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Pis’ma Zh. Eksp. Teor. Fiz., 21 (1998)
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A. Altland, B D. Simons, and D. Taras-Semchuk, Pis’ma Zh. Eksp. Teor. Fiz. 67, 21 (1998)[JETP Lett.67, 22 (1998)].
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Altland, A.1
Simons, B.D.2
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0032501014
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R. Bundschuh, C. Casanello, D. Serban, and M R. Zirnbauer, Nucl. Phys. B532, 689 (1998);
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Serban, D.3
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6
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T. Senthil, M P A. Fisher, L. Balents, and C. Nayak, Phys. Rev. Lett.81, 4704 (1998);
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Senthil, T.1
Fisher, M.P.A.2
Balents, L.3
Nayak, C.4
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11
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0034224274
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P W. Brouwer, A. Furusaki, I A. Gruzberg, and C. Mudry, Phys. Rev. Lett.85, 1064 (2000).
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13
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0002448247
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Interestingly, the thick-wire limit is a necessary step in the derivation of the one-dimensional nonlinear sigma model, see, e.g., and
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Interestingly, the thick-wire limit is a necessary step in the derivation of the one-dimensional nonlinear sigma model, see, e.g., A D. Mirlin, A. Müller-Groeling, and M R. Zirnbauer, Ann. Phys. (N.Y.)236, 325 (1994).
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Mirlin, A.D.1
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Zirnbauer, M.R.3
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14
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0001484848
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The Fokker-Planck approach is often used without the thick-wire limit, though equivalence of the Fokker-Planck and field-theoretic approach is only established if the thick-wire limit is taken; see, and
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The Fokker-Planck approach is often used without the thick-wire limit, though equivalence of the Fokker-Planck and field-theoretic approach is only established if the thick-wire limit is taken; see P W. Brouwer and K M. Frahm, Phys. Rev. B53, 1490 (1996).
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Brouwer, P.W.1
Frahm, K.M.2
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15
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0000197543
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To illustrate this point, note that an infinitesimal magnetic field already changes the, of the Hamiltonian from orthogonal to unitary. However, for a wire of finite thickness, one needs a finite magnetic field to reach the unitary class, while in the thick-wire limit an infinitesimal field is sufficient. See, e.g., and
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To illustrate this point, note that an infinitesimal magnetic field already changes the symmetry of the Hamiltonian from orthogonal to unitary. However, for a wire of finite thickness, one needs a finite magnetic field to reach the unitary class, while in the thick-wire limit an infinitesimal field is sufficient. See, e.g., H. Schomerus and C W J. Beenakker, Phys. Rev. Lett.84, 3927 (2000).
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Phys. Rev. Lett.
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Schomerus, H.1
Beenakker, C.W.J.2
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16
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0002972775
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P W. Brouwer, C. Mudry, B D. Simons, and A. Altland, Phys. Rev. Lett.81, 862 (1998).
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Brouwer, P.W.1
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Altland, A.4
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20
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85038299899
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For (formula presented) or (formula presented) the class D result (4) is obtained already for wire lengths, of the order of the mean free path
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For (formula presented) or (formula presented) the class D result (4) is obtained already for wire lengths L of the order of the mean free path.
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21
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85038342644
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Note that the limit (formula presented) of the scaling function (formula presented) is a different quantity than the limit (formula presented) of the Lyapunov exponent, which is defined by taking the limit (formula presented), the limit (formula presented) in Eq. (8)
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Note that the limit (formula presented) of the scaling function (formula presented) is a different quantity than the limit (formula presented) of the Lyapunov exponent, which is defined by taking the limit (formula presented) before the limit (formula presented) in Eq. (8).
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