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The Fermi-Pasta-Ulam problem: fifty years of progress.

G P Berman¹, F M Izrailev

¹Theoretical Division and CNLS, Los Alamos National Laboratory, Los Alamos, NM 87545, USA.

Chaos (Woodbury, N.Y.)

|April 20, 2005

Summary

The Fermi-Pasta-Ulam paradox, a foundational problem in nonlinear mechanics, is reviewed. Its resolutions connect to ergodicity, chaos, and quantum systems, offering insights into modern physics.

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Area of Science:

Physics
Nonlinear Mechanics
Quantum Systems

Background:

The Fermi-Pasta-Ulam (FPU) paradox presents an unexpected behavior in dynamical systems, challenging early assumptions about energy equipartition.
It serves as a crucial historical case study in the development of nonlinear dynamics and chaos theory.

Purpose of the Study:

To provide a comprehensive review of the Fermi-Pasta-Ulam (FPU) paradox.
To explore its suggested resolutions and connections to broader physical problems.
To trace the historical development of key concepts in nonlinear mechanics.

Main Methods:

Review of historical theoretical and numerical findings related to the FPU paradox.
Analysis of the FPU problem's connection to concepts like ergodicity, integrability, and chaos.
Consideration of emerging research directions.

Main Results:

The FPU paradox highlighted the complexity of nonlinear systems, revealing phenomena beyond simple statistical mechanics predictions.
Key concepts such as solitons, chaos, and KAM tori emerged from the study of the FPU problem.
The paradox's principles are now linked to modern areas like Bose-Einstein condensation.

Conclusions:

The FPU paradox remains a cornerstone in understanding nonlinear dynamics and chaos.
Its study has profoundly influenced the development of modern nonlinear mechanics.
New research avenues connect the FPU paradox to quantum phenomena and interacting Bose-particles.

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