Abstract
Liquids are equilibrium systems which represent a longstanding problem for physics and chemistry. We now know a great deal about their structures and properties in conditions without large fluctuations, and the physics of liquids near the critical point has now been elucidated. Proteins and DNA in water are the current target of physics. The physics and chemistry of amorphous metals have made much progress during the last thirty years and they are now widely used in industry. Quasicrystals were discovered in 1984 and this brought about a kind of revolution in our understanding of materials: until then, every textbook had stated in the first few pages that the five-fold rotational symmetry was prohibited in long-range ordered systems. We now know that this is not the case. Furthermore, quite a few quasicrystalline systems are in an equilibrium phase.
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References
P. Hohenberg and W. Kohn: Phys. Rev. B 136, 864 (1964)
W. Kohn and L.J. Sham, Phys. Rev. 140, A1133 (1965)
W. Kohn: Rev. Mod. Phys. 71, 1253 (1999)
O.K. Andersen: Phys. Rev. B 12, 3060 (1975)
D.R. Hamann, M. Schlüter, and C. Chiang: Phys. Rev. Lett. 43, 1494 (1979)
G.B. Bachelet, D.R. Hamann, and M. Schlüter: Phys. Rev. B 26, 4199 (1982)
D. Vanderbilt: Phys. Rev. B 41, 7892 (1990)
R. Car and M. Parrinello: Phys. Rev. Lett. 55, 2471 (1985)
P.A. Lee and T.V. Ramakrishnan: Rev. Mod. Phys. 57, 287 (1985)
G.S. Cargill: Solid State Phys. 30, 227 (1975)
Y. Waseda: The Structure of Non-Crystalline Materials (McGraw-Hill, New York, 1980)
R. Car and M. Parrinello: Phys. R.v. Lett. 25, 2471 (1985)
J.D. Bernal: Nature 183, 141 (1959)
J.D. Bernal: Nature 185, 68 (1960)
J.D. Bernal: Proc. Roy. Soc. A 280, 299 (1964)
C.H. Bennett: J. Appl. Phys. 43, 272 (1972)
T. Ichikawa: Phys. Stat. Sol. (a) 29, 293 (1975)
R. Yamamoto and M. Doyama: J. Phys. F9, 617 (1979)
C. Hausleitner and J. Hafner: Phys. Rev. B 45, 128 (1992)
O.K. Andersen, O. Jepsen, and D. Glötzel: In Highlights of Condensed Matter Theory, ed. by F. Bassani, F. Fumi, and M.P. Tosi (North-Holland, New York, 1985)
T. Fujiwara: J. Non-Cryst. Solids 61–62, 1039 (1984)
O.K. Andersen: Phys. Rev. B 12, 3060 (1975)
H.L. Skriver: The LMTO Method (Springer-Verlag, Berlin, 1984)
H.J. Nowak, O.K. Andersen, T. Fujiwara, O. Jepsen, and P. Vargas: Phys. Rev. B 44, 3577 (1991)
R. Haydock, V. Heine, and M.J. Kelly: J. Phys. C 8, 2591 (1975)
V. Heine: Solid State Phys. 35, 1 (1980)
K. Yakubo, T. Nakayama, and J. Maris: J. Phys. Soc. Jpn. 60, 3249 (1991)
H. Tanaka and T. Fujiwara: Phys. Rev. B 49, 11440 (1994)
T. Iitaka: Computing the Real- Time Green’s Functions of Large Hamiltonian matrices, High Performance Computing in RIKEN 1995 (ISSN-1342–3428), 241 (1996)
H. Tanaka: Phys. Rev. B 57, 2168 (1998)
H. Tanaka and M. Itoh: Phys. Rev. Lett. 81, 3727 (1998)
T. Mizoguchi, K. Yamaguchi, and H. Miyajima: In Amorphous Magnetism, ed. by H.O. Hooper and A.M. de Graaf (Plenum, New York, 1973)
T. Mizoguchi: AIP Conf. Proc. 30, 286 (1976)
R. Hasegawa, R.C. O’Handley, L. Tanner, R. Ray, and S. Kavesh: Appl. Phys. Lett. 29, 219 (1976)
R.C. O’Handley, R. Hasegawa, R. Ray, and C.-P. Chou: Appl. Phys. Lett. 29, 330 (1976)
R.C. O’Handley, R. Hasegawa, R. Ray, and C.-P. Chou: J. Appl. Phys. 48, 2095 (1976)
H. Hiroyoshi and K. Fukamichi: Phys. Lett. 85 A, 242 (1981)
H. Hiroyoshi and K. Fukamichi: J. Appl. Phys. 53, 2226 (1982)
N. Saito, H. Hiroyoshi, K. Fukamichi, and Y. Nakagawa: J. Phys. F 16, 911 (1986)
J.M.D. Coey, D.H. Ryan, and R. Buder: Phys. Rev. Lett. 26, 385 (1987)
J.M.D. Coey, E. Batalla, Z. Altonian, and J.O. Ström-Olsen: Phys. Rev. B 35, 8630 (1987)
H. Wakabayashi, K. Fukamichi, H. Komatsu, T. Goto, and K. Kuroda: Proc. Int. Symposium on Physics of Magnetic Materials (World Scientific, Singapore, 1987) p. 342
K. Fukamichi, T. Goto, H. Komatsu, and H. Wakabayashi: Proc. 4th Int. Conf. on Phys. Magn. Mater. (Poland), ed. by W. Gorkowski, H.K. Lachowics, and H. Szymczak (World Scientific, Singapore, 1989) p. 354
K. Fukamichi, T. Goto, and U. Mizutani: IEEE Trans. on Magn. MAG-23, 3590 (1987)
L.J. Tao, S. Kirkpatrick, R.J. Gambino, and J.J. Cuomo: Solid State Cornmun. 13, 1491 (1973)
R. Taylor and A. Gangulee: J. Appl. Phys. 47, 4666 (1976)
V.L. Moruzzi, J.F. Janak, and A.R. Williams: Calculated Electronic Properties of Metals (Pergamon, New York, 1978)
H. Tanaka and S. Takayama: J. Phys.: Condens. Matter 4, 8203 (1992)
A. Lienald and J.P. Rebouillat: J. Appl. Phys. 49, 1680 (1978)
M.A. Fremy, D. Gignoux, A. Lienald: J. Magn. Magn. Mater. 44, 263 (1984)
K.H.J. Buschow: Proc. Materials Research Society Conf. (Strasbourg), ed. by M. von Allmen (Les Editions de Physique, Les Ulis, 1984) p. 313
N. Heinman and N. Kazama: Phys. Rev. B 17, 2215 (1978)
R.C. Taylor and A. Gangulee: J. Appl. Phys. 47, 4666 (1976)
U. Mizutani, M. Hasegawa, K. Fukamichi, Y. Hattori, Y. Yamada, H. Tanaka, and S. Takayama: Phys. Rev. B 47, 2678 (1993)
F.E. Luborsky: Ferromagnetic Materials, Vol. 1, ed. by K.H.J. Bushow and E.P. Wohlfarth (North-Holland, Amsterdam, 1980) p. 451
K. Moorjani and J.M.D. Coey: Magnetic Glasses (Elsevier, Amsterdam, 1984)
P. Hansen: in Handbook of Magnetic Materials, Vol. 6, ed. by K.H.J. Bushow (North-Holland, Amsterdam, 1991) p. 289
O. Beckmann and L. Lundgren: in Handbook of Magnetic Materials, Vol. 6, ed. by K.H.J. Buschow (North-Holland, Amsterdam 1991)
Y. Waseda: Prog. Mater. Sci. 26, 1 (1981)
T. Fujiwara and Y. Ishii: J. Phys. F: Met. Phys. 10, 1901 (1980)
S. Krompiewski, U. Krey, U. Krauss, and H. Ostermeier: J. Magn. Magn. Matter. 73, 5 (1988)
W.Y. Ching and Y.-N. Xu: J. Appl. Phys. 70, 6305 (1991)
C.L. Chien and K.M. Unruh: Nucl. Instrum. & Methods 199, 193 (1982)
H. Tanaka, S. Takayama, M. Hasegawa, T. Fukunaga, U. Mizutani, A. Fujita, and K. Fukamichi: Phys. Rev. B 47, 2671 (1993)
K. Yamaguchi and T. Mizoguchi: J. Phys. Soc. Jpn. 39, 541 (1975)
R.A. Alben, J.I. Budnick, and G.S. Cargill: In Metallic Glasses, eds. J.J. Gilman and H.J. Leamy (American Society of Metals, Metals Park, Ohio, 1978)
H. Tanaka, S. Takayama, and T. Fujiwara: Phys. Rev. B 46, 7390 (1992)
K.H.J. Buschow, M. Brouha, J.M.N. Biesterbos, and A.G. Dirks: Physica B 91, 261 (1977)
G. Güintherodt and N.J. Shevchik: AIP Conf. Proc. No. 29, 174 (1976)
H. Tanaka and S. Takayama: J. Appl. Phys. 70, 6577 (1991)
S.S. Jaswal, D.J. Sellmyer, M. Engelhardt, and Z. Zhao: Phys. Rev. B 35, 996 (1991)
K. Fukamichi, K. Shirakawa, Y. Satoh, T. Masumoto, and T. Kaneko: J. Magn. Magn. Mater. 54–57, 231 (1986)
S. Asano and S. Ishida: J. Phys. F: Met. Phys. 18, 501 (1988)
J. Inoue and M. Shimizu: J. Phys. F: Met. Phys. 15, 1525 (1985)
Y. Kakehashi, H. Tanaka, and M. Yu: Phys. Rev. B 47, 7736 (1993)
M. Matsuura, H. Wakabayashi, T. Goto, H. Komatsu, and K. Fukamichi: J. Phys. Condens. Matter 1, 2077 (1989)
Y. Kakehashi: Phys. Rev. B 40, 11059 (1989)
Y. Kakehashi: Phys. Rev. B 41, 9207 (1990)
Y. Kakehashi: Phys. Rev. B 42, 10820 (1991)
M. Yu, Y. Kakehashi, and H. Tanaka: Phys. Rev. B 49, 352 (1994)
T. Uchida and Y. Kakehashi: J. Appl. Phys. 81, 3859 (1997)
T. Uchida and Y. Kakehashi: Physica B 239, 504 (1997)
T. Uchida and Y. Kakehashi: Phys. Rev. B 64, 4402 (2001)
H. Wakabayashi, T. Goto, K. Fukamichi, H. Komatsu, S. Morimoto, and A. Ito: J. Phys. Soc. Jpn. 58, 3383 (1989)
I. Vincze, D. Kaptás, T. Kemény, L.F. Kiss, and J. Balogh: Phys. Rev. Lett. 73, 496 (1994)
H. Ren and D.H. Ryan: Phys. Rev. B 51, 15885 (1995)
K. Fukamichi, T. Goto, H. Komatsu, and H. Wakabayashi: In Proc. 4th Intern’l Conf. on the Physics of Magnetic Materials (Poland, 1988), ed. by W. Gorkowski, H.K. Lachowics, and H. Szymczak (World Scientific, Singapore, 1989) p. 354
J.A. Fernandez-Baca, J.J. Rhyne, G.E. Fish, M. Hennion, and B. Hennion: J. Appl. Phys. 67, 5223 (1990)
L.E. Ballentine and J.E. Hammerberg: Phys. Rev. B 28, 1107 (1983)
L.J. Ballentine and M. Kolár: J. Phys. C: Solid State Phys. 19, 981 (1986)
G.-L. Zhao, Y. He, and W.Y. Ching: Phys. Rev. B 42, 10887 (1990)
S.K. Bose, O. Jepsen, and O.K. Andersen: Phys. Rev. B 48, 4265 (1993)
S.K. Bose, O. Jepsen, and O.K. Andersen: J. Phys.: Condens. Matter 6, 2145 (1994)
B. Kramer and D. Weaire: J. Phys. C: Solid State Phys. 11, L5 (1978)
J.G. Wright: Inst. Phys. Conf. Ser. 30, 251 (1976)
H.-J. Güntherodt and H.U. Küniz: Phys. Condens. Mater. 16, 117 (1973)
U. Mizutani: Prog. Mater. Sci. 28, 97 (1983)
M. Itoh: Phys. Rev. B 45, 4241 (1992)
D. Levine and P.J. Steinhardt: Phys. Rev. Lett. 53, 2477 (1984)
P.J. Steinhardt and S. Ostlund: The Physics of Quasicrystals (World Scientific, Singapore, 1987)
C.L. Henley: In Quasicrystals, ed. by T. Fujiwara and T. Ogawa, Springer Series in Solid State Sciences 93 (Springer-Verlag, Heidelberg, 1990)
A.P. Tsai, J.Q. Guo, E. Abe, H. Takakura, and T.J. Sato: Nature 408, 537 (2000)
J.Q. Guo, E. Abe, and A.P. Tsai: Phys. Rev. B 62, 14605 (2000)
H. Takakura, J.Q. Guo, and A.P. Tsai: submitted to Philos. Mag. Lett. (2000)
M. Kohmoto, L.P. Kadanoff, and C. Tang: Phys. Rev. Lett. 50, 1870 (1983)
S. Ostlund, R. Pandit, D. Rand, H.J. Schellnhuber, and E.D. Siggia: Phys. Rev. Lett. 50, 1873 (1983)
M. Kohmoto, B. Sutherland, and C. Tang: Phys. Rev. B 35, 1025 (1987)
T. Fujiwara, M. Kohmoto, and T. Tokihiro: Phys. Rev. B 40, 7413 (1989)
H. Tsunetsugu, T. Fujiwara, K. Ueda, and T. Tokihiro: J. Phys. Soc. J. n. 55, 1420 (1986)
H. Tsunetsugu, T. Fujiwara, K. Ueda, and T. Tokihiro: Phys. Rev. B 43, 8879 (1991)
T. Fujiwara and H. Tsunetsugu, Quasicrystals: The States of the Art, ed. by D.P. DiVincenxo and P.J. Steinhardt (World Scientific, Singapore, 1991)
D. Mayou: Lectures on Quasicrystals, ed. by F. Hippert and D. Gratias (Les Editions de Physique, Les Ulis, 1994)
C. Sire: Lectures on Quasicrystals, ed. by F. Hippert and D. Gratias (Les Editions de Physique, Les Ulis, 1994)
K. Kimura and S. Takeuchi: Quasicrystals: The States of the Art, ed. by D.P. DiVincenxo and P.J. Steinhardt (World Scientific, Singapore, 1991)
J.S. Poon: Adv. Phys. 41, 303 (1992)
C. Berger: Lectures on Quasicrystals, ed. by F. Hippert and D. Gratias (Les Editions de Physique, Les Ulis, 1994)
T. Fujiwara: Phys. Rev. B 40, 942 (1989)
T. Fujiwara and T. Yokokawa: Phys. Rev. Lett. 63, 333 (1991)
T. Fujiwara, G. Trambly de Laissardière, and S. Yamamoto: Mater. S.i. Eng. A 179–180, 118 (1994)
G. Trambly de Laissardière and T. Fujiwara: Phys. Rev. B 50, 5999 (1994)
G. Trambly de Laissardière and T. Fujiwara: Phys. Rev. B 50, 9843 (1994)
S. Yamamoto and T. Fujiwara: Phys. Rev. B 51, 8841 (1995)
T. Fujiwara, T. Mitsui, and S. Yamamoto: Phys. Rev. B 53, R2910 (1996)
M. Kohmoto: Phys. Rev. B 34, 5043 (1986)
B. Sutherland and M. Kohmoto: Phys. Rev. B 36, 5877 (1987)
H. Hiramoto and M. Kohmoto: Int. J. Mod. Phys. B 6, 281 (1992)
M. Gardner: Sci. Am. 236, 110 (1977)
N.G. de Bruijn: Indag. Math. Proc. Ser. A, 84 27, 39, 53 (1981)
H. Tsunetsugu and K. Ueda: Phys. Rev. B 43, 8892 (1991)
J. Friedel: Helv. Phys. Acta 61, 538 (1988)
V.G. Vaks, V.V. Kamyshenko, and G.D. Samolyuk: Phys. Lett. A 132, 131 (1988)
A.E. Carlsson and R. Phillips: Quasicrystals: The States of the Art, ed. by D.P. DiVincenxo and P.J. Steinhardt (World Scientific, Singapore, 1991)
G. Trambly de Laissardière, N. Nguyen Manh, L. Magaud, J.P. Julien, F. Cyrot-Lackmann, and D. Mayou: Phys. Rev. B 52, 7920 (1995)
G. Trambly de Laissardière and D. Mayou: Phys. Rev. B 55, 1 (1997)
E.S. Zijlstra: Euro. Phys. Lett. 52, 578 (2000)
A.P. Smith and N.W. Ashcroft: Phys. Rev. Lett. 59, 1365 (1987)
V. Elser and C.L. Henley: Phys. Rev. Lett. 55, 2883 (1985)
P. Guyot and M. Audier: Phil. Mag. B 51, L15 (1985)
E. Cokayne, R. Phillips, X.B. Kan, S.C. Moss, J.L. Robertson, T. Ishimasa, and M. Mori: J. Non-Cryst. Solids 153–154, 140 (1993)
S. Roche and T. Fujiwara: unpublished work and paper presented at the Conference Aperiodic 97
H. Yamada, W. Iwakami, T. Yakeuchi, U. Mizutani, M. Tanaka, S. Yamaguchi, and T. Matsuda: Proc. of 6th International Conference on Quasicrystals, ed. by T. Fujiwara and S. Takeuchi (World Scientific, Singapore, 1997)
A. Waseda, H. Morioka, K. Kimura, and H. Ino: Phil. Mag. Lett. 65, 25 (1992)
M. Krajčí, M. Windisch, J. Hafner, G. Kresse, and M. Mihalkovič: Phys. Rev. B 51, 17355 (1995)
H. Akiyama, Y. Honda, T. Hashimoto, K. Edagawa, and S. Takeuchi: Jpn. J. Appl. Phys. 32, L1003 (1993)
F.S. Pierce, S.J. Poon, and Q. Guo: Science 261, 737 (1993)
Q. Guo and S.J. Poon: Phys. Rev. B 54, 12793 (1996)
A.D. Bianchi, F. Bommeli, M.A. Chernikov, U. Gubler, L. Degiorgi, and H.R. Ott: Phys. Rev. B 55, 5730 (1997); Q. Guo and S.J. Poon: to be published in Phys. Rev. B
H. Sawada, R. Tamura, K. Kimura, and H. Ino: Proc. of 6th International Conference on Quasicrystals, ed. by T. Fujiwara and S. Takeuchi (World Scientific, Singapore, 1997) p. 631
C. Gignoux, C. Berger, G. Fourcaudot, J.C. Grieco, and H. Rakoto: Euro. Phys. Lett. 39, 171 (1997)
M. Takeda, R. Tamura, Y. Sakairi, and K. Kimura: Proc. of 6th International Conference on Quasicrystals, ed. by T. Fujiwara and S. Takeuchi (World Scientific, Singapore, 1997)
M. Windisch, M. Krajčí, and J. Hafner: J. Phys. Condens. Matter 6, 6977 (1994)
J. Hafner and M. Krajčí: Phys. Rev. Lett. 66, 333 (1991)
J. Hafner and M. Krajčí: Phys. Rev. B 47, 11795 (1993)
U. Mizutani and T. Takeuchi: to be published in Phil. Mag. B
U. Mizutani, W. Iwakami, and T. Fujiwara: Proc. of 6th International Conference on Quasicrystals, ed. by T. Fujiwara and S. Takeuchi (World Scientific, Singapore, 1997)
Y. Ishii and T. Fujiwara: Phys. Rev. Lett. 87, 206408 (2001)
S.E. Burkov: Phys. Rev. Lett. 67, 614 (1991)
S.E. Burkov: J. Phys. I France 2, 695 (1992)
S.E. Burkov: Phys. Rev. B 47, 12325 (1993)
S. Martin, A.F. Hebard, A.R. Kortan, and F.A. Thiel: Phys. Rev. Lett. 67, 719 (1991)
W. Yun-ping and Z. Dian-lin: Phys. Rev. B 49, 13204 (1994)
W. Yun-ping, L. Li, and Z. Dian-lin: J. Non-Crys. Solids 153–154, 361 (1993)
M. Krajčí, J. Hafner, and M. Windisch: Phys. Rev. B 55, 843 (1997)
Z.M. Stadnik, D. Purdie, M. Garnier, Y. Baer, A.-P. Tsai, A. Inoue, K. Edagawa, S. Takeuchi, and K.H.J. Buschow: Phys. Rev. B 55, 10938 (1997)
E. Belin and A. Traverse: J. Phys. Condens. Matt. 3, 2157 (1991)
E. Belin and D. Mayou: Phys. Scr. T 49, 356 (1993)
E. Belin, Z. Dankhazi, A. Sadoc, and J.-M. Dubois: J. Phys. Condens. Matt. 6, 8771 (1994)
M. Mori, S. Matsuo, T. Ishimasa, T. Matsuura, K. Kamiya, H. Inokuchi, and T. Matsukawa: J. Phys. Condens. Matt. 3, 767 (1991)
H. Matsubara, S. Ogawa, T. Kinoshita, K. Kishi, S. Takeuchi, K. Kimura, S. Suga: Jpn. J. Appl. Phys. 30, L389 (1991)
T. Klein and O.G. Symko: Phys. Rev. Lett. 73, 2248 (1994)
T. Klein, O.G. Symko, D.N. Davydov, and A.G.M. Jansen: Phys. Rev. Lett. 74, 3656 (1995)
F. Hippert, L. Kandel, Y. Calvayrac, and B. Dubost: Phys. Rev. Lett. 69, 2086 (1992)
X.-P. Tang, W.A. Hill, S.K. Wonnell, S.J. Poon, and Y. Wu: Phys. Rev. Lett. 79, 1070 (1997)
A. Sahnoune, J.O. Ström-Olsen, and A. Zaluska: Phys. Rev. B 46, 10629 (1992)
T. Klein, H. Rakoto, C. Berger, G. Fourcaudot, and F. Cyrot-Lackmann: Phys. Rev. B 45, 2046 (1992)
Y. Akahama, Y. Mori, M. Kobayashi, H. Kawamura, K. Kimura, and S. Takeuchi: J. Phys. Soc. Jpn. 58, 2231 (1989)
T. Fujiwara, S. Yamamoto, and G. Trambly de Laissardière: Phys. Rev. Lett. 71, 4166 (1993)
C.R. Lin, S.L. Chou, and S.T. Lin: J. Phys. Condens. Matter 8, L725 (1996)
J. Delahaye, J.P. Brison, and C. Berger: Phys. Rev. Lett. 81, 4204 (1998)
L. Guohong, H. Haifeng, W. Yunpin, L. Li, L. Shanlin, J. Xiunian, and Z. Dianlin: Phys. Rev. Lett. 82, 1229 (1999)
D.N. Davydov, D. Mayou, C. Berger, and A.G.M. Jansen: Int. J. Mod. Phys. B 12, 503 (1998)
R. Car and M. Parrinello: Phys. Rev. Lett. 55, 2471 (1985)
M.C. Payne, M.P. Teter, D.C. Allen, T.A. Arias, and J.D. Joannapoulos: Rev. Mod. Phys. 64, 1045 (1992)
G. Kress and J. Furthmüller: Comp. Mat. Sci. 6, 15 (1996)
V. Heine: Solid State Phys. 24, 1 (1970)
W.A. Harrison: Phys. Rev. A 136, 1109 (1964)
J. Hafner and V. Heine: J. Phys. F 13, 2479 (1983)
J. Hafner: From Hamiltonians to Phase Diagrams (New York, SpringerVerlag, 1987)
J. Hafner and W. Jank: J. Phys. Condens. Matter 2, SA239 (1990)
I. Stich, R. Car, and M. Parrinello: Phys. Rev. Lett. 63, 2240 (1989)
G. Galli, R.M. Martin, R. Car, and M. Parrinello: Phys. Rev. B 42, 7470 (1990)
B.J.C. Cabral and J.L. Martin: Phys. Rev. B 51, 872 (1995)
F. Shimojo, Y. Zempo, K. Hoshino, and M. Watabe: Phys. Rev. B 52, 9320 (1995)
A. Pasquarello, K. Laaronen, R. Car, C. Lee, and D. Vanderbilt: Phys. Rev. Lett. 69, 1982 (1992)
F.H. Stillinger and A. Rahman: J. Chem. Phys. 60, 1545 (1974)
K. Laasonen, M. Spik, and M. Parrinello: J. Chem. Phys. 99, 9080 (1993)
M. Spik, J. Hutter, and M. Parrinello: J. Chem. Phys. 105, 1142 (1996)
L.M. Ramaniah, M. Bernasconi, and M. Parrinello: J. Chem. Phys. 109, 6839 (1998)
C. Lee, D. Vanderbilt, K. Laasonen, R. Car, and M. Parrinello: Phys. Rev. Lett. 69, 462 (1992)
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Tanaka, H., Fujiwara, T. (2003). Electronic Structure in Aperiodic Systems. In: Kawazoe, Y., Waseda, Y. (eds) Structure and Properties of Aperiodic Materials. Advances in Materials Research, vol 5. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-10116-2_1
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