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Gradient marker: a universal wave pattern in an inhomogeneous continuum.

A E Kaplan1

  • 1Electrical and Computer Engineering Department, The Johns Hopkins University, Baltimore, Maryland 21218, USA. alexander.kaplan@jhu.edu

Physical Review Letters
|October 30, 2012
PubMed
Summary
This summary is machine-generated.

A universal wave pattern, the "gradient marker," emerges near gradient extrema in media with slow spatial variations. This finding applies to optics and quantum mechanics, revealing simple, non-trivial wave profiles.

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Area of Science:

  • Physics
  • Wave Phenomena
  • Mathematical Physics

Background:

  • Wave propagation in inhomogeneous media is complex.
  • Understanding universal behaviors in wave transport is crucial.
  • Previous studies lacked a unified description for gradient-induced wave patterns.

Purpose of the Study:

  • To identify and characterize universal wave patterns in media with slow spatial gradients.
  • To investigate the applicability of these patterns across different wave propagation domains.
  • To explore related phenomena like resonant states in continuum.

Main Methods:

  • Analytical derivation of wave transport equations.
  • Development of the
  • gradient marker
  • concept.
  • Numerical simulations for specific wave equation examples.
  • Analysis of quantum well systems for resonant states.

Main Results:

  • A universal wave pattern, the
  • gradient marker
  • , was discovered near gradient extrema.
  • This pattern exhibits an analytically derived, simple, non-trivial profile.
  • The pattern's universality was confirmed across optics and quantum mechanics.
  • Resonant states in continuum were identified in quantum wells, with existence criteria formulated.

Conclusions:

  • The
  • gradient marker
  • provides a unifying framework for wave transport in slowly varying media.
  • This discovery has implications for diverse fields including optics and quantum mechanics.
  • The findings open avenues for exploring and controlling wave behavior in engineered materials.