### Abstract

We compute the spectral dimensionality d of random superconducting-normal networks by directly examining the low-frequency density of states at the percolation threshold. We find that d=4.1±0.2 and 5.8±0.3 in two and three dimensions, respectively, which confirms the scaling relation d=2d/(2-s/ν), where s is the superconducting exponent and ν the correlation-length exponent for percolation. We also consider the one-dimensional problem where scaling arguments predict, and our numerical simulations confirm, that d=0. A simple argument provides an expression for the density of states of the localized high-frequency modes in this special case. We comment on the connection between our calculations and the ''termite'' problem of a random walker on a random superconducting-normal network and point out difficulties in inferring d from simulations of the termite problem.

Original language | English (US) |
---|---|

Pages (from-to) | 4930-4935 |

Number of pages | 6 |

Journal | Physical Review B |

Volume | 37 |

Issue number | 10 |

DOIs | |

State | Published - 1988 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Condensed Matter Physics

### Cite this

*Physical Review B*,

*37*(10), 4930-4935. https://doi.org/10.1103/PhysRevB.37.4930

**Spectral dimensionality of random superconducting networks.** / Day, A. R.; Xia, W.; Thorpe, Michael.

Research output: Contribution to journal › Article

*Physical Review B*, vol. 37, no. 10, pp. 4930-4935. https://doi.org/10.1103/PhysRevB.37.4930

}

TY - JOUR

T1 - Spectral dimensionality of random superconducting networks

AU - Day, A. R.

AU - Xia, W.

AU - Thorpe, Michael

PY - 1988

Y1 - 1988

N2 - We compute the spectral dimensionality d of random superconducting-normal networks by directly examining the low-frequency density of states at the percolation threshold. We find that d=4.1±0.2 and 5.8±0.3 in two and three dimensions, respectively, which confirms the scaling relation d=2d/(2-s/ν), where s is the superconducting exponent and ν the correlation-length exponent for percolation. We also consider the one-dimensional problem where scaling arguments predict, and our numerical simulations confirm, that d=0. A simple argument provides an expression for the density of states of the localized high-frequency modes in this special case. We comment on the connection between our calculations and the ''termite'' problem of a random walker on a random superconducting-normal network and point out difficulties in inferring d from simulations of the termite problem.

AB - We compute the spectral dimensionality d of random superconducting-normal networks by directly examining the low-frequency density of states at the percolation threshold. We find that d=4.1±0.2 and 5.8±0.3 in two and three dimensions, respectively, which confirms the scaling relation d=2d/(2-s/ν), where s is the superconducting exponent and ν the correlation-length exponent for percolation. We also consider the one-dimensional problem where scaling arguments predict, and our numerical simulations confirm, that d=0. A simple argument provides an expression for the density of states of the localized high-frequency modes in this special case. We comment on the connection between our calculations and the ''termite'' problem of a random walker on a random superconducting-normal network and point out difficulties in inferring d from simulations of the termite problem.

UR - http://www.scopus.com/inward/record.url?scp=35949010196&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=35949010196&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.37.4930

DO - 10.1103/PhysRevB.37.4930

M3 - Article

VL - 37

SP - 4930

EP - 4935

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 0163-1829

IS - 10

ER -