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This study reveals wave reciprocity in asymmetric 1D systems with nonlinear scatterers. Reciprocity conditions depend on system symmetry and can be periodically achieved by adjusting potential widths.

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Area of Science:

  • Nonlinear physics
  • Wave phenomena
  • Condensed matter theory

Background:

  • Wave reciprocity is a fundamental principle in physics, often observed in symmetric systems.
  • Asymmetric systems typically break wave reciprocity, posing challenges for wave manipulation.
  • Nonlinear scatterers introduce complex behaviors not typically found in linear systems.

Purpose of the Study:

  • To investigate the conditions for wave reciprocity in 1D asymmetric systems with nonlinear scatterers.
  • To propose a general criterion for wave reciprocity based on transfer matrix symmetry.
  • To explore how resonance conditions and system configurations affect wave reciprocity.

Main Methods:

  • Formulating a general reciprocal condition using rotation symmetry of forward and backward transfer matrices.
  • Deriving specific resonance conditions for the nonlinear scatterers.
  • Analyzing the behavior of the system by varying parameters like potential widths.

Main Results:

  • A general condition for wave reciprocity in terms of rotation symmetry of transfer matrices was proposed.
  • Resonance conditions were derived, leading to effective merging of scatterers into simpler configurations.
  • Wave reciprocity was shown to appear periodically with the variation of linear potential widths.
  • Replacing linear potentials with other transparent scatterers did not violate wave reciprocity.

Conclusions:

  • Wave reciprocity can be achieved in 1D asymmetric systems with nonlinear scatterers under specific conditions.
  • The proposed reciprocal condition provides a theoretical framework for designing such systems.
  • The findings have implications for controlling wave propagation in complex, engineered media.