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Work distribution and edge singularities for generic time-dependent protocols in extended systems.

Pietro Smacchia1, Alessandro Silva

  • 1SISSA, International School for Advanced Studies, via Bonomea 265, 34136 Trieste, Italy and INFN, Sezione di Trieste, I-34127 Trieste, Italy.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
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Summary

We analyzed work statistics in bosonic field theory and the Ising chain. The low-energy work distribution shows a universal edge singularity, robust across different protocols and systems.

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Area of Science:

  • Statistical mechanics
  • Quantum field theory
  • Condensed matter physics

Background:

  • The study of work statistics in quantum systems provides insights into fundamental thermodynamic principles.
  • Investigating phase transitions and critical phenomena is crucial for understanding complex quantum systems.

Purpose of the Study:

  • To derive exact formulas for the full statistics of work done in a free bosonic field theory and a 1D Ising chain.
  • To analyze the behavior of work distribution, particularly edge singularities, under various global and local protocols.
  • To examine the robustness of condensation transitions in bosonic systems against different quenching protocols.

Main Methods:

  • Utilizing generic protocols to globally change mass in a bosonic field theory with relativistic dispersion.
  • Applying global and local changes to the transverse field in a 1D Ising chain, starting from the critical point.
  • Describing systems in the scaling limit and deriving exact formulas for work statistics.

Main Results:

  • Exact formulas for the complete work statistics were obtained for all studied cases.
  • A universal edge singularity was identified in the low-energy part of the work distribution, independent of protocol specifics.
  • The exponent of the edge singularity depends only on the initial and final states relative to the critical point.
  • The condensation transition in bosonic systems is shown to be robust against protocol variations.

Conclusions:

  • The work distribution in these quantum systems exhibits universal features, particularly an edge singularity.
  • The findings highlight the resilience of quantum phase transitions and related phenomena to the details of applied perturbations.
  • This research contributes to a deeper understanding of non-equilibrium quantum dynamics and statistical mechanics.