Abstract
We have derived explicitly, the large scale distribution of quantum Ohmic resistance of a disordered one-dimensional conductor. We show that in the thermodynamic limit this distribution is characterized by two independent parameters for strong disorder, leading to a two-parameter scaling theory of localization. Only in the limit of weak disorder we recover single parameter scaling, consistent with existing theoretical treatments.
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Abrahams E, Anderson P W, Licciardello D C and Ramakrishnan T V 1979Phys. Rev. Lett. 42 673
Abrahams E and Stephen M 1980J. Phys. C13 L377
Abrikosov A A 1981Solid State Commun. 37 997
Altshuler B L and Khmelnitskii D E 1985Pis’ma Zh. Eksp. Teor. Fiz. 42 291 [JETP Lett. 198542 359]
Altshuler B L, Kravtsov V E and Lerner I V 1986Pis’ma Zh. Eksp. Teor. Fiz. 43 342 [JETP Lett. 198643 441]
Anderson P W, Thouless D J, Abrahams E and Fisher D S 1980Phys. Rev. B22 3519
Bellman R and Wing G M 1976An introduction to invariant imbedding (New York: Wiley)
Bishop D J and Dolan G J 1985Phys. Rev. Lett. 55 2911
Chandrasekhar S 1960Radiative transfer (New York: Dover)
Cohen A, Roth Y and Shapiro B 1988Phys. Rev. B38 12125
Efetov K B 1984Pis’ma Zh. Eksp. Teor. Fiz. 40 17 [JETP Lett. 198440 738]
Erdos P and Herndon R C 1982Adv. Phys. 31 63
Farrell M E, Bishop M F, Kumar N and Lawrence W E 1985Phys. Rev. Lett. 55 626
Giordano N 1980Phys. Rev. B22 5635
Heinrichs J 1986Phys. Rev. B33 5261
Heinrichs J, Jayannavar A M and Kumar N 1988Solid State Commun. 67 1103
Heinrichs J 1990J. Phys. Condens. Matter,2 1559
Ioffe L B, Sagdeev I R and Vinokur V M 1985J. Phys. C18 L641
Jayannavar A M and Kumar N 1982Phys. Rev. Lett. 48 553
Jayannavar A M 1990Solid State Commun. 73 247
Kumar N 1983J. Phys. C16 L109
Kumar N 1985Phys. Rev. B31 5513
Kumar N and Jayannavar A M 1986J. Phys. C19 L85
Landauer R 1970Philos. Mag. 21 863
Lee P A and Stone A D 1985Phys. Rev. Lett. 55 1622
Melnikov V I 1980Zh. Eksp. Teor. Fiz. Pis’ma 32 244 [JETP Lett. 198032 225]
Novikov E A 1964Zh. Eksp. Teor. Fiz. 47 1919 [Sov. Phys. JETP 196520 1290]
Rammal R and Doucot B 1987J. Phys. (Paris) 48 509
Risken H 1984The Fokker-Planck equations (Berlin: Springer)
Schleich W and Scully M O 1988Phys. Rev. A37 1261
Shapiro B 1987Philos. Mag. 56 1031
Stone A D, Allan D C and Joannopoulos J D 1983Phys. Rev. B27 836
van Kampen N G 1976Phys. Rep. C24 172
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Jayannavar, A.M. Scaling theory of quantum resistance distributions in disordered systems. Pramana - J Phys 36, 611–619 (1991). https://doi.org/10.1007/BF02845799
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DOI: https://doi.org/10.1007/BF02845799