### Abstract

We present an asymptotic analysis for the quantum Liouville equation in the classical limit for discontinuous potentials. Such discontinuities arise when the quantum Liouville equation is used to model transport phenomena in novel semiconductor devices, as a result of the presence of heterojunctions. The structure of the solutions close to the junctions is examined, and equations for the outer and inner solutions are given.

Original language | English (US) |
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Title of host publication | Asymptotic Analysis and the Numerical Solution of Partial Differential Equations |

Publisher | CRC Press |

Pages | 185-196 |

Number of pages | 12 |

ISBN (Electronic) | 9781482277067 |

ISBN (Print) | 9780824785383 |

State | Published - Jan 1 1991 |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Ringhofer, C. (1991). An asymptotic analysis of the quantum liouville equation. In

*Asymptotic Analysis and the Numerical Solution of Partial Differential Equations*(pp. 185-196). CRC Press.