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## On the minimal energy state of a mixture of charged classical and quantum fluids

- The paper concerns the equilibrium state of ultra small semiconductor devices. Due to the quantum drift diffusion model, electrons and holes behave as a mixture of charged quantum fluids. Typically the involved scaled Plancks constants of holes, \(\xi\), is significantly smaller than the scaled Plancks constant of electrons. By setting formally \(\xi=0\) a well-posed differential-algebraic system arises. Existence and uniqueness of an equilibrium solution is proved. A rigorous asymptotic analysis shows that this equilibrium solution is the limit (in a rather strong sense) of quantum systems as \(\xi \to 0\). In particular the ground state energies of the quantum systems converge to the ground state energy of the differential-algebraic system as \(\xi \to 0\).

Author: | Nirmalendu Chaudhuri, Andreas Unterreiter |
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URN (permanent link): | urn:nbn:de:hbz:386-kluedo-10481 |

Serie (Series number): | Berichte der Arbeitsgruppe Technomathematik (AGTM Report) (230) |

Document Type: | Preprint |

Language of publication: | English |

Year of Completion: | 2000 |

Year of Publication: | 2000 |

Publishing Institute: | Technische Universität Kaiserslautern |

Date of the Publication (Server): | 2000/08/16 |

Tag: | charged fluids; mixture of quantum fluids and classical fluids; semi-classical limits; thermal equilibrium state |

Faculties / Organisational entities: | Fachbereich Mathematik |

DDC-Cassification: | 5 Naturwissenschaften und Mathematik / 510 Mathematik |

MSC-Classification (mathematics): | 35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Bxx Qualitative properties of solutions / 35B45 A priori estimates |

Licence (German): | Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011 |