Skip to main content
Log in

Gross–Pitaevskii Equation for the Density Matrix in the Position Representation

  • Published:
Journal of Russian Laser Research Aims and scope

Abstract

We consider the generalized pure-state density matrix, which depends on different time moments, and obtain the evolution equation for this density matrix for the case where the density matrix corresponds to solutions of the Gross–Pitaevskii equation.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. E. Schrödinger, Naturwissenchaften, 14, 664 (1926).

    Article  ADS  MATH  Google Scholar 

  2. L. D. Landau, Z. Physik, 45, 430 (1927).

    Article  ADS  MATH  Google Scholar 

  3. J. von Neumann, Nach. Ges. Wiss. Göttingen, 11, 245 (1927).

    Google Scholar 

  4. J. von Neumann, Mathematische Grundlagen der Quantenmechanik, Springer, Berlin (1932).

    MATH  Google Scholar 

  5. E. P. Gross, Nuovo Cim., 20, 454 (1961).

    Article  MATH  Google Scholar 

  6. L. P. Pitaevskii, Sov. Phys. JETP, 13, 451 (1961).

    MathSciNet  Google Scholar 

  7. M. A. Man’ko and V. I. Man’ko, “Tomographic entropic inequalities in the probability representation of quantum mechanics,” in: R. Bijker (Ed.), Beauty in Physics: Theory and Experiment, AIP Conf. Proc., 1488, 110 (2012).

  8. E. Wigner, Phys. Rev., 40, p. 749 (1932).

    Article  ADS  Google Scholar 

  9. S. De Nicola, R. Fedele, M. A. Man’ko, and V. I. Man’ko, Eur. Phys. J. B, 36, 385 (2003).

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Olga V. Man’ko.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chernega, V.N., Man’ko, O.V. & Man’ko, V.I. Gross–Pitaevskii Equation for the Density Matrix in the Position Representation. J Russ Laser Res 36, 135–138 (2015). https://doi.org/10.1007/s10946-015-9486-z

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10946-015-9486-z

Keywords

Navigation