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Curving the space by non-Hermiticity.

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Area of Science:

  • Quantum Physics
  • Condensed Matter Physics
  • Geometry

Background:

  • Quantum systems are typically classified as Hermitian or non-Hermitian.
  • Non-Hermitian systems exhibit unique phenomena such as the non-Hermitian skin effect and sensitivity to boundary conditions.
  • These phenomena were previously thought to be exclusive to non-Hermitian systems.

Purpose of the Study:

  • To demonstrate that extraordinary non-Hermitian phenomena arise from a duality with Hermitian systems in curved spaces.
  • To reveal the underlying geometric principles governing non-Hermitian quantum physics.
  • To establish a novel connection between Hermitian and non-Hermitian physics.

Main Methods:

  • Establishing a duality between non-Hermitian models in flat spaces and Hermitian counterparts in curved spaces.
  • Utilizing one-dimensional (1D) chains with chiral tunnelings as a model system.
  • Exploring the equivalence to two-dimensional (2D) hyperbolic spaces, with and without magnetic fields.
  • Investigating how non-uniform tunnelings influence local curvatures.

Main Results:

  • Demonstrated that phenomena like the non-Hermitian skin effect can be naturally explained by geometric duality.
  • Showcased the equivalence of 1D non-Hermitian chains to 2D hyperbolic spaces.
  • Revealed that local curvatures can be engineered by manipulating tunnelings.
  • Uncovered deep geometric roots of non-Hermitian phenomena.

Conclusions:

  • Non-Hermitian phenomena possess profound geometric origins, linked to curved spaces.
  • A new theoretical framework connects Hermitian and non-Hermitian quantum physics through geometric duality.
  • This duality offers practical applications for engineering quantum systems and exploring non-Hermitian physics experimentally.