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Quantum Tunneling and Complex Dynamics in the Suris's Integrable Map.

Yasutaka Hanada1,2, Akira Shudo2

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Entropy (Basel, Switzerland)
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Summary
This summary is machine-generated.

Quantum tunneling in integrable maps shows similar splitting to Hamiltonian systems but differs in wave function tails. Complex plane dynamics reveal branch points influence tunneling behavior, highlighting quantum tunneling

Keywords:
complex classical dynamicsdynamical tunnelingintegrable map

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Area of Science:

  • Quantum mechanics
  • Mathematical physics
  • Dynamical systems

Background:

  • Quantum tunneling is a phenomenon where particles pass through potential barriers.
  • Integrable maps offer a simplified model for studying quantum dynamics.
  • Previous studies focused on tunneling splitting, with less attention to wave function tails.

Purpose of the Study:

  • To investigate quantum tunneling in a two-dimensional integrable map.
  • To compare tunneling behavior with associated one-dimensional Hamiltonian systems.
  • To explore the origins of differences in wave function tunneling tails.

Main Methods:

  • Analyzing orbits confined to curves defined by a one-dimensional Hamiltonian.
  • Comparing tunneling splitting in the integrable map and Hamiltonian system.
  • Superposing eigenfunctions to form doublets and examining wave function tails.
  • Observing classical dynamics in the complex plane to identify potential influences.

Main Results:

  • Tunneling splitting in the integrable map and Hamiltonian system are qualitatively similar.
  • Significant differences are observed in the tunneling tails of wave functions.
  • Classical dynamics in the complex plane reveal the role of branch points.
  • Branch points in the potential function are linked to non-trivial tunneling tail behavior.

Conclusions:

  • Quantum tunneling in integrable maps shares similarities with Hamiltonian systems regarding splitting.
  • Wave function tunneling tails exhibit distinct behaviors not fully explained by real-plane dynamics.
  • Complex plane dynamics, particularly branch points, are crucial for understanding subtle quantum tunneling effects.
  • A comprehensive understanding of quantum tunneling requires considering dynamics beyond the real plane.