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A Large Deviation Principle in Many-Body Quantum Dynamics.

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Quantum many-body systems evolving under mean-field interactions exhibit fluctuations. These fluctuations align with established central limit theorems, providing insights into quantum dynamics.

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Area of Science:

  • Quantum mechanics
  • Statistical physics

Background:

  • The behavior of many-body quantum systems is complex.
  • Understanding quantum evolution in the mean-field regime is crucial.

Purpose of the Study:

  • To analyze quantum fluctuations in many-body systems.
  • To connect these fluctuations with existing statistical theorems.

Main Methods:

  • Analysis of factorized initial data in quantum evolution.
  • Application of mean-field theory.
  • Derivation of large deviation estimates.

Main Results:

  • Fluctuations around Hartree dynamics were quantified.
  • Large deviation estimates for these fluctuations were established.
  • Consistency with central limit theorems was demonstrated.

Conclusions:

  • The study provides a rigorous framework for understanding quantum fluctuations.
  • Results confirm theoretical predictions in quantum statistical mechanics.
  • This work bridges quantum dynamics and statistical fluctuation theory.