## Abstract

We demonstrate that the statistical behavior of the random line shapes of single tetra-tert-butylterrylene chromophores embedded in an amorphous polyisobutylene matrix at T=2 K is described by Lévy statistics. Recently, Barkai et al., suggested to characterize random line shapes of single molecules in glasses by their cumulants κ_{1},κ _{2},κ_{3}, etc. Using Geva-Skinner model for single-molecule spectroscopy in low-temperature glasses, which is based on the standard tunneling model, the theory predicts that probability densities P(κ_{1}), P(κ_{2}), etc., are Lévy stable laws provided that the glass dynamics is described by a slow modulation limit. Analyzing our experimental data we show that the distributions of the first two cumulants are indeed compatible with Lévy statistics; thus, the generalized central limit theorem is applicable to this system. The emergence of Lévy stable laws in this system is due to long-range interactions between two-level systems and the single molecule. The widths of the distribution functions P(κ_{1}) and P(κ_{2}) are non-universal in the sense that they depend on the coupling of the molecule to the host glass. We investigate a universal amplitude ratio (i.e., ratio of widths) which shows that our results are in agreement with the assumptions of the standard tunneling model of low-temperature glasses. We briefly discuss other long-range interacting systems and models, for which Lévy statistics plays an important role.

Original language | English |
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Pages (from-to) | 21-31 |

Number of pages | 11 |

Journal | Journal of Luminescence |

Volume | 107 |

Issue number | 1-4 |

DOIs | |

State | Published - May 2004 |

Externally published | Yes |

Event | Proceedings of the 8th International Meeting on Hole Burning, HBSM 2003 - Bozeman, MT., United States Duration: 26 Jul 2003 → 31 Jul 2003 |

## Keywords

- Long-range interaction
- Low-temperature glass
- Lévy statistics
- Single-molecule spectroscopy