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Volumn 37, Issue 10, 1996, Pages 4986-5018

Riemannian symmetric superspaces and their origin in random-matrix theory

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EID: 0030515852     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.531675     Document Type: Article
Times cited : (672)

References (47)
  • 1
    • 0001328019 scopus 로고
    • The mobility edge problem: Continuous symmetry and a conjecture
    • F. Wegner, "The mobility edge problem: Continuous symmetry and a conjecture," Z. Phys. B 35, 207-210 (1979).
    • (1979) Z. Phys. B , vol.35 , pp. 207-210
    • Wegner, F.1
  • 2
    • 0000175084 scopus 로고
    • Disordered system with n orbitals per site: Lagrange formulation, hyperbolic symmetry, and Goldstone modes
    • L. Schäfer and F. Wegner, "Disordered system with n orbitals per site: Lagrange formulation, hyperbolic symmetry, and Goldstone modes," Z. Phys. B 38, 113-126 (1980).
    • (1980) Z. Phys. B , vol.38 , pp. 113-126
    • Schäfer, L.1    Wegner, F.2
  • 3
    • 0020498290 scopus 로고
    • Supersymmetry and theory of disordered metals
    • K. B. Efetov, "Supersymmetry and theory of disordered metals," Adv. Phys. 32, 53-127 (1983).
    • (1983) Adv. Phys. , vol.32 , pp. 53-127
    • Efetov, K.B.1
  • 4
    • 0043017775 scopus 로고
    • Grassmann variables in stochastic quantum physics: The case of compound-nucleus scattering
    • J. J. M. Verbaarschot, H. A. Weidenmüller, and M. R. Zirnbauer, "Grassmann variables in stochastic quantum physics: The case of compound-nucleus scattering," Phys. Rep. 129, 367-438 (1985).
    • (1985) Phys. Rep. , vol.129 , pp. 367-438
    • Verbaarschot, J.J.M.1    Weidenmüller, H.A.2    Zirnbauer, M.R.3
  • 5
    • 35549006412 scopus 로고
    • Statistical theory of the energy levels of complex systems
    • F. J. Dyson, "Statistical theory of the energy levels of complex systems," J. Math. Phys. 3, 140 (1962).
    • (1962) J. Math. Phys. , vol.3 , pp. 140
    • Dyson, F.J.1
  • 6
    • 0040634490 scopus 로고
    • Anderson metal-insulator transition in a system of metal granules: Existence of a minimum metallic conductivity and a maximum dielectric constant
    • K. B. Efetov, "Anderson metal-insulator transition in a system of metal granules: Existence of a minimum metallic conductivity and a maximum dielectric constant," Zh. Eksp. Teor. Fiz. 88, 1032-1052 (1985).
    • (1985) Zh. Eksp. Teor. Fiz. , vol.88 , pp. 1032-1052
    • Efetov, K.B.1
  • 7
    • 22244460032 scopus 로고
    • Localization transition on the bethe lattice
    • M. R. Zirnbauer, "Localization transition on the Bethe lattice," Phys. Rev. B 34, 6394-6408 (1986).
    • (1986) Phys. Rev. B , vol.34 , pp. 6394-6408
    • Zirnbauer, M.R.1
  • 8
    • 0001311162 scopus 로고
    • Localization transition in the anderson model on the Bethe lattice: Spontaneous symmetry breaking and correlation functions
    • A. D. Mirlin and Y. V. Fydorov, "Localization transition in the Anderson model on the Bethe lattice: Spontaneous symmetry breaking and correlation functions," Nucl. Phys. B 366, 507-532 (1991).
    • (1991) Nucl. Phys. B , vol.366 , pp. 507-532
    • Mirlin, A.D.1    Fydorov, Y.V.2
  • 9
    • 0000014801 scopus 로고
    • Kinetics of a quantum particle in a long metallic wire
    • K. B. Efetov and A. I. Larkin, "Kinetics of a quantum particle in a long metallic wire," Zh. Eksp. Teor. Fiz. 85, 764-778 (1983).
    • (1983) Zh. Eksp. Teor. Fiz. , vol.85 , pp. 764-778
    • Efetov, K.B.1    Larkin, A.I.2
  • 10
    • 0005144792 scopus 로고
    • Fourier analysis on a hyperbolic supermanifold of constant curvature
    • M. R. Zirnbauer, "Fourier analysis on a hyperbolic supermanifold of constant curvature," Commun. Math. Phys. 141, 503-522 (1991).
    • (1991) Commun. Math. Phys. , vol.141 , pp. 503-522
    • Zirnbauer, M.R.1
  • 11
    • 4243641159 scopus 로고
    • Super Fourier analysis and localization in disordered wires
    • M. R. Zirnbauer, "Super Fourier analysis and localization in disordered wires," Phys. Rev. Lett. 69, 1584-1587 (1992).
    • (1992) Phys. Rev. Lett. , vol.69 , pp. 1584-1587
    • Zirnbauer, M.R.1
  • 12
    • 0002448247 scopus 로고
    • Conductance fluctuations of disordered wires: Fourier analysis on supersymmetric spaces
    • A. D. Mirlin, A. Müller-Groeling, and M. R. Zirnbauer, "Conductance fluctuations of disordered wires: Fourier analysis on supersymmetric spaces," Ann. Phys. 236, 325-373 (1994).
    • (1994) Ann. Phys. , vol.236 , pp. 325-373
    • Mirlin, A.D.1    Müller-Groeling, A.2    Zirnbauer, M.R.3
  • 13
    • 0001484848 scopus 로고    scopus 로고
    • Quantum transport in disordered wires: Equivalence of the one dimensional σ model and the Dorokhov-Mello-Pereyra-Kumar equation
    • P. W. Brouwer and K. Frahm, "Quantum transport in disordered wires: Equivalence of the one dimensional σ model and the Dorokhov-Mello-Pereyra-Kumar equation," Phys. Rev. B 53, 1490-1501 (1996).
    • (1996) Phys. Rev. B , vol.53 , pp. 1490-1501
    • Brouwer, P.W.1    Frahm, K.2
  • 14
    • 0001722690 scopus 로고
    • Nearly localized states in weakly disordered conductors
    • B. A. Muzykantskii and D. E. Khmelnitskii, "Nearly localized states in weakly disordered conductors," Phys. Rev. B 51, 5480-5483 (1995).
    • (1995) Phys. Rev. B , vol.51 , pp. 5480-5483
    • Muzykantskii, B.A.1    Khmelnitskii, D.E.2
  • 15
    • 0000677443 scopus 로고
    • Statistics of pre-localized states in disordered conductors
    • V. I. Falko and K. B. Efetov, "Statistics of pre-localized states in disordered conductors," Phys. Rev. B 52, 17 413-17 429 (1995).
    • (1995) Phys. Rev. B , vol.52 , pp. 17413-17429
    • Falko, V.I.1    Efetov, K.B.2
  • 16
    • 0000685790 scopus 로고    scopus 로고
    • Distribution of local density of states in disordered metallic samples: Logarithmically normal asymptotics
    • A. D. Mirlin, "Distribution of local density of states in disordered metallic samples: Logarithmically normal asymptotics," Phys. Rev. B 53, 1186-1192 (1996).
    • (1996) Phys. Rev. B , vol.53 , pp. 1186-1192
    • Mirlin, A.D.1
  • 17
    • 0003004692 scopus 로고
    • Crossover from orthogonal to unitary symmetry for ballistic electron transport in chaotic microstructures
    • Z. Pluhař, H. A. Weidenmüller, J. A. Zuk, C. H. Lewenkopf, and F. J. Wegner, "Crossover from orthogonal to unitary symmetry for ballistic electron transport in chaotic microstructures," Ann. Phys. 243, 1-64 (1995).
    • (1995) Ann. Phys. , vol.243 , pp. 1-64
    • Pluhař, Z.1    Weidenmüller, H.A.2    Zuk, J.A.3    Lewenkopf, C.H.4    Wegner, F.J.5
  • 19
    • 0002177376 scopus 로고
    • Effective action in the theory of quasiballistic disordered conductors
    • B. A. Muzykantskii and D. E. Khmelnitskii, "Effective action in the theory of quasiballistic disordered conductors," Pis'ma Zh. Eksp. Teor. Fiz. 62, 68-74 (1995).
    • (1995) Pis'ma Zh. Eksp. Teor. Fiz. , vol.62 , pp. 68-74
    • Muzykantskii, B.A.1    Khmelnitskii, D.E.2
  • 21
    • 4244017133 scopus 로고
    • Anderson localization for sublattice models
    • R. Gade, "Anderson localization for sublattice models," Nucl. Phys. B 398, 499-515 (1993).
    • (1993) Nucl. Phys. B , vol.398 , pp. 499-515
    • Gade, R.1
  • 22
    • 4243561258 scopus 로고
    • Spectrum of the QCD dirac operator and chiral random matrix theory
    • J. J. M. Verbaarschot, "Spectrum of the QCD Dirac operator and chiral random matrix theory," Phys. Rev. Lett. 72, 2531-33 (1994).
    • (1994) Phys. Rev. Lett. , vol.72 , pp. 2531-2533
    • Verbaarschot, J.J.M.1
  • 23
    • 0000323807 scopus 로고
    • Supersymmetry applied to the spectrum edge of random matrix ensembles
    • A. V. Andreev, B. D. Simons, and N. Taniguchi, "Supersymmetry applied to the spectrum edge of random matrix ensembles," Nucl. Phys. B 432, 487-517 (1994).
    • (1994) Nucl. Phys. B , vol.432 , pp. 487-517
    • Andreev, A.V.1    Simons, B.D.2    Taniguchi, N.3
  • 24
    • 0000142334 scopus 로고    scopus 로고
    • Random matrix theory of a chaotic Andreev quantum dot
    • A. Altland and M. R. Zirnbauer, "Random matrix theory of a chaotic Andreev quantum dot," Phys. Rev. Lett. 76, 3420 (1996).
    • (1996) Phys. Rev. Lett. , vol.76 , pp. 3420
    • Altland, A.1    Zirnbauer, M.R.2
  • 27
    • 0000834553 scopus 로고
    • Graded manifolds, graded Lie theory, and prequantization
    • B. Kostant, "Graded manifolds, graded Lie theory, and prequantization," Lect. Notes Math. 570, 177-406 (1977).
    • (1977) Lect. Notes Math. , vol.570 , pp. 177-406
    • Kostant, B.1
  • 30
    • 84967768778 scopus 로고
    • Integration on noncompact supermanifolds
    • M. J. Rothstein, "Integration on noncompact supermanifolds," Trans. Am. Math. Soc. 299, 387-396 (1987).
    • (1987) Trans. Am. Math. Soc. , vol.299 , pp. 387-396
    • Rothstein, M.J.1
  • 31
    • 0040634491 scopus 로고
    • On the existence of global integral superforms on supermanifolds
    • A. Rogers, "On the existence of global integral superforms on supermanifolds," J. Math. Phys. 26, 2749-2753 (1985).
    • (1985) J. Math. Phys. , vol.26 , pp. 2749-2753
    • Rogers, A.1
  • 32
    • 84967787244 scopus 로고
    • The axioms of supermanifolds and a new structure arising from them
    • M. J. Rothstein, "The axioms of supermanifolds and a new structure arising from them," Trans. Am. Math. Soc. 297, 159-180 (1986).
    • (1986) Trans. Am. Math. Soc. , vol.297 , pp. 159-180
    • Rothstein, M.J.1
  • 33
    • 36749111350 scopus 로고
    • A global theory of supermanifolds
    • A. Rogers, "A global theory of supermanifolds," J. Math. Phys. 21, 1352-1365 (1980).
    • (1980) J. Math. Phys. , vol.21 , pp. 1352-1365
    • Rogers, A.1
  • 34
    • 0001138262 scopus 로고
    • Graded manifolds, supermanifolds and infinite-dimensional Grassmann algebras
    • A. Rogers, "Graded manifolds, supermanifolds and infinite-dimensional Grassmann algebras," Commun. Math. Phys. 105, 375-384 (1986).
    • (1986) Commun. Math. Phys. , vol.105 , pp. 375-384
    • Rogers, A.1
  • 35
    • 49449126179 scopus 로고
    • Lie superalgebras
    • V. G. Kac, "Lie superalgebras," Adv. Math. 26, 8-46 (1977).
    • (1977) Adv. Math. , vol.26 , pp. 8-46
    • V G, K.1
  • 36
    • 0002780902 scopus 로고
    • The theory of Lie superalgebras
    • Springer, Berlin
    • M. Scheunert, "The theory of Lie superalgebras," Lecture Notes in Mathematics (Springer, Berlin, 1979), Vol. 716.
    • (1979) Lecture Notes in Mathematics , vol.716
    • Scheunert, M.1
  • 37
    • 0039449045 scopus 로고    scopus 로고
    • note
    • TT=σAσ.
  • 39
    • 0040041180 scopus 로고    scopus 로고
    • note
    • Here we do not distinguish between the orthogonal groups in even and odd dimension.
  • 40
    • 0040041177 scopus 로고    scopus 로고
    • note
    • Since we always have the option of expanding with respect to the anticommuting parameters that may be contained in X, no information is lost by not considering the full left ℋ module of superderivations of ℋ; cf. the last paragraph of Sec. II B.
  • 41
    • 0011706953 scopus 로고
    • Grassmann variables and supersymmetry in the theory of disordered systems
    • E. Brézin, "Grassmann variables and supersymmetry in the theory of disordered systems," Lect. Notes Phys. 216, 115-123 (1984).
    • (1984) Lect. Notes Phys. , vol.216 , pp. 115-123
    • Brézin, E.1
  • 43
    • 0001914480 scopus 로고
    • The Anderson model for electron localization, nonlinear σ model, asymptotic gauge invariance
    • A. A. W. Pruisken and L. Schäfer, "The Anderson model for electron localization, nonlinear σ model, asymptotic gauge invariance," Nucl. Phys. B 200, 20-44 (1982).
    • (1982) Nucl. Phys. B , vol.200 , pp. 20-44
    • Pruisken, A.A.W.1    Schäfer, L.2
  • 44
    • 0040634493 scopus 로고    scopus 로고
    • Supersymmetry for systems with unitary disorder: Circular ensembles
    • submitted
    • M. R. Zirnbauer, "Supersymmetry for systems with unitary disorder: Circular ensembles," submitted to J. Phys. A.
    • J. Phys. A
    • Zirnbauer, M.R.1
  • 45
    • 0040041178 scopus 로고    scopus 로고
    • note
    • For lack of a better word we borrow the terminology from manifolds. Of course what is meant here is the supermanifold of solutions in Gl(W) of the nonlinear equations g = γ̂(g)= τ̂(g).
  • 46
    • 0039430657 scopus 로고
    • Correlations between eigenvalues of a random matrix
    • F. J. Dyson, "Correlations between eigenvalues of a random matrix," Commun. Math. Phys. 19, 235-250 (1970).
    • (1970) Commun. Math. Phys. , vol.19 , pp. 235-250
    • Dyson, F.J.1
  • 47
    • 0040634495 scopus 로고    scopus 로고
    • note
    • Since the orthogonal group here always appears with an even dimension, we use the simplified notation D|C, instead of BD|C as in Table II.


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