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In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
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Dynamical tunneling in many-dimensional chaotic systems.

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Dynamical tunneling in many-dimensional systems is greatly enhanced when chaotic states delocalize due to the Anderson transition. This suggests amphibious states are common in complex systems.

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Area of Science:

  • Quantum chaos
  • Statistical mechanics
  • Dynamical systems theory

Background:

  • Dynamical tunneling allows systems to transition between localized states.
  • Understanding tunneling in complex, many-dimensional systems is crucial.
  • Anderson transition describes delocalization of states in disordered systems.

Purpose of the Study:

  • To investigate dynamical tunneling in many-dimensional systems.
  • To explore the role of Anderson transition in tunneling rates.
  • To determine the prevalence of amphibious states in higher dimensions.

Main Methods:

  • Utilizing a quasiperiodically modulated kicked rotor model.
  • Analyzing the behavior of chaotic states' delocalization.
  • Calculating tunneling rates from torus to chaotic regions.

Main Results:

  • Tunneling rate is drastically enhanced when chaotic states delocalize.
  • Anderson transition significantly impacts tunneling dynamics.
  • Evidence suggests amphibious states are not limited to one dimension.

Conclusions:

  • Amphibious states, previously observed in 1D, appear common in many-dimensional systems.
  • Delocalization of chaotic states via Anderson transition is key to enhanced tunneling.
  • This finding broadens the understanding of quantum transport in complex systems.