Continuum mechanics for quantum many-body systems: Linear response regime

Physical Review B - Condensed Matter and Materials Physics

Volumn 81, Issue 19, 2010, Pages

  Gao, Xianlong ^a   Tao, Jianmin ^b   Vignale, G ^c   Tokatly, I V ^d,e  

^a ZHEJIANG NORMAL UNIVERSITY   (China)

^b CENTER FOR NONLINEAR STUDIES   (United States)

^c UNIVERSITY OF MISSOURI   (United States)

^d BASQUE FOUNDATION FOR SCIENCE   (Spain)

^e UNIVERSITY OF THE BASQUE COUNTRY UPV EHU   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77955583814     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.81.195106     Document Type: Article

References (52)

1. W. M. C. Foulkes, L. Mitas, R. J. Needs, and G. Rajagopal, Rev. Mod. Phys. 73, 33 (2001). 10.1103/RevModPhys.73.33
2. Time-Dependent Density Functional Theory, Lecture Notes in Physics Vol. 706, edited by, M. A. L. Marques,,, C. A. Ullrich,,, F. Nogueira,,, A. Rubio,,, K. Burke,, and, E. K. U. Gross, (Springer, Berlin, 2006). 10.1007/b11767107
3. E. K. U. Gross, J. F. Dobson, and M. Petersilka, in Density Functional Theory, Topics in Current Chemistry Vol. 181, edited by, R. F. Nalewajski, (Springer-Verlag, Berlin, 1996). 10.1007/BFb0016643
4. M. E. Casida, in Recent Advances in Density Functional Methods, edited by, D. P. Chong, (World Scientific, Singapore, 1995), p. 155.
5. N. T. Maitra, Fan Zhang, R. J. Cave, and K. Burke, J. Chem. Phys. 120, 5932 (2004). 10.1063/1.1651060
6. J. F. Dobson and B. P. Dinte, in Density Functional Theory, edited by, J. F. Dobson,,, G. Vignale,, and, M. P. Das, (Plenum, New York, 1998).
7. D. Ter Haar, Introduction to the Physics of Many-Body Systems (Interscience, London, 1958).
8. E. Madelung, Z. Phys. 40, 322 (1927). 10.1007/BF01400372
9. F. Bloch, Z. Phys. 81, 363 (1933). 10.1007/BF01344553
10. S. K. Ghosh and B. M. Deb, Phys. Rep. 92, 1 (1982). 10.1016/0370-1573(82) 90134-X
11. E. Runge and E. K. U. Gross, Phys. Rev. Lett. 52, 997 (1984). 10.1103/PhysRevLett.52.997
12. R. van Leeuwen, Phys. Rev. Lett. 82, 3863 (1999). 10.1103/PhysRevLett.82. 3863
13. E. Zaremba and H. C. Tso, Phys. Rev. B 49, 8147 (1994). 10.1103/PhysRevB.49.8147
14. S. Conti and G. Vignale, Phys. Rev. B 60, 7966 (1999). 10.1103/PhysRevB.60.7966
15. I. V. Tokatly and O. Pankratov, Phys. Rev. B 60, 15550 (1999). 10.1103/PhysRevB.60.15550
16. I. V. Tokatly and O. Pankratov, Phys. Rev. B 62, 2759 (2000). 10.1103/PhysRevB.62.2759
17. J. F. Dobson and H. M. Le, J. Mol. Struct.: THEOCHEM 501-502, 327 (2000) 10.1016/S0166-1280(99)00443-1
18. J. F. Dobson and H. M. Le, Phys. Rev. B 66, 075301 (2002). 10.1103/PhysRevB.66.075301
19. I. V. Tokatly, Phys. Rev. B 71, 165104 (2005). 10.1103/PhysRevB.71.165104 (Pubitemid 41749447)
20. I. V. Tokatly, Phys. Rev. B 71, 165105 (2005). 10.1103/PhysRevB.71.165105 (Pubitemid 41749455)
21. I. V. Tokatly, Phys. Rev. B 75, 125105 (2007). 10.1103/PhysRevB.75.125105
22. J. Tao, G. Vignale, and I. V. Tokatly, Phys. Rev. B 76, 195126 (2007). 10.1103/PhysRevB.76.195126
23. M. Brewczyk, C. W. Clark, M. Lewenstein, and K. Rzazewski, Phys. Rev. Lett. 80, 1857 (1998) 10.1103/PhysRevLett.80.1857
24. P. Hering, M. Brewczyk, and C. Cornaggia, Phys. Rev. Lett. 85, 2288 (2000) 10.1103/PhysRevLett.85.2288
25. Y. E. Kim and A. L. Zubarev, Phys. Rev. A 70, 033612 (2004). 10.1103/PhysRevA.70.033612
26. J. Tao, X. Gao, G. Vignale, and I. V. Tokatly, Phys. Rev. Lett. 103, 086401 (2009). 10.1103/PhysRevLett.103.086401
27. L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields (Pergamon Press, Reading, Massachussetts, 1962), p. 83.
28. R. D. Puff and N. S. Gillis, Ann. Phys. 46, 364 (1968). 10.1016/0003-4916(68)90248-0
29. O. H. Nielsen and R. M. Martin, Phys. Rev. B 32, 3780 (1985). 10.1103/PhysRevB.32.3780
30. C. L. Rogers and A. M. Rappe, Phys. Rev. B 65, 224117 (2002). 10.1103/PhysRevB.65.224117
31. To be completely accurate, we point out that the Hamiltonian H̃̂ (t), which governs the time evolution of the quantum state | ψ̃ 〈(t) 〉 in the comoving reference frame, does not coincide with the instantaneously deformed hamiltonian Ĥ u [u]. The difference arises from the fact that the coordinate transformation to the comoving frame is time dependent, and this generates an additional vector potential (also a functional of u), which guarantees the vanishing of the current density in the comoving frame. Consistent with this, the Hamiltonian that appears in the definition of P̃ μν in Eq. should be H̃̂ (t), not Ĥ u [u]. Fortunately, the difference between HH̃̂ (t) and Ĥ u [u] becomes irrelevant in the high-frequency limit, and therefore does not contribute to the elastic approximation proposed in this paper.
32. Following the nomenclature of mechanics we call "virtual" a variation in the displacement field that occurs while time is held constant. It is called virtual rather than real because no actual variation can take place without the passage of time.
33. J. F. Dobson, Phys. Rev. Lett. 73, 2244 (1994). 10.1103/PhysRevLett.73. 2244
34. G. Vignale and W. Kohn, Phys. Rev. Lett. 77, 2037 (1996). 10.1103/PhysRevLett.77.2037
35. G. Vignale, C. A. Ullrich, and S. Conti, Phys. Rev. Lett. 79, 4878 (1997). 10.1103/PhysRevLett.79.4878
36. I. V. Tokatly, Lect. Notes Phys. 706, 123 (2006). 10.1007/3-540-35426-3-8 (Pubitemid 44468544)
37. C. A. Ullrich and I. V. Tokatly, Phys. Rev. B 73, 235102 (2006). 10.1103/PhysRevB.73.235102 (Pubitemid 43848266)
38. J. P. Perdew, V. N. Staroverov, J. Tao, and G. E. Scuseria, Phys. Rev. A 78, 052513 (2008). 10.1103/PhysRevA.78.052513
39. M. Seidl, J. P. Perdew, and S. Kurth, Phys. Rev. Lett. 84, 5070 (2000). 10.1103/PhysRevLett.84.5070
40. M. Seidl, P. Gori-Giorgi, and A. Savin, Phys. Rev. A 75, 042511 (2007). 10.1103/PhysRevA.75.042511 (Pubitemid 46633637)
41. G. F. Giuliani and G. Vignale, Quantum Theory of the Electron Liquid (Cambridge University Press, Cambridge, 2005). 10.1017/CBO9780511619915
42. R. P. Feynman, Statistical Mechanics (Benjamin, Reading, MA, 1972)
43. see also S. M. Girvin, A. H. MacDonald, and P. M. Platzman, Phys. Rev. B 33, 2481 (1986) 10.1103/PhysRevB.33.2481
44. Alternatively, we could set V 0 = 0 and include the q = 0 singularity in the structure factor: ρ 2 (q) = n 2 δ (q) + n [S (q) - 1].
45. K. N. Pathak and P. Vashishta, Phys. Rev. B 7, 3649 (1973). 10.1103/PhysRevB.7.3649
46. P. Gori-Giorgi, F. Sacchetti, and G. B. Bachelet, Phys. Rev. B 61, 7353 (2000) 10.1103/PhysRevB.61.7353
47. P. Gori-Giorgi, F. Sacchetti, and G. B. Bachelet, Phys. Rev. B 66, 159901 (E) (2002). 10.1103/PhysRevB.66.159901
48. M. Dion, H. Rydberg, E. Schroder, D. C. Langreth, and B. I. Lundqvist, Phys. Rev. Lett. 92, 246401 (2004). 10.1103/PhysRevLett.92.246401
49. J. F. Dobson, Jun Wang, B. P. Dinte, K. McLennan and H. M. Le, Int. J. Quantum Chem. 101, 579 (2005). 10.1002/qua.20314 (Pubitemid 40264534)
50. G. Onida, L. Reining, and A. Rubio, Rev. Mod. Phys. 74, 601 (2002). 10.1103/RevModPhys.74.601
51. V. U. Nazarov, I. V. Tokatly, S. Pittalis, and G. Vignale, arXiv:1003.0990 (unpublished).
52. I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products, 7th ed. (Academic, London, 2007).