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Progressive quenching (PQ) reveals a hidden martingale property by linking quenched and thermal ensembles. This study expands PQ to Markovian and non-Markovian dynamics, showing how it can preserve system properties.

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Area of Science:

  • Statistical Mechanics
  • Stochastic Processes
  • Quantum Systems

Background:

  • Progressive quenching (PQ) is a method to sequentially fix system degrees of freedom.
  • A hidden martingale property has been observed in PQ.
  • Understanding the underlying mechanisms of this property is crucial.

Purpose of the Study:

  • To attribute the martingale property in PQ to the canonicity of quenched and thermal ensembles.
  • To extend PQ to Markovian and non-Markovian dynamics.
  • To investigate the impact of non-Markovian dynamics and delayed interactions on PQ.

Main Methods:

  • Analysis of the canonicity of two-layer ensembles (quenched and thermal).
  • Demonstration of Markovian property and detailed balance (DB) underpinning canonicity.
  • Expansion of PQ to transition networks without DB requirement.
  • Examination of PQ for systems with non-Markovian dynamics.
  • Analytical and numerical investigation of non-Markovian spin systems with delayed interactions.

Main Results:

  • The martingale property in PQ is attributed to the canonicity of the ensemble, underpinned by Markovian property and DB.
  • PQ is successfully extended to Markovian dynamics on transition networks where DB is not required.
  • For non-Markovian dynamics, PQ can occasionally maintain canonical ensemble structure if trajectory-wise DB holds.
  • PQ can compensate for the reduction of spin correlations in non-Markovian spin systems with delayed interactions.

Conclusions:

  • The canonicity of the ensemble is key to the martingale property in PQ under Markovian dynamics with DB.
  • PQ is a versatile technique applicable to broader classes of dynamics, including non-Markovian systems.
  • PQ offers a method to manage system correlations in complex, non-Markovian scenarios.