Random Matrix Theory and Maximum Entropy Models for Disordered Conductors

Stone, A. Douglas; Mello, Pier A.; Muttalib, K. A.; Pichard, Jean‐Louis

doi:10.1016/b978-0-444-88454-1.50015-2

Cited by 77 publications

(174 citation statements)

References 58 publications

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“…The faster increase of ξ(W ) in the RFM model indicates a weakening of the localization due to the random magnetic fields. The increase of the localization length is, however, much larger than the factor of 2 expected from RMT [19] for the breaking of the time reversal symmetry.…”

Section: Resultsmentioning

confidence: 72%

Energy-level statistics and localization of 2d electrons in random magnetic fields

Batsch

Schweitzer

Krämer

1998

Physica B: Condensed Matter

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Using the method of energy-level statistics, the localization properties of electrons moving in two dimensions in the presence of a perpendicular random magnetic field and additional random disorder potentials are investigated. For this model, extended states have recently been proposed to exist in the middle of the band. In contrast, from our calculations of the large-s behavior of the nearest neighbor level spacing distribution P (s) and from a finite size scaling analysis we find only localized states in the suggested energy and disorder range.

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Section: Resultsmentioning

confidence: 72%

Energy-level statistics and localization of 2d electrons in random magnetic fields

Batsch

Schweitzer

Krämer

1998

Physica B: Condensed Matter

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“…the same value of Tr tt † ), the supercurrents differ because the distribution of transmission eigenvalues is different. In a tunnel junction all N eigenvalues are ≪ 1, while in the disordered system a fraction l/L of the eigenvalues is of order unity, the remainder being exponentially small [34].…”

Section: Average Supercurrentmentioning

confidence: 99%

“…The inverse localization length is uniformly distributed between 0 and 1/ζ min ≃ 1/l for l ≪ L ≪ N l [34]. One can therefore write…”

Section: Average Supercurrentmentioning

confidence: 99%

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Three “Universal” Mesoscopic Josephson Effects

Beenakker

1992

Springer Series in Solid-State Sciences

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Abstract. A recent theory is reviewed for the sample-to-sample fluctuations in the critical current of a Josephson junction consisting of a disordered point contact or microbridge. The theory is based on a relation between the supercurrent and the scattering matrix in the normal state. The root-mean-square amplitude rms I c of the critical current I c at zero temperature is given by rms I c ≃ e∆ 0 /h, up to a numerical coefficient of order unity (∆ 0 is the energy gap). This is the superconducting analogue of "Universal Conductance Fluctuations" in the normal state. The theory can also be applied to a ballistic point contact, where it yields the analogue of the quantized conductance, and to a quantum dot, where it describes supercurrent resonances. All three phenomena provide a measurement of the supercurrent unit e∆ 0 /h, and are "universal" through the absence of a dependence on junction parameters.

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“…For example, the dependence of the conductivity on the eigenvalues and eigenvectors is different in the quantum and classical cases. Moreover, in quantum conduction a magnetic field breaks time reversability, yielding a Hermitian random matrix and a crossover to universal WD statistics of the Gaussian unitary ensemble (GUE), instead of the GOE associated with time reversability and a real-symmetric random matrix [25]. The Anderson transition to GUE universality has been captured by an exactly solvable model [4,7], while the transition to GOE universality remains open.…”

Section: Introductionmentioning

confidence: 99%

Anderson Transition for Classical Transport in Composite Materials

2017

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The Anderson transition in solids and optics is a wave phenomenon where disorder induces localization of the wavefunctions. We find here that the hallmarks of the Anderson transition are exhibited by classical transport at a percolation threshold -without wave interference or scattering effects. As long range order or connectedness develops, the eigenvalue statistics of a key random matrix governing transport crossover toward universal statistics of the Gaussian orthogonal ensemble, and the field eigenvectors delocalize. The transition is examined in resistor networks and sea ice structures.

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Random Matrix Theory and Maximum Entropy Models for Disordered Conductors

Cited by 77 publications

References 58 publications

Energy-level statistics and localization of 2d electrons in random magnetic fields

Energy-level statistics and localization of 2d electrons in random magnetic fields

Three “Universal” Mesoscopic Josephson Effects

Anderson Transition for Classical Transport in Composite Materials

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