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Numerical method for the stochastic projected Gross-Pitaevskii equation.

S J Rooney1, P B Blakie1, A S Bradley1

  • 1Jack Dodd Centre for Quantum Technology, Department of Physics, University of Otago, Dunedin, New Zealand.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 4, 2014
PubMed
Summary

We developed an efficient method to solve the stochastic projected Gross-Pitaevskii equation (SPGPE) for Bose gases. Our approach accurately handles low-energy modes and scattering processes, demonstrating physical consistency and fast convergence.

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Area of Science:

  • Quantum mechanics and condensed matter physics.
  • Ultracold atomic gases and Bose-Einstein condensates.

Background:

  • The stochastic projected Gross-Pitaevskii equation (SPGPE) models complex quantum systems like Bose gases.
  • Accurately evolving low-energy modes and scattering terms presents significant computational challenges.

Purpose of the Study:

  • To present an accurate and efficient numerical method for solving the SPGPE.
  • To address the challenges of low-energy mode evolution and scattering reservoir processes.

Main Methods:

  • Utilized a Hermite-polynomial based spectral-Galerkin representation for scattering terms.
  • Implemented a low-energy mode restriction precisely.
  • Employed the weak semi-implicit Euler method for stochastic integration.

Main Results:

  • Developed an accurate and efficient procedure for evaluating scattering terms.
  • Achieved a faster-than-expected rate of stochastic convergence.
  • Demonstrated physical consistency through thermalization of random initial states.

Conclusions:

  • The presented method effectively solves the SPGPE for Bose gases in harmonic potentials.
  • The algorithm offers high accuracy and efficiency, suitable for studying quantum gas dynamics.