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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 \(\xi \to 0\).

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Author:Nirmalendu Chaudhuri, Andreas Unterreiter
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