Livermore National Laboratory (LLNL) researchers have measured how forces move through 3D granular materials, determining how this important class of materials might pack and behave in processes ...


Please sign in to add a comment. Registration is free, and takes less than a minute. Read more

Click here to reset your password.
Sign in to get notified via email when new comments are made.