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Correlation function and generalized master equation of arbitrary age.

Paolo Allegrini1, Gerardo Aquino, Paolo Grigolini

  • 1INFM, unità di Como, Via Valleggio 11, 22100 Como, Italy.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 11, 2005
PubMed
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This study analyzes a two-state statistical process with aging, finding that non-Poisson distributions lead to infinite memory. An approximated formula for the correlation function demonstrates high accuracy, offering insights into blinking quantum dots.

Area of Science:

  • Statistical Physics
  • Quantum Optics

Background:

  • Two-state statistical processes with non-Poisson sojourn times exhibit aging.
  • Conventional Markovian approximations are insufficient due to infinite memory effects.

Purpose of the Study:

  • To investigate aging in non-Poisson statistical processes.
  • To develop and validate accurate correlation functions for arbitrary ages.
  • To connect these findings to blinking quantum dot phenomena.

Main Methods:

  • Defining and calculating correlation functions using three distinct methods.
  • Comparing an approximated analytical formula with numerical treatments.
  • Establishing a link between correlation functions and generalized master equations.

Main Results:

Related Experiment Videos

  • Three methods yield exact expressions for the correlation function.
  • An approximated analytical formula for the correlation function is found to be highly accurate.
  • A connection is established between correlation functions and generalized master equations.

Conclusions:

  • The study provides an accurate analytical approach to correlation functions in aging systems.
  • This formalism offers a method for statistically treating blinking quantum dots, overcoming Liouville treatment limitations.