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Researchers developed a simple formula for calculating heating rates in many-body systems under periodic driving. This formula, derived using a dressed Hamiltonian and high-frequency expansion, accurately predicts heating dynamics beyond linear response.

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Area of Science:

  • Statistical Physics
  • Quantum Many-Body Systems
  • Non-equilibrium Dynamics

Background:

  • Heating under periodic driving is a fundamental concept in non-equilibrium statistical physics.
  • Deriving accurate heating rates in these systems presents a significant theoretical challenge.

Purpose of the Study:

  • To develop a simple and quantitatively accurate formula for the heating rate in classical and quantum many-body systems subjected to fast and strong periodic driving.
  • To explore the connection between high-frequency expansions and heating dynamics.

Main Methods:

  • Constructing a time-dependent dressed Hamiltonian by transforming to a rotating frame.
  • Utilizing a truncation of the high-frequency expansion of the micromotion operator.
  • Applying linear-response theory to the dressed system.

Main Results:

  • A simple formula for the heating rate under fast and strong periodic driving was derived.
  • The second-order truncation of the high-frequency expansion was found to yield quantitatively accurate heating rates.
  • Accuracy extends beyond the regime typically described by linear-response theory.

Conclusions:

  • The derived formula provides a powerful tool for understanding heating in driven many-body systems.
  • Heating dynamics information is encoded in the initial terms of the high-frequency expansion.
  • This work offers new insights into non-equilibrium statistical physics phenomena.