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The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
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Dynamic protected states in the non-Hermitian system.

Lei Chen1,2, Zhen-Xia Niu3, Xingran Xu4

  • 1School of Information, Hunan University of Humanities, Science and Technology, Loudi, 417000, China.

Scientific Reports
|September 17, 2024
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Summary

Gaussian wavepackets in non-Hermitian systems self-accelerate towards boundaries, exhibiting unique dynamic behaviors. This study reveals momentum-dependent amplitude growth, linked to the non-Hermitian skin effect.

Keywords:
Dynamic behaviorNon-Hermitian HamiltonianPhotonic latticeSkin effect

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Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics
  • Topological Physics

Background:

  • Non-Hermitian systems exhibit unique phenomena like the non-Hermitian skin effect, where eigenstates localize at boundaries.
  • Unlike Hermitian systems, non-Hermitian systems feature complex eigenenergies and boundary-sensitive behaviors.

Purpose of the Study:

  • To theoretically investigate the dynamic propagation of Gaussian wavepackets in non-Hermitian lattices.
  • To analyze the self-acceleration of bulk states and wavepackets towards system boundaries.

Main Methods:

  • Theoretical analysis of Gaussian wavepacket dynamics.
  • Investigation of momentum-space properties and energy dispersion.
  • Verification using 1D and 2D toy models.

Main Results:

  • Gaussian wavepackets propagate towards boundaries and approach a specific momentum value.
  • This momentum corresponds to the maximum imaginary component of energy dispersion.
  • Wavepackets covering this momentum exhibit exponentially increasing amplitudes, demonstrating dynamic protection.

Conclusions:

  • The study confirms the correspondence between the non-Hermitian skin effect and dynamic protected states.
  • Non-Hermitian lattice dynamics show self-acceleration and boundary localization phenomena.
  • Momentum-space properties are crucial for understanding wavepacket evolution in non-Hermitian systems.