Abstract
A real-space formulation of the Quantum Bogolyubov-Born-Green-Kirkwood-Yvon (QBBGKY)-hierarchy is worked out in a form particularly suitable for applications to the optical response of many-electron systems. Comparison is made to Coupled-Cluster approaches. A new hierarchy of contraction-free correlation functions is presented, that overcomes the problem of violated trace relation inherent in the truncated QBBGKY-hierarchy.
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References
Nonlinear Optical Effects in Organic Polymers, NATO Advanced Study Institute, Series E, edited by J. Mrssier, F. Kajzar, P.N. Prasad, D.R. Ulrich (Kluwer Academic, Dordrecht, 1989), Vol. 162.
S. Etemad, Z.G. Soos, in Spectroscopy of Advanced Materials, edited by R.J.H. Clark, R.E. Hester (Wiley, New York, 1991), pp. 87, and references therein.
Nonlinear Optical Properties of Organic Molecules and Crystals, Vol. 1,2, eds. J. Zyss, D.S. Chemla (Academic Press, Florida, 1987
D. Mukhopadhyay, G.W. Hayden, Z.G. Soos, Phys. Rev. B 51, 9476 (1995).
Z.G. Soos, S. Ramasesha, D.S. Galvão, Phys. Rev. Lett. 71, 1609 (1993).
S. Abe, M. Schreiber, W.P. Su, J. Yu, J. Lumin 53, 519 (1992); S. Abe, M. Schreiber, W.P. Su, J. Yu, Phys. Rev. B 45, 9432 (1992); S. ABE, J. Yu, W.P. Su, Phys. Rev. B 45, 8264 (1992); S. Abe, M. Schreiber, W.P. Su, Chem. Phys. Lett. 192, 425 (1992).
D. Beljonne, Z. Shuai, J.L. Bredas, J. Chem. Phys. 98, 8819 (1993).
Z. Shuai, J.L. Brédas, Phys. Rev. B 44, 5962 (1991).
D. Yaron, R. Silbey, Phys. Rev. B 45, 11655 (1992).
Z.G. Soos, Mol. Cryst. liq. Cryst. 256, 35 (1994).
Z.G. Soos, D.S. GalvãO, S. Etemad, Adv. Mater. 6, 280 (1994); Z.G. Soos, S. Ramasesha, D.S. Gãlvao, S. Etemad, Phys. Rev. B 47, 1742 (1993); Z.G. Soos, S. Ramasesha, D.S. Gãlvao, R.G. Kepler, S. Etemad, Synth. Metals 54, 35 (1993); Z.G. Soos, S. Ramasesha, J. Chem. Phys. 90, 1067 (1988); Z.G. Soos, S. Ramasesha, Phys. Rev. B 29, 5410 (1984).
S. Abe, M. Schreiber, W.P. Su, J. Yu, Synth. Metals, 57, 4004 (1993).
G. Chen, S. Mukamel, D. Beljonne, J.L. Brédas, J. Chem. Phys. 104, 5406 (1996).
M. Jaszuński, P. Jørgensen, H. Koch, H. Agren, T. Helgaker, J. Chem. Phys. 98, 7229 (1993).
J. Olsen, P. Jørgensen, J. Chem. Phys. 82, 3225 (1985).
H.-D. Meyer, U. Manthe, L.S. Cederbaum, Chem. Phys. Lett. 165, 73 (1990).
H. Ishihara, K. Cho, Phys. Rev. B 42, 1724 (1990).
Z. Soos, G. Hayden, P. McWilliams, Conjugated Polymeric Materials: Opportunities in Electronics, Optoelectronics and Molecular Electronics (Kluver, Dordrecht, 1990), pp. 495–508.
H. Koch, R. Kobayashi, A. Sanchez de Merás, P. Jørgensen, J. Chem. Phys. 100, 4393 (1994).
V. Chernyak, S. Mukamel, J. Chem. Phys. 104, 444 (1996).
D. Guo, Mol. Cryst. Liq. Cryst. 256, 105 (1994); D. Guo, S. Mazumdar, S.N. Dixit, Synth. Metals 49, 1 (1993); S. Mazumdar, D. Guo, S.N. Dixit, J. Chem. Phys. 96, 6962 (1992); S. Mazumdar, D. Guo, S.N. Dixit, SPIE Proc. 1436, 136 (1991); S.N. Dixit, D. Guo, S. Mazumdar, Phys. Rev. B 43, 6781 (1990).
D. Guo, S. Mazumdar, S.N. Dixit, F. Kajzar, F. Jarka, Y. Kawabe, N. Peyghambrarian, Phys. Rev. B 48, 1433 (1993); S. Mazumdar, D. Guo, S.N. Dixit, Synth. Metals 55-57, 3881 (1993); Y. Kawabe, F. Jarka, N. Peyghambrarian, D. Guo, S. Mazumdar, S.N. Dixit, F. Kajzar, Phys. Rev. B 44, 6530 (1991); D. Guo, S. Mazumdar, G.I. Stegeman, M. Cha, D. Neher, S. Aramaki, W. Torruellas, R. Zanoni, Electrical, Optical, and Magnetic Properties of Organic Solid State Materials, eds. L.Y. Chiang, A.F. Garito, D.J. Sand-Man, 151 (1992); S. Mazumdar, F. Guo, J. Chem. Phys. 100, 1665 (1994).
S. Abe, Y. Shimoi, V.A. Shakin, K. Harigaya, Mol. Cryst. liq. Cryst. 256, 97 (1994).
V.A. Shakin, S. Abe, Phys. Rev. B 50, 4306 (1994).
Y. Shimoi, S. Abe, Phys. Rev. B 49 (1994).
S. Abe, Prog. Theor. Phys. Supp. 113, 83 (1993).
A. Szabo, N.S. Ostlund, Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory (McGraw-Hill, New York, 1989).
S. Mukamel, A. Takahashi, H.X. Wang, G. Chen, Science 266, 250 (1994).
M. Hartmann, V. Chernyak, S. Mukamel, Phys. Rev. B 52, 2528 (1995); M. Hartmann, S. Mukamel, J. Chem. Phys. 99, 1597 (1993)
A. Takahashi, S. Mukamel, J. Chem. Phys. 100, 2366 (1994).
S. Mukamel, H.X. Wang, Phys. Rev. Lett. 69, 65 (1992); H.X. Wang, S. Mukamel, J. Chem. Phys. 97, 8019 (1992).
P. Ring, P. Schuck, The Nuclear Many-Body Problem (Springer-Verlag, New York, 1976).
B.E. Kohler, G. Sprangler, C. Westerfield, J. Chem. Phys. 89, 5422 (1988).
L.A. Heimbrook, B.E. Kohler, I.J. Levy, J. Chem. Phys. 81, 1592 (1984); L.A. Heimbrook, J.E. Kenny, B.E. Kohler, G.W. Scott, J. Chem. Phys. 75, 4338 (1981).
M.F. Granville, G.R. Holtom, B.E. Kohler, J. Chem. Phys. 72, 4671 (1980).
J.M. Leng, S. Jeglinski, X. Wei, R.E. Brenner, Z.V. Vardeney, F. Guo, S. Mazumdar, Phys. Rev. Lett. 72, 156 (1994).
P.D. Townsend, W.S. Fann, S. Etemad, G.L. Baker, Z.G. Soos, P.C.M. McWilliams, Chem. Phys. Lett. 180, 485 (1991).
P.C.M. McWilliams, G.W. Hayden, Z.G. Soos, Phys. Rev. B 43, 9777 (1991).
F. Guo, D. Guo, S. Mazumdar, Phys. Rev. B 49, 10102 (1994).
I. Ohmine, M. Karplus, K. Schulten, J. Chem. Phys. 68, 2298 (1978).
M. Chandross, F. Guo, S. Mazumdar, Synth. Metals 69, 625 (1995); F. Guo, M. Chandross, S. Mazumdar, Phys. Rev. Lett. 74, 2086 (1995).
K. Ishida, H. Aoki, T. Ogawa, Phys. Rev. B 52, 8980 (1995).
V.A. Shakin, S. Abe, IEEE Nonlinear Optics: Materials, Fundamentals, and Applications (Cat.No. 94CH3370-4), p. 114 (1994).
F. Guo, M. Chandross, S. Mazumdar, Mol. Cryst. liq. Cryst. 256, 53 (1994).
S.A. Kucharski, R.J. Bartlett, J. Chem. Phys. 97, 4282 (1992); J. Chem. Phys. 95, 8227 (1991).
J.F. Stanton, J. Gauss, J.D. Watts, R.J. Bartlett, J. Chem. Phys. 94, 4334 (1991).
J.D. Watts, R.J. Bartlett, Chem. Phys. Lett. 190, 19 (1992); J. Chem. Phys. 97, 3445 (1992).
S.R. Gwaltney, M. Nooijen, R.J. Bartlett, Chem. Phys. Lett. 248, 189 (1996); S.R. Gwaltney, R.J. Bartlett, Chem. Phys. Lett. 241, 26 (1995).
H. Koch, H. Jørgen, A. Jensen, P. Jørgensen, T. Helgaker, J. Chem. Phys. 93, 3345 (1990).
M. Nooijen, J.G. Snijders, J. Chem. Phys. 102, 1681 (1995).
Wang Shun-**, W. Cassing, Annals of Physics 159, 328 (1985).
R. Balescu, Equilibrium and nonequilibrium statistical mechanics, New York London Sydney Toronto: Wiley (1975), pp. 100.
P.C. Martin, J. Schwinger, Phys. Rev. 115, 1342 (1959).
K. Ohno, Theor. Chim. Acta 2, 219 (1964).
D. Baeryswyl, D.K. Campbell, S. Mazumdar, in Conducting Polymers, ed. H. Kiess, Topics in Current Physics (Springer-Verlag, Heidelberg, 1992), p. 7.
T. Kuhn, Ladungsträgerdynamik in Halbleitersystemen fern vom Gleichgewicht: Elektronisches Rauschen und kohärente Prozesse (Verlag Shaker, Aachen, 1994). In this book, the cluster decomposition is used to truncate the hierarchy of equations of motion for a direct semiconductor. In practical application to these systems, the decoupling procedure is usually followed by a series of further simplifying steps finally leading to the so called scattering contributions to the semiconductor Bloch equations (see also [58]).
A. Stahl, I. Balslev, Electrodynamic at the semiconductor band edge Springer Tracts in Modern Physics Vol. 110 (Springer-Verlag, Berlin Heidelberg New York, 1987).
H. Haug, S.W. Koch, Quantum theory of optical and electronic properties of semiconductors. Secoond edition, Singapore, New Jersey, London, Hong Kong: World Scientific.
K.-J. Schmitt, P.-G. Reinhar, O. Toepffer, Z. Phys. A, 336, 123 (1990); Phys. Rev. A 40, 474 (1989).
M. Tohyama, P. Schuck, S.J. Wang, Z. Phys. A 339, 341 (1991).
S. Mukamel, in Nonlinear Optical Properties of Organic Molecules and Crystals, Vol. 3, Editor J. Zyss, Academic Press, 1993.
S. Mukamel, Principles of Nonlinear Optical Spectroscopy (Oxford, New York) (1995).
V.M. Axt, A. Stahl, Z. Phys. B 93, 195 (1994).
K. Victor, V.M. Axt, A. Stahl, Phys. Rev. B 51, 14164 (1995); V.M. Axt, K. Victor, A. Stahl, Phys. Rev. B 53, 7244 (1996).
M.Z. Maialle, L.J. Sham, Phys. Rev. Lett. 73, 3310 (1994).
P.-G. Reinhard, C. Toepffer, Int. J. Mod. Phys. E, Vol. 3 Supp., 435 (1994).
J. A. Leegwater, S. Mukamel, Phys. Rev. A 46, 452 (1992).
V.M. Axt, A. Stahl, Z. Phys. B 93, 205 (1994); V.M. Axt, A. Stahl, E.J. Mayer, P. Haring Bolivar, S. Nüsse, K. Ploog, K. Köhler, Phys. Stat. Sol. (b) 188, 447 (1995).
M. Lindberg, Y.Z. Hu, R. Binder, S.W. Koch, Phys. Rev. B 50, 18060 (1994).
T. Üstreich, K. Schönhammer, L.J. Sham, Phys. Rev. Lett. 75, 2554 (1995); Phys. Rev. Lett. 74, 4698 (1995).
V.M. Axt, G. Bartels, A. Stahl, Phys. Rev. Lett. 76, 2543 (1996); G. Bartels, V.M. Axt, K. Victor, A. Stahl, P. Leisching, K. Köhler, Phys. Rev. B 51, 11217 (1995).
W. Schäfer, D.S. Kim, J. Shah, T.C. Damen, J.E. Cunningham, K.W. Goossen, L.N. Pfeiffer, K. Köhler, Phys. Rev. B 53, 16429 (1996).
J.M. Häuser, W. Cassing, A. Peter, Nucl. Phys. A A585, 727 (1995).
F.V. DeBlasio, W. Cassing, M. Tohyama, P.F. Bortington, R.A. Broglia, Phys. Rev. Lett. 88, 1663 (1992).
M. Gong, M. Tohyama, Z. Phys. A 335, 153 (1990); M. Gong, M. Tohyama, J. Randrup, Z. Phys. A 335, 331 (1990); M. Tohyama, M. Gong, Z. Phys. A 332 (1989).
W. Cassing, S.J. Wang, Z. Phys. A 328, 423 (1987).
P.G. Szalay, M. Nooijen, R.J. Bartlett, J. Chem. Phys. 103, 281 (1995).
H. Koch, R. Kobayashi, P. Jørgensen, Int. J. Quantum Chemestry 49, 835 (1994).
R. Kobayashi, H. Koch, P. Jørgensen, T.J. Lee, Chem. Phys. Lett. 211, 94 (1993).
P. Fulde, Electron correlations in molecules and solids (Springer-Verlag, Berlin, New York, 2nd edition 1993).
W. Cassing, A. Pfitzner, Z. Phys. A 342, 161 (1992).
J.S. Arponen, R.F. Bishop, E. Pajanne, Phys. Rev. A 36, 2519–2539 (1987).
R.F. Bishop, J.S. Arponen, Int. J. Quant. Chem.: Quantum Chemistry Symposium 24, 197 (1990); R.F. Bishop, J.S. Arponen, Int. J. Quantum Chemistry: Quantum Chemistry Symposium 24, 197 (1990).
H. Koch, P. Jørgensen, J. Chem. Phys. 93, 3333 (1990).
R. Kobayashi, H. Koch, P. Jørgensen, Chem. Phys. Lett. 219, 30 (1994).
E. Dalgaard, H.J. Monkhorst, Phys. Rev. A 28, 1217 (1983).
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Axt, V.M., Mukamel, S. (1998). Real-Space Density-Matrix Description of Dynamic Correlations in the Optical Response of Many-Electron Systems. In: Moloney, J.V. (eds) Nonlinear Optical Materials. The IMA Volumes in Mathematics and its Applications, vol 101. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1714-5_2
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