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Jarzynski Equality in PT-Symmetric Quantum Mechanics.

Sebastian Deffner1, Avadh Saxena1

  • 1Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.

Physical Review Letters
|May 2, 2015
PubMed
Summary

The quantum Jarzynski equality applies to PT-symmetric quantum mechanics with unbroken PT symmetry. However, it fails in broken PT symmetry regimes, as shown in coupled optical waveguides.

Area of Science:

  • Quantum mechanics
  • Non-Hermitian physics
  • Thermodynamics

Background:

  • The Jarzynski equality relates non-equilibrium work to equilibrium free energy.
  • Parity-time (PT) symmetry is a key concept in non-Hermitian quantum mechanics.
  • Understanding the interplay between quantum dynamics and thermodynamics is crucial.

Purpose of the Study:

  • To investigate the generalization of the quantum Jarzynski equality in PT-symmetric quantum mechanics.
  • To explore the validity of the Jarzynski equality in both unbroken and broken PT symmetry regimes.
  • To analyze the behavior of the phase transition at the PT symmetry breaking point.

Main Methods:

  • Theoretical analysis of the quantum Jarzynski equality.
  • Study of PT-symmetric quantum systems, specifically two coupled optical waveguides.

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  • Investigation of CPT norm preservation during quantum dynamics.

    • Main Results:

    • The quantum Jarzynski equality is shown to generalize to PT-symmetric quantum mechanics with unbroken PT symmetry.
    • The Jarzynski equality does not hold in the broken PT symmetry regime.
    • The CPT norm is not preserved during dynamics in the broken PT symmetry regime.
    • The phase transition between unbroken and broken PT symmetry is thermodynamically inhibited due to diverging irreversible work.

    Conclusions:

    • The quantum Jarzynski equality's applicability is contingent on PT symmetry.
    • Broken PT symmetry leads to a breakdown of the Jarzynski equality and CPT norm preservation.
    • The divergence of irreversible work at the critical point inhibits the phase transition in experimentally relevant systems.