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Crossover from Classical to Quantum Kibble-Zurek Scaling.

Pietro Silvi1, Giovanna Morigi2, Tommaso Calarco1

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The Kibble-Zurek mechanism explains defect formation in phase transitions. This study reveals distinct scaling behaviors for slow (quantum) and fast (classical) quenches, bridging theoretical predictions with experimental observations.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Dynamics
  • Statistical Mechanics

Background:

  • The Kibble-Zurek (KZ) hypothesis describes defect formation during phase transitions in out-of-equilibrium systems.
  • It predicts defect scaling based on quench speed, applicable to both classical and quantum phase transitions.
  • Understanding the crossover between quantum and classical dynamics is crucial for complex systems.

Purpose of the Study:

  • To investigate the crossover in defect formation scaling between slow (quantum-dominated) and fast (classical-dominated) quenches.
  • To determine the critical quench rate separating these two dynamical regimes.
  • To extend the predictive power of the Kibble-Zurek mechanism in diverse physical systems.

Main Methods:

  • Theoretical analysis of out-of-equilibrium dynamics in critical systems.
  • Numerical simulations of many-body dynamics for a ϕ⁴ model.
  • Estimation of the quench rate that delineates quantum and classical scaling regimes.

Main Results:

  • Identified two distinct power-law scalings corresponding to slow and fast quench regimes.
  • Demonstrated agreement with Kibble-Zurek theory predictions for both quantum and classical phase transitions.
  • Estimated the crossover quench rate separating the quantum and classical dynamics.

Conclusions:

  • The study successfully bridges quantum and classical scaling regimes predicted by the Kibble-Zurek mechanism.
  • Results provide insights into defect dynamics in systems like cold atoms and ions.
  • Confirms the extended applicability of the Kibble-Zurek hypothesis across different quench dynamics.