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In curved beams, unlike straight beams, the stress distribution across the cross-section is not uniform due to the beam's curvature. This non-uniformity arises because the neutral axis, where stress is zero, does not align with the centroid of the section. In a curved beam, the strain varies along the section as a function of the distance from the neutral axis.
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Absence of Weak Localization on Negative Curvature Surfaces.

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Disrupting Anderson localization in 2D is possible by tuning manifold curvature. Negative curvature introduces an infrared cutoff, restoring diffusive transport by reducing quantum interference effects.

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Area of Science:

  • Condensed matter physics
  • Quantum mechanics
  • Geometry

Background:

  • Anderson localization describes the absence of diffusive transport in disordered systems due to quantum interference.
  • In two dimensions, disorder is generally believed to induce localization of all states at sufficient length scales.
  • Quantum interference effects are crucial in understanding electron transport in disordered materials.

Purpose of the Study:

  • To investigate mechanisms for disrupting Anderson localization in two dimensions.
  • To explore the role of manifold curvature in quantum interference and transport phenomena.
  • To determine if negative curvature can prevent weak localization.

Main Methods:

  • Theoretical analysis of quantum interference and particle trajectories on curved manifolds.
  • Calculation of the Cooperon in hyperbolic space to assess weak-localization corrections.
  • Investigation of the impact of negative and mixed curvature on diffusive transport.

Main Results:

  • Negative curvature manifolds exhibit an infrared cutoff for self-returning paths, suppressing localization.
  • Hyperbolic space leads to a proliferation of quantum trajectories, diminishing interference effects and restoring diffusion.
  • Intermittency in variable curvature manifolds causes hyperbolic regions to dominate, arresting weak localization.

Conclusions:

  • Manifold curvature offers a novel mechanism to counteract Anderson localization in two dimensions.
  • Negative curvature and specific mixed-curvature surfaces can prevent weak localization, potentially relevant for 2D materials and disordered films.
  • The findings suggest experimental verification using quantum simulators and offer insights into realistic material properties.