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This summary is machine-generated.

The Kibble-Zurek mechanism (KZM) predicts defect formation during phase transitions. This study extends KZM by analyzing defect number fluctuations using large deviations theory, revealing universal scaling laws beyond equilibrium predictions.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Phase Transitions
  • Statistical Mechanics

Background:

  • The Kibble-Zurek mechanism (KZM) describes topological defect formation during phase transitions.
  • KZM predicts a universal scaling law for the average defect number with quench time.
  • Near equilibrium, defect number fluctuations are often Gaussian, consistent with the central limit theorem.

Purpose of the Study:

  • To investigate the universality of defect number fluctuations beyond the standard Kibble-Zurek mechanism.
  • To characterize the exact form of the rate function for large deviations in the transverse-field quantum Ising model.
  • To generalize the analysis of large deviation scaling for arbitrary continuous phase transitions.

Main Methods:

  • Application of large deviations theory to analyze defect number distributions.
  • Exact calculation of the rate function for the transverse-field quantum Ising model.
  • Theoretical characterization of scaling laws for large deviations in continuous phase transitions.

Main Results:

  • Identified universal scaling laws for defect number fluctuations beyond the Kibble-Zurek mechanism.
  • Determined the precise form of the rate function governing large deviations in the transverse-field quantum Ising model.
  • Established a framework for understanding large deviation scaling in a broad class of continuous phase transitions.

Conclusions:

  • The universality of defect number distributions extends beyond equilibrium predictions and the standard Kibble-Zurek mechanism.
  • Large deviations theory provides a powerful tool for characterizing the full distribution of topological defects.
  • Findings offer new insights into the non-equilibrium dynamics of quantum and continuous phase transitions.