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Hyperuniformity and its generalizations.

Salvatore Torquato1

  • 1Department of Chemistry, Department of Physics, Princeton Center for Theoretical Science, Program of Applied and Computational Mathematics, Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, New Jersey 08544, USA.

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This study generalizes hyperuniformity, a unique state of matter between crystals and liquids, to new systems. These advancements reveal exotic anisotropic properties in materials, offering novel technological applications for wave manipulation.

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Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Statistical Mechanics

Background:

  • Disordered many-particle hyperuniform systems are exotic amorphous states exhibiting crystal-like suppression of density fluctuations and liquid-like isotropy.
  • These systems are crucial in physical, mathematical, and biological sciences, possessing novel physical properties with technological importance.

Purpose of the Study:

  • To broaden the concept of hyperuniformity by generalizing it to diverse systems and phenomena.
  • To explore the mathematical underpinnings and consequences of these generalized hyperuniformity concepts.

Main Methods:

  • Generalization of hyperuniformity to interfacial area fluctuations in heterogeneous media and evolving microstructures.
  • Extension to random scalar fields, divergence-free random vector fields, and statistically anisotropic many-particle systems.
  • Formulation of mathematical frameworks and provision of illustrative calculations, including analysis of spectral functions and nonanalyticities at the origin in Fourier space.

Main Results:

  • Demonstration of generalized hyperuniformity for interfacial-area fluctuations and anisotropic systems, requiring accounting for directional spectral functions.
  • Placement of isotropic turbulence energy spectra within the context of generalized hyperuniformity.
  • Discovery of many-particle ground states with directional hyperuniformity exhibiting exotic anisotropic physical properties (elastic, optical, acoustic).

Conclusions:

  • The generalized hyperuniformity framework provides new insights into a broad range of phenomena across various scientific fields.
  • Directional hyperuniformity offers potential for technological applications, such as novel methods for manipulating light and sound waves.
  • Disordered many-particle systems responding to external fields are promising candidates for exhibiting directional hyperuniformity.