### Abstract

We study electron tunneling between two infinite potential square wells connected via an opaque barrier and find that time evolution of the probability of the presence of a Gaussian wave packet, localized initially in one of the wells, shares the fractal behavior of tunneling in a quartic potential, discovered by Dekker (H. Dekker, Phys. Rev. A35, 1825 (1987). However, the fractal dimensions are found to be closer to those of a conventional Weierstrass function than those appropriate to the quasi-Weierstrass behavior of Dekker. It is argued that the usual exponential decay predicted by conventional relaxation processes can be recovered only as an effect of thermal fluctuations.

Original language | English |
---|---|

Pages (from-to) | 59-66 |

Number of pages | 8 |

Journal | Fractals |

Volume | 6 |

Issue number | 1 |

Publication status | Published - Mar 1998 |

Externally published | Yes |

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### ASJC Scopus subject areas

- General
- Geometry and Topology

### Cite this

*Fractals*,

*6*(1), 59-66.

**Fractal dimensions in tunneling processes and effects of environmental fluctuations.** / Kovanis, Vassilios; Grigolini, Paolo; Kenkre, V. M.; Tsironis, G. P.

Research output: Contribution to journal › Article

*Fractals*, vol. 6, no. 1, pp. 59-66.

}

TY - JOUR

T1 - Fractal dimensions in tunneling processes and effects of environmental fluctuations

AU - Kovanis, Vassilios

AU - Grigolini, Paolo

AU - Kenkre, V. M.

AU - Tsironis, G. P.

PY - 1998/3

Y1 - 1998/3

N2 - We study electron tunneling between two infinite potential square wells connected via an opaque barrier and find that time evolution of the probability of the presence of a Gaussian wave packet, localized initially in one of the wells, shares the fractal behavior of tunneling in a quartic potential, discovered by Dekker (H. Dekker, Phys. Rev. A35, 1825 (1987). However, the fractal dimensions are found to be closer to those of a conventional Weierstrass function than those appropriate to the quasi-Weierstrass behavior of Dekker. It is argued that the usual exponential decay predicted by conventional relaxation processes can be recovered only as an effect of thermal fluctuations.

AB - We study electron tunneling between two infinite potential square wells connected via an opaque barrier and find that time evolution of the probability of the presence of a Gaussian wave packet, localized initially in one of the wells, shares the fractal behavior of tunneling in a quartic potential, discovered by Dekker (H. Dekker, Phys. Rev. A35, 1825 (1987). However, the fractal dimensions are found to be closer to those of a conventional Weierstrass function than those appropriate to the quasi-Weierstrass behavior of Dekker. It is argued that the usual exponential decay predicted by conventional relaxation processes can be recovered only as an effect of thermal fluctuations.

UR - http://www.scopus.com/inward/record.url?scp=2842545134&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=2842545134&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:2842545134

VL - 6

SP - 59

EP - 66

JO - Fractals

JF - Fractals

SN - 0218-348X

IS - 1

ER -