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Operator dynamics in a Brownian quantum circuit.

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Summary
This summary is machine-generated.

Operator spreading in chaotic evolution is modeled as height growth. Mean operator height grows exponentially with N-spin models and saturates, offering insights into quantum chaos dynamics and bounds.

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Area of Science:

  • Quantum Information Science
  • Statistical Mechanics
  • High Energy Physics

Background:

  • Chaotic evolution in quantum systems leads to operator spreading.
  • Operator size, represented by height, increases during chaotic dynamics.
  • Understanding operator spreading is crucial for quantum chaos and scrambling.

Purpose of the Study:

  • To model operator spreading in chaotic evolution as a stochastic height growth process.
  • To investigate the dynamics of operator height in N-spin models.
  • To connect operator height growth to quantum scrambling time and chaos bounds.

Main Methods:

  • Formulating operator spreading as a stochastic height growth process.
  • Analyzing N-spin models with all two-body interactions.
  • Deriving an exact solution for the mean operator height.

Main Results:

  • Mean operator height grows exponentially, proportional to the squared commutator.
  • Exponential growth occurs within logN scrambling time.
  • Height growth saturates following a logistic function, dependent on N.

Conclusions:

  • The height picture provides a framework for understanding chaotic operator spreading.
  • Scrambling time is linked to the exponential growth phase of operator height.
  • Temperature dependence of chaos bounds may relate to initial operator height distributions.