### Abstract

In the context of determining the extent of dynamical heterogeneity of relaxation processes, it has proven useful to represent the ensemble-averaged autocorrelation function φ(t) in the general form φ(t) =f g(τ)Χ(t/τ)d τ, instead of focusing on the usual special case in which the basis functions Χ(t/τ) are exponentials. In practice, φ(t) is often fit by a stretched exponential, φ(t) = exp[-(t/τ)^{β}. Here we analyze the properties of the probability density g(τ) for the case in which φ(t) is a superposition of stretched exponentials, and is itself a stretched exponential, with a stretching exponent greater than or equal to those of the basis functions, Χ(t/τ). Various degrees of nonexponentiality intrinsic in each basis function translate into different values for the time-dependent variance σ^{2}(t) of the stochastic quantity Χ(t/τ), in which τ is considered to be a spatially varying characteristic time scale. We state a simple but exact solution for σ^{2}(t), and assess its relation to experimental data on the inhomogeneous optical linewidth σ_{inh}(t), measured in the course of solvation processes in a supercooled liquid.

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

Pages (from-to) | 779-784 |

Number of pages | 6 |

Journal | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 58 |

Issue number | 1 |

State | Published - 1998 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Condensed Matter Physics
- Statistical and Nonlinear Physics

### Cite this

**Dynamic heterogeneity, spatially distributed stretched-exponential patterns, and transient dispersions in solvation dynamics.** / Richert, Ranko; Richert, Manfred.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Dynamic heterogeneity, spatially distributed stretched-exponential patterns, and transient dispersions in solvation dynamics

AU - Richert, Ranko

AU - Richert, Manfred

PY - 1998

Y1 - 1998

N2 - In the context of determining the extent of dynamical heterogeneity of relaxation processes, it has proven useful to represent the ensemble-averaged autocorrelation function φ(t) in the general form φ(t) =f g(τ)Χ(t/τ)d τ, instead of focusing on the usual special case in which the basis functions Χ(t/τ) are exponentials. In practice, φ(t) is often fit by a stretched exponential, φ(t) = exp[-(t/τ)β. Here we analyze the properties of the probability density g(τ) for the case in which φ(t) is a superposition of stretched exponentials, and is itself a stretched exponential, with a stretching exponent greater than or equal to those of the basis functions, Χ(t/τ). Various degrees of nonexponentiality intrinsic in each basis function translate into different values for the time-dependent variance σ2(t) of the stochastic quantity Χ(t/τ), in which τ is considered to be a spatially varying characteristic time scale. We state a simple but exact solution for σ2(t), and assess its relation to experimental data on the inhomogeneous optical linewidth σinh(t), measured in the course of solvation processes in a supercooled liquid.

AB - In the context of determining the extent of dynamical heterogeneity of relaxation processes, it has proven useful to represent the ensemble-averaged autocorrelation function φ(t) in the general form φ(t) =f g(τ)Χ(t/τ)d τ, instead of focusing on the usual special case in which the basis functions Χ(t/τ) are exponentials. In practice, φ(t) is often fit by a stretched exponential, φ(t) = exp[-(t/τ)β. Here we analyze the properties of the probability density g(τ) for the case in which φ(t) is a superposition of stretched exponentials, and is itself a stretched exponential, with a stretching exponent greater than or equal to those of the basis functions, Χ(t/τ). Various degrees of nonexponentiality intrinsic in each basis function translate into different values for the time-dependent variance σ2(t) of the stochastic quantity Χ(t/τ), in which τ is considered to be a spatially varying characteristic time scale. We state a simple but exact solution for σ2(t), and assess its relation to experimental data on the inhomogeneous optical linewidth σinh(t), measured in the course of solvation processes in a supercooled liquid.

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UR - http://www.scopus.com/inward/citedby.url?scp=0000735680&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0000735680

VL - 58

SP - 779

EP - 784

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

SN - 1539-3755

IS - 1

ER -