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Area of Science:

  • Quantum physics
  • Condensed matter theory
  • Quantum optics

Background:

  • Quantum many-body systems with long-range interactions are crucial in quantum optics, nuclear magnetic resonance, and nuclear physics.
  • These systems are amenable to numerical study and are expected to follow mean-field theory in the thermodynamic limit.
  • Experimental advancements allow precise control over long-range interacting systems, enabling exploration of nonequilibrium phases like time crystals and chaotic regimes.

Purpose of the Study:

  • To rigorously prove the exact applicability of mean-field theory to time-dependent infinite-range interacting systems in the thermodynamic limit.
  • To address the challenges in numerically establishing emergent phases in these systems.
  • To provide bounds for finite-size effects and their time dependence.

Main Methods:

  • Theoretical analysis of quantum many-body systems.
  • Rigorous mathematical proof of mean-field theory's exactness.
  • Derivation of bounds for finite-size corrections.

Main Results:

  • Mean-field theory is proven to exactly capture the dynamics of infinite-range interacting quantum systems in the thermodynamic limit.
  • Established bounds quantify finite-size effects and their dependence on evolution time.
  • Resolved the debate on mean-field theory's applicability to time-dependent infinite-range systems.

Conclusions:

  • Mean-field theory provides an exact description for the dynamics of quantum many-body systems with infinite-range interactions in the thermodynamic limit.
  • The findings clarify the theoretical framework for studying complex quantum phenomena in these systems.
  • Provides a foundation for future research into quantum dynamics and emergent phenomena.