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Current-Density Functional Theory of Time-Dependent Linear Response in Quantal Fluids: Recent Progress

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New Approaches to Problems in Liquid State Theory

Part of the book series: NATO Science Series ((ASIC,volume 529))

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Abstract

Vignale and Kohn have recently formulated a local density approximation to the time-dependent linear response of an inhomogeneous electron system in terms of a vector potential for exchange and correlation. The vector potential depends on the induced current density through spectral kernels to be evaluated on the homogeneous electron gas. After a brief review of their theory, the case of inhomogeneous Bose superfluids is considered, with main focus on dynamic Kohn-Sham equations for the condensate in the linear response regime and on quantal generalized hydrodynamic equations in the weak inhomogeneity limit. We also present the results of calculations of the exchange-correlation spectra in both electron and superfluid boson systems.

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References

  1. Jin, D.S., Ensher, J.R., Matthews, M.R., Wieman, C.E., and Cornell, E.A. (1996) Collective excitations of a Bose-Einstein condensate in a dilute gas, Phys. Rev. Lett. 77, 420–423.

    Article  ADS  Google Scholar 

  2. Mewes, M.-O., Andrews, M.R., van Druten, N.J., Kurn, D.M., Durfee, D.S., Townsend, C.G., and Ketterle, W. (1996) Collective excitations of a Bose-Einstein condensate in a magnetic trap, Phys. Rev. Lett. 77, 988–991.

    Article  ADS  Google Scholar 

  3. Jin, D.S., Matthews, M.R., Ensher, J.R., Wieman, C.E., and Cornell, E.A. (1997) Temperature-dependent damping and frequency shifts in collective excitations of a dilute Bose-Einstein condensate, Phys. Rev. Lett. 78, 764–767.

    Article  ADS  Google Scholar 

  4. Andrews, M. R., Kurn, D.M., Miesner, H.-J., Durfee, D.S., Townsend, C.G., Inouye, S., and Ketterle, W. (1997) Propagation of sound in a Bose condensate, Phys. Rev. Lett. 79, 553–557.

    Article  ADS  Google Scholar 

  5. Stamper-Kurn, D.M., Miesner, H.-J., Inouye, S., Andrews, M. R., and Ketterle, W. (1998) Excitations of a Bose-Einstein condensate at non-zero temperature: a study of zeroth, first, and second sound, cond-mat/9801262.

    Google Scholar 

  6. Minguzzi, A., Chiofalo, M. L., and Tosi, M. P. (1997) Generalized quantum hydrodynamics of a trapped dilute Bose gas, Phys. Lett. A 236, 237–244.

    Article  Google Scholar 

  7. Hohenberg, P.C. and Martin, P.C. (1965) Microscopic theory of superfluid Helium, Ann. Phys. (NY) 34, 291–359.

    Article  ADS  Google Scholar 

  8. Griffin, A. (1993) Excitations in a Bose-condensed Liquid, University Press, Cambridge.

    Book  Google Scholar 

  9. Gross, E.K.U. and Kohn, W. (1990) Time-dependent density-functional theory, Adv. Quantum Chem. 21, 255–291.

    Article  ADS  Google Scholar 

  10. Gross, E.K.U., Dobson, J.F., and Petersilka, M. (1996), Density functional theory of time-dependent phenomena, in R. F. Nalewajski (ed.), Topics in Current Chemistry, Springer Verlag, Berlin.

    Google Scholar 

  11. Vignale, G. and Kohn, W. (1996) Current-dependent exchange-correlation potential for dynamical linear response theory, Phys. Rev. Lett. 77, 2037–2040.

    Article  ADS  Google Scholar 

  12. Vignale, G. and Kohn, W. (1997) Current density functional theory of time-dependent linear response: the local density approximation, in J. Dobson, M. P. Das and G. Vignale (eds.), Electronic Density Functional Theory, Plenum Press, New York.

    Google Scholar 

  13. Conti, S., Nifosí, R., and Tosi, M. P. (1997) The exchange-correlation potential for current-density functional theory of frequency-dependent linear response, J. Phys.: Condens. Matter 9, L475–L482.

    Article  ADS  Google Scholar 

  14. Vignale, G., Ullrich, C. A., and Conti, S. (1997) Time-dependent density functional theory beyond the adiabatic local density approximation, Phys. Rev. Lett. 79, 4878–4881.

    Article  ADS  Google Scholar 

  15. Nifosì, R., Conti, S., and Tosi, M.P. (1998) Dynamic exchange-correlation potentials for the electron gas in dimensionality D = 3 and D = 2, Phys. Rev. B (in press).

    Google Scholar 

  16. Chiofalo, M. L., Minguzzi, A., and Tosi, M.P. (1998) Time-dependent linear response of an inhomogeneous Bose superfluid, to be published.

    Google Scholar 

  17. Minguzzi, A., Conti, S., and Tosi, M.P. (1997) The internal energy and condensate fraction of a trapped interacting Bose gas, J. Phys.: Condens. Matter, 9, L33–L38.

    Article  ADS  Google Scholar 

  18. Huang, K. and Klein, A. (1964) Phonons in liquid Helium, Ann. Phys. (NY) 30, 203–234.

    Article  MathSciNet  ADS  Google Scholar 

  19. Forster, D. (1975) Hydrodynamic Fluctuations, Broken Symmetry, and Correlation Functions, Benjamin, Reading.

    Google Scholar 

  20. Hasegawa, M. and Watabe, M. (1969) Theory of plasmon damping in metals, J. Phys. Soc. Japan 27, 1393–1414.

    Article  ADS  Google Scholar 

  21. Glick, A.J. and Long, W.F. (1971) High-frequency damping in a degenerate electron gas, Phys. Rev. B 4, 3455–3460.

    Article  ADS  Google Scholar 

  22. Gross, E.K.U. and Kohn, W. (1985) Local density-functional theory of frequency-dependent linear response, Phys. Rev. Lett. 55, 2850–2853.

    Article  ADS  Google Scholar 

  23. Böhm, H.M., Conti, S., and Tosi, M.P. (1996) Plasmon dispersion and dynamic exchange-correlation potentials from two-pair excitations in degenerate plasmas, J. Phys.: Condens. Matter 8, 781–797.

    Article  ADS  Google Scholar 

  24. vom Felde, A., Sprösser-Prou, J., and Fink, J. (1989) Valence-electron excitations in the alkali metals, Phys. Rev. B 40, 10181–10193.

    Article  Google Scholar 

  25. Conti, S., Minguzzi, A., and Tosi, M. P. (1998) Dissipation spectra at long wavelength in dilute Bose gases, to be published.

    Google Scholar 

  26. Popov, V.N. (1972) Hydrodynamic Hamiltonian for a nonideal Bose gas, Theor. Math. Phys. 11, 478–486.

    Article  Google Scholar 

  27. Wong, V.K. and Gould, H. (1974) Long-wavelength excitations in a Bose gas at zero temperature, Ann. Phys. (NY) 83, 252–302.

    Article  ADS  Google Scholar 

  28. Ullrich, C.A. and Vignale, G. (1998) Linewidths of collective excitations of the inhomogeneous electron gas: application to two-dimensional quantum strips, Phys. Rev. B (to appear).

    Google Scholar 

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Tosi, M.P., Chiofalo, M.L., Minguzzi, A., Nifosì, R. (1999). Current-Density Functional Theory of Time-Dependent Linear Response in Quantal Fluids: Recent Progress. In: Caccamo, C., Hansen, JP., Stell, G. (eds) New Approaches to Problems in Liquid State Theory. NATO Science Series, vol 529. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4564-0_28

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  • DOI: https://doi.org/10.1007/978-94-011-4564-0_28

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-0-7923-5671-4

  • Online ISBN: 978-94-011-4564-0

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