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Understanding the stability of equilibrium configurations is a fundamental part of mechanical engineering. In any system, there are three distinct types of equilibrium: stable, neutral, and unstable.
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Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
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Quantum systems equilibrate rapidly for most observables.

Artur S L Malabarba1, Luis Pedro García-Pintos2, Noah Linden2

  • 1H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol, BS8 1TL, United Kingdom.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 15, 2014
PubMed
Summary
This summary is machine-generated.

Most measurements equilibrate rapidly, even with few outcomes. For specific initial states, observables initially out of equilibrium also show fast equilibration, particularly low-rank, two-outcome measurements.

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Area of Science:

  • Quantum mechanics
  • Statistical physics
  • Quantum information theory

Background:

  • Understanding equilibration in quantum systems is crucial for quantum information processing.
  • Most measurements in quantum systems are expected to reach equilibrium quickly.

Purpose of the Study:

  • To investigate the conditions and types of measurements that lead to nontrivial equilibration in quantum systems.
  • To identify which measurements equilibrate rapidly under various initial states and Hamiltonians.

Main Methods:

  • Analysis of quantum systems under arbitrary Hamiltonians and initial states.
  • Focus on measurements with a limited number of outcomes relative to system dimension.
  • Examination of observables for which the initial state is an eigenstate.

Main Results:

  • The majority of measurements with few outcomes are found to be already equilibrated.
  • Observables, for specific initial states spread over many energy levels, equilibrate rapidly even if initially out of equilibrium.
  • All two-outcome measurements involving a low-rank projector demonstrate rapid equilibration.

Conclusions:

  • Nontrivial equilibration phenomena are observable under restricted measurement sets.
  • Rapid equilibration is a common feature for many quantum measurements, especially those with low-rank projectors.
  • The findings provide insights into the dynamics and thermalization of quantum states.