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Area of Science:

  • Quantum mechanics
  • Statistical physics
  • Condensed matter theory

Background:

  • Quantum measurements yield outcome distributions, not single values.
  • Full counting statistics (FCS) and charged moments offer deeper insights than average observables.
  • These statistics characterize entanglement in systems with global symmetries.

Purpose of the Study:

  • Investigate the time evolution of FCS and charged moments after a quantum quench in a U(1) symmetric system.
  • Explore the behavior of these quantities in finite regions and at large scales.
  • Develop methods to determine FCS and charged moments in non-equilibrium quantum dynamics.

Main Methods:

  • Analysis of U(1) charge evolution in a finite region post-quench.
  • Application of large-deviation theory to describe FCS and charged moments.
  • Utilizing a space-time duality for out-of-equilibrium dynamics.
  • Derivation of exact expressions for interacting integrable models.

Main Results:

  • FCS and charged moments exhibit distinct temporal regimes: a stationary state at long times and time-dependent behavior at short times.
  • A space-time duality relates the leading out-of-equilibrium order to a stationary value in a space-time-exchanged system.
  • Exact expressions for FCS and charged moments were derived for interacting integrable models.
  • The derived expressions were validated against known results in quantum cellular automata and spin chains.

Conclusions:

  • The study provides a novel method to understand non-equilibrium quantum dynamics using space-time duality.
  • The findings offer general properties of FCS and charged moments out of equilibrium.
  • The derived exact expressions are crucial for analyzing complex quantum many-body systems.