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The arithmetic mean is usually skewed towards the larger values in the data set. Therefore, to avoid this inherent bias towards smaller values, the harmonic mean is used.
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To determine the energy of a simple harmonic oscillator, consider all the forms of energy it can have during its simple harmonic motion. According to Hooke's Law, the energy stored during the compression/stretching of a string in a simple harmonic oscillator is potential energy. As the simple harmonic oscillator has no dissipative forces, it also possesses kinetic energy. In the presence of conservative forces, both energies can interconvert during oscillation, but the total energy remains...
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The key characteristic of the simple harmonic motion is that the acceleration of the system and, therefore, the net force are proportional to the displacement and act in the opposite direction to the displacement. Additionally, the period and frequency of a simple harmonic oscillator are independent of its amplitude. For example, diving boards move faster or slower based on their thickness. A stiff, thick diving board has a large force constant, which causes it to have a smaller period, while a...
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Harmonic non-Hermitian skin effect.

Qicheng Zhang1, Liwei Xiong1, Shuaishuai Tong1

  • 1Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan, China.

Nature Communications
|January 30, 2026
PubMed
Summary
This summary is machine-generated.

Researchers explored the harmonic non-Hermitian skin effect (NHSE) in acoustic systems. They demonstrated controllable switching between unipolar and bipolar NHSEs by reconfiguring frequencies, opening new avenues in non-Hermitian physics.

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Area of Science:

  • Condensed Matter Physics
  • Acoustics
  • Non-Hermitian Systems

Background:

  • The non-Hermitian skin effect (NHSE) describes boundary localization in non-Hermitian systems.
  • Floquet engineering is a key method for expanding NHSE applications.
  • The harmonic response in Floquet systems remains underexplored.

Purpose of the Study:

  • To introduce and experimentally demonstrate the harmonic non-Hermitian skin effect (NHSE).
  • To investigate the role of dynamic couplings and spectral topology in harmonic NHSE.
  • To achieve controllable switching of NHSE properties in an acoustic platform.

Main Methods:

  • Theoretical modeling using a dynamic-coupled Hatano-Nelson model.
  • Experimental implementation in a programmable acoustic lattice with unidirectional couplers.
  • Frequency reconfiguration to control excitation and modulation parameters.

Main Results:

  • A single-frequency input generates multiple harmonics with distinct skin morphologies.
  • Each harmonic's morphology is governed by spectral winding topology at its specific frequency.
  • Controllable switching between unipolar and bipolar harmonic NHSEs was achieved.
  • Unipolar and bipolar NHSEs exhibited uniform and opposite sound gathering, respectively.

Conclusions:

  • The study introduces the novel concept of harmonic NHSE.
  • Demonstrates experimental realization and control of harmonic NHSE in acoustics.
  • Highlights the potential for investigating non-Hermitian physics with harmonic effects.