### Abstract

We analyze the free boson gas on a Cayley tree using two alternative methods. The spectrum of the lattice Laplacian on a finite tree is obtained using a direct iterative method for solving the associated characteristic equation and also using a random walk representation for the corresponding fermion lattice gas. The existence of the thermodynamic limit for the pressure of the boson lattice gas is proven and it is shown that the model exhibits boson condensation into the ground state. The random walk representation is also used to derive an expression for the Bethe approximation to the infinite-volume spectrum. This spectrum turns out to be continuous instead of a dense point spectrum, but there is still boson condensation in this approximation. © 1992 Plenum Publishing Corporation.

Original language | English |
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Pages (from-to) | 307-328 |

Number of pages | 22 |

Journal | Journal of Statistical Physics |

Volume | 69 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - Oct 1992 |

### Keywords

- Boson condensation
- Cayley tree, random walk representation

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## Cite this

*Journal of Statistical Physics*,

*69*(1-2), 307-328. https://doi.org/10.1007/BF01053795