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Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
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Wave-number dependent current correlation for a harmonic oscillator.

August Wierling1, Isao Sawada

  • 1Institut für Physik, Universität Rostock, 18051 Rostock, Germany. august.wierling@uni-rostock.de

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 15, 2011
PubMed
Summary

This study derives an analytic expression for the wave-number dependent current-correlation function of a harmonic oscillator. The findings offer insights into quantum systems and correlation functions across different limits.

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Area of Science:

  • Physics
  • Quantum Mechanics
  • Statistical Mechanics

Background:

  • The current-correlation function is crucial for understanding quantum systems.
  • Harmonic oscillator models are fundamental in various physics domains.
  • Analyzing wave-number dependence reveals system dynamics.

Purpose of the Study:

  • To derive an explicit analytic expression for the wave-number dependent current-correlation function.
  • To compare the derived expression with numerical and recurrence relation methods.
  • To investigate specific limiting cases (long-wavelength and deep inelastic).

Main Methods:

  • Derivation of an explicit analytic expression for the Laplace transformed correlation function.
  • Comparison with numerical solutions.
  • Analysis using the recurrence relation method.
  • Examination of limiting cases k→0 and k→∞.

Main Results:

  • An explicit analytic expression for the wave-number dependent current-correlation function was derived.
  • The derived expression shows good agreement with numerical and recurrence relation methods.
  • The deep inelastic limit (k→∞) allows for explicit summation of the continued fraction.
  • An approximation scheme for intermediate wave-numbers was developed.

Conclusions:

  • The study provides a robust analytic method for calculating the current-correlation function.
  • The derived expression is validated across different limits and methods.
  • The findings contribute to a deeper understanding of quantum harmonic oscillator dynamics.