Skip to main content

Numerically-Exact Schrödinger Dynamics of Closed and Open Many-Boson Systems with the MCTDHB Package

  • Conference paper
  • First Online:
High Performance Computing in Science and Engineering ‘13

Abstract

The quantum many-body dynamics of indistinguishable, interacting particles are described by the time-dependent many-body Schrödinger equation (TDSE). The TDSE constitutes a difficult problem and is not solvable analytically in most cases. The present review article expedites and benchmarks the capabilities of a novel theoretical method, the multiconfigurational time-dependent Hartree method for bosons (MCTDHB) that is designed for solving the TDSE of interacting bosonic particles. The MCTDHB package is a software implementation that solves the equations of motion of MCTDHB numerically. It is assessed with a benchmark versus an analytically treatable model of trapped interacting bosons (a closed system) that the MCTDHB is capable of solving the TDSE for bosons numerically exactly, i.e., to any desired numerical precision. Furthermore, the structure and parallelization of the MCTDHB package as well as an application to the tunneling to open space dynamics [Proc. Natl. Acad. Sci. USA, 109, 13521 (2012)] are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 1.

    Open Multi-Processing.

  2. 2.

    Message Passing Interface.

  3. 3.

    Non-Uniform Memory Access.

References

  1. M.H. Anderson, J.R. Ensher, M.R. Matthews, C.E. Wieman, E.A. Cornell, Science 269, 198 (1995)

    Article  Google Scholar 

  2. C.C. Bradley, C.A. Sackett, J.J. Tollett, R.G. Hulet, Phys. Rev. Lett. 75, 1687 (1995)

    Article  Google Scholar 

  3. K.B. Davis, M.-O. Mewes, M.R. Andrews, N.J. van Druten, D.S. Durfee, D.M. Kurn, W. Ketterle, Phys. Rev. Lett. 75, 3969 (1995)

    Article  Google Scholar 

  4. F. Dalfovo, S. Giorgini, L.P. Pitaevskii, S. Stringari, Rev. Mod. Phys. 71, 463 (1999)

    Article  Google Scholar 

  5. A.J. Leggett, Rev. Mod. Phys. 73, 307 (2001)

    Article  Google Scholar 

  6. I. Bloch, J. Dalibard, W. Zwerger, Rev. Mod. Phys. 80, 885 (2008)

    Article  Google Scholar 

  7. A. Polkovnikov, K. Sengupta, A. Silva, M. Vengalattore, Rev. Mod. Phys. 83, 863 (2011)

    Article  Google Scholar 

  8. A.I. Streltsov, O.E. Alon, L.S. Cederbaum, Phys. Rev. Lett. 99, 030402 (2007)

    Article  Google Scholar 

  9. O.E. Alon, A.I. Streltsov, L.S. Cederbaum, Phys. Rev. A 77, 033613 (2008)

    Article  Google Scholar 

  10. K. Sakmann, A.I. Streltsov, O.E. Alon, L.S. Cederbaum, Phys. Rev. Lett. 103, 220601 (2009)

    Article  Google Scholar 

  11. A.U.J. Lode, K. Sakmann, O.E. Alon, L.S. Cederbaum, A.I. Streltsov, Phys. Rev. A 86, 063606 (2012)

    Article  Google Scholar 

  12. A.I. Streltsov, K. Sakmann, O.E. Alon, L.S. Cederbaum, Phys. Rev. A 83, 043604 (2011)

    Article  Google Scholar 

  13. K. Sakmann, A.I. Streltsov, O.E. Alon, L.S. Cederbaum, Phys. Rev. A 78, 023615 (2008)

    Article  Google Scholar 

  14. I. Březinová, A.U.J. Lode, A.I. Streltsov, O.E. Alon, L.S. Cederbaum, J. Burgdörfer, Phys. Rev. A 86, 013630 (2012)

    Article  Google Scholar 

  15. A.I. Streltsov, K. Sakmann, A.U.J. Lode, O.E. Alon, L.S. Cederbaum, The Multiconfigurational Time-Dependent Hartree for Bosons Package, Version 2.3 (Many-body Theory of Bosons Group, University of Heidelberg, Heidelberg, 2013); see the MCTDHB Homepage: http://mctdhb.org

  16. A.I. Streltsov, O.E. Alon, L.S. Cederbaum, Phys. Rev. A 81, 022124 (2010)

    Article  Google Scholar 

  17. bwGRiD Homepage: http://www.bw-grid.de

  18. L. Cohen, C. Lee, J. Math. Phys. 26, 3105 (1985)

    Article  MathSciNet  Google Scholar 

  19. J. Yan, J. Stat. Phys. 113, 623 (2003)

    Article  MATH  Google Scholar 

  20. A.U.J. Lode, A.I. Streltsov, K. Sakmann, O.E. Alon, L.S. Cederbaum, Proc. Natl. Acad. Sci. USA 109, 13521 (2012)

    Article  Google Scholar 

  21. http://www.pro-physik.de/details/news/2717321/Vielteilchentunnelprozess_erstmals_exakt_beschrieben.html and http://www.innovations-report.de/html/berichte/physik_astronomie/mechanismus_vielteilchentunnelprozesses_erstmals_203395.html

  22. A.U.J. Lode, I. Streltsov, O.E. Alon, H.-D. Meyer, L.S. Cederbaum, J. Phys. B 42, 044018 (2009); A.U.J. Lode, I. Streltsov, O.E. Alon, H.-D. Meyer, L.S. Cederbaum, J. Phys. B 43, 029802 (2010)

    Google Scholar 

  23. A.I. Streltsov, Phys. Rev. A 88, 041602(R) (2013)

    Google Scholar 

  24. R.A. Doganov, S. Klaiman, O.E. Alon, A.I. Streltsov, L.S. Cederbaum, Phys. Rev. A 87, 033631 (2013)

    Article  Google Scholar 

  25. O.E. Alon, A.I. Streltsov, K. Sakmann, A.U.J. Lode, J. Grond, L.S. Cederbaum, Chem. Phys. 401, 2 (2012)

    Article  Google Scholar 

  26. J. Grond, A.I. Streltsov, L.S. Cederbaum, O.E. Alon, Phys. Rev. A 86, 063607 (2012); J. Grond, A.I. Streltsov, A.U.J. Lode, K. Sakmann, L.S. Cederbaum, O.E. Alon, Phys. Rev. A 88, 023606 (2013)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Axel U. J. Lode .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer International Publishing Switzerland

About this paper

Cite this paper

Lode, A.U.J. et al. (2013). Numerically-Exact Schrödinger Dynamics of Closed and Open Many-Boson Systems with the MCTDHB Package. In: Nagel, W., Kröner, D., Resch, M. (eds) High Performance Computing in Science and Engineering ‘13. Springer, Cham. https://doi.org/10.1007/978-3-319-02165-2_7

Download citation

Publish with us

Policies and ethics