### Abstract

The detailed correspondence between the Emin-Holstein scaling theory and Feynman path-integral method for small-polaron formation is presented. In particular it is shown that the first-cumulant approximation to the path integral using a harmonic trial action in the adiabatic limit is identical to the use of a Gaussian trial wave function in the Emin-Holstein one-parameter scaling theory for the ground-state energy with polaron radius. This is then generalized to a simple two-parameter scaling theory involving both the polaron radius as well as nonadiabaticity of the electron-phonon interaction.

Original language | English (US) |
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Pages (from-to) | 2428-2433 |

Number of pages | 6 |

Journal | Physical Review B |

Volume | 34 |

Issue number | 4 |

DOIs | |

State | Published - Jan 1 1986 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Condensed Matter Physics

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## Cite this

John, S., & Cohen, M. H. (1986). Relationship between path-integral and scaling theories of small polarons.

*Physical Review B*,*34*(4), 2428-2433. https://doi.org/10.1103/PhysRevB.34.2428