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Planck's quantum-driven integer quantum Hall effect in chaos.

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We discovered a quantum phenomenon in chaotic systems analogous to the quantum Hall effect. This phenomenon exhibits distinct metallic and insulating phases, with topological properties arising from chaos.

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Area of Science:

  • Quantum Chaos
  • Condensed Matter Physics
  • Topological Matter

Background:

  • The integer quantum Hall effect (IQHE) is a topological phenomenon observed in 2D electron systems.
  • Chaotic systems often exhibit complex dynamics that can be difficult to analyze.
  • Understanding the interplay between chaos and quantum mechanics is a fundamental challenge.

Purpose of the Study:

  • To investigate quantum phenomena in a canonical chaotic system, the kicked spin-1/2 rotor.
  • To explore analogies between chaos-driven phenomena and established topological effects like the IQHE.
  • To identify conditions under which topological quantum phenomena emerge from classical chaos.

Main Methods:

  • Analysis of the kicked spin-1/2 rotor model.
  • Investigation of energy growth dynamics as a function of Planck's quantum (he).
  • Characterization of system phases (metallic/insulating) and topological properties.

Main Results:

  • A Planck's quantum (he)-driven phenomenon analogous to the IQHE was identified in the kicked spin-1/2 rotor.
  • The system exhibits an unbounded energy growth ('metallic' phase) at critical he values and bounded growth ('insulating' phase) otherwise.
  • The 'insulating' phase is topological, characterized by a quantized Hall conductance that changes by unity at critical he values.

Conclusions:

  • Rich topological quantum phenomena can emerge from chaotic dynamics.
  • The kicked spin-1/2 rotor serves as a model system for studying chaos-induced topological effects.
  • This work bridges the fields of quantum chaos and topological matter physics.