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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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.
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.
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.
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.
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.
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.
Hohenberg, P.C. and Martin, P.C. (1965) Microscopic theory of superfluid Helium, Ann. Phys. (NY) 34, 291–359.
Griffin, A. (1993) Excitations in a Bose-condensed Liquid, University Press, Cambridge.
Gross, E.K.U. and Kohn, W. (1990) Time-dependent density-functional theory, Adv. Quantum Chem. 21, 255–291.
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.
Vignale, G. and Kohn, W. (1996) Current-dependent exchange-correlation potential for dynamical linear response theory, Phys. Rev. Lett. 77, 2037–2040.
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.
Conti, S., NifosÃ, 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.
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.
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).
Chiofalo, M. L., Minguzzi, A., and Tosi, M.P. (1998) Time-dependent linear response of an inhomogeneous Bose superfluid, to be published.
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.
Huang, K. and Klein, A. (1964) Phonons in liquid Helium, Ann. Phys. (NY) 30, 203–234.
Forster, D. (1975) Hydrodynamic Fluctuations, Broken Symmetry, and Correlation Functions, Benjamin, Reading.
Hasegawa, M. and Watabe, M. (1969) Theory of plasmon damping in metals, J. Phys. Soc. Japan 27, 1393–1414.
Glick, A.J. and Long, W.F. (1971) High-frequency damping in a degenerate electron gas, Phys. Rev. B 4, 3455–3460.
Gross, E.K.U. and Kohn, W. (1985) Local density-functional theory of frequency-dependent linear response, Phys. Rev. Lett. 55, 2850–2853.
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.
vom Felde, A., Sprösser-Prou, J., and Fink, J. (1989) Valence-electron excitations in the alkali metals, Phys. Rev. B 40, 10181–10193.
Conti, S., Minguzzi, A., and Tosi, M. P. (1998) Dissipation spectra at long wavelength in dilute Bose gases, to be published.
Popov, V.N. (1972) Hydrodynamic Hamiltonian for a nonideal Bose gas, Theor. Math. Phys. 11, 478–486.
Wong, V.K. and Gould, H. (1974) Long-wavelength excitations in a Bose gas at zero temperature, Ann. Phys. (NY) 83, 252–302.
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).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
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
Download citation
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
eBook Packages: Springer Book Archive