Ricorrenza di Fermi-Pasta-Ulam

The Physical Origin of the Déjà-vu Phenomenon

An international research team, coordinated by the Sapienza Department of Physics, has investigated and experimentally verified, for the first time, the phenomenon of recurrences in Physics, demonstrating that their apparition can be explained through exact mathematical equations. The results of the study have been published on Physical Review X

What is a “déjà-vu”? Can the perception that a given past event is happening again have a true basis?

From a physical point of view, an analogous phenomenon was discovered by Scientists Enrico Fermi, John Pasta and Stanislaw Ulam more than sixty years ago: The Fermi-Pasta-Ulam Problem. While working on the first calculation device that would become the modern computer, Enrico Fermi unexpectedly discovered that, during their natural evolution, certain complex non-linear systems (systems with a great number of interacting variables) could spontaneously return to the starting point in a cyclical manner, without ever reaching a final equilibrium.

The study conducted by the Sapienza Department of Physics, in collaboration with the National Research Council (Cnr) Institute for Complex Systems, Shenzhen University, the Hebrew University of Jerusalem and the Landau Institute for Theoretical Physics, experimentally demonstrated for the first time how the Fermi-Pasta-Ulam Problem originates from a precise collective motion of the system and how this motion may be predicted, obtaining exact mathematical solutions from the model equations. The results of the study have been published on Physical Review X.

“These recurrent exact solutions,” explains Davide Pierangeli, one of the study’s authors, “predict infinite “déjà-vus” and were previously hypothesized by Grinevich and Santini in the context of non-linear optic and hydrodynamic systems; however, the possibility of directly observing them was not a given.”

Thanks to an innovative experimental strategy employing a crystal made extremely photosensitive by external electromagnetic fields (non-linear crystal), the team observed, for the first time, how specific optic waves can reappear during the propagation of laser light. More specifically, the combination of three laser beams was used to excite the optical equivalent of a very weak musical note, which, propagating through the crystal, generated a rich optical melody that naturally evolves in space until it returns to the initial note, before repeating the cycle.

Notwithstanding the fact that this recurrent evolution of light takes place in a volume the size of a tenth of a human hair, the team was able to precisely follow its behavior by acting on the properties of the initial note – or wave. Moreover, the researchers demonstrated that it is possible to backtrack this complex dynamic optical field activity and obtain the specific wave that generated that recurring motion. 

This allowed the team to unambiguously identify the physical mechanism underlying this type of “dèjà-vu” phenomenon.

“The attempt to understand this recurrence,” adds Team Coordinator Eugenio Del Re, “has characterised the entire development of non-linear science, an ongoing challenge known as the FPU Problem.”

Until today, in fact, none of the proposed theoretical explanations was every experimentally verified, as recurrences are an extremely sensitive phenomenon to the minute fluctuations and disturbances that characterise every natural system. 

“The results of our study,” concludes Prof. Del Re, “shed light on the fascinating and controversial Fermi-Pasta-Ulam Problem and represent an avant-garde test for the theory of non-linear waves, opening up unique opportunities to predict the evolution of high chaotic systems, as well as the control of highly-concentrated energy flows of different natures, ranging from tsunamis to plasmas to electromagnetic waves.” 



Observation of Fermi-Pasta-Ulam-Tsingou Recurrence and Its Exact Dynamics - D. Pierangeli, M. Flammini, L. Zhang, G. Marcucci, A. J. Agranat, P. G. Grinevich, P. M. Santini, C. Conti, and E. Del Re - Physical Review 2018 X  DOI: https://journals.aps.org/prx/abstract/10.1103/PhysRevX.8.041017


Further information

Eugenio Del Re 
Department of Physics, Sapienza University of Rome

Davide Pierangeli
Department of Physics, Sapienza University of Rome


Friday, 30 November 2018

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