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Once the fields have been calculated using Maxwell's four equations, the Lorentz force equation gives the force that the fields exert on a charged particle moving with a certain velocity. The Lorentz force equation combines the force of the electric field and of the magnetic field on the moving charge. Maxwell's equations and the Lorentz force law together encompass all the laws of electricity and magnetism. The symmetry that Maxwell introduced into his mathematical framework may not be...
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When a structural member undergoes plastic deformation due to bending, it is crucial to understand the position of the neutral axis and the stress distribution. This member, characterized by a single plane of symmetry, exhibits a uniform stress distribution, with negative stress above the neutral axis and positive stress below. Notably, the neutral axis does not align with the centroid of the cross-section. This misalignment is typical in cases where the cross-section is not rectangular or...
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Evolution of discrete symmetries.

Peter Schmelcher1

  • 1Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany and The Hamburg Centre for Ultrafast Imaging, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany.

Physical Review. E
|November 18, 2023
PubMed
Summary

Local symmetries in wave physics create one-dimensional lattices with transient and periodic behaviors. These lattices exhibit dense symmetry skeletons, influencing asymptotic properties and eigenstate localization.

Area of Science:

  • Wave Physics
  • Condensed Matter Physics
  • Materials Science

Background:

  • Symmetries are fundamental to physical properties and wave physics design.
  • Local symmetries, confined to finite spatial domains, can arise from self-organization or synthetic design.

Purpose of the Study:

  • To investigate the structural and dynamical properties of one-dimensional lattices generated by extending finite chains with local symmetry operations.
  • To analyze the asymptotic behavior, unit cell decomposition, and transient characteristics of these lattices.
  • To explore the impact of dense local symmetries on the energy spectra and eigenstates of tight-binding Hamiltonians.

Main Methods:

  • Application of local symmetry operations to extend finite chains, creating one-dimensional lattices.

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  • Analysis of lattice properties, including transient and periodic behaviors, based on overlapping local symmetries.
  • Investigation of tight-binding Hamiltonians, including their energy eigenvalue spectra and eigenstates.

    • Main Results:

    • The resulting one-dimensional lattices exhibit a transient behavior followed by periodicity.
    • The lattices possess a dense skeleton of overlapping local symmetries.
    • Analysis of tight-binding models reveals significant variability in eigenstate localization due to numerous local symmetries.

    Conclusions:

    • Local symmetries serve as a powerful design principle for creating complex lattice structures with predictable asymptotic properties.
    • The dense network of local symmetries profoundly influences the electronic and wave propagation characteristics within the lattice.
    • Understanding these symmetry-induced properties is crucial for designing novel wave-based materials and devices.