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: | urn:nbn:de:hbz:386-kluedo-10481 |
Series (Serial Number): | Berichte der Arbeitsgruppe Technomathematik (AGTM Report) (230) |
Document Type: | Preprint |
Language of publication: | English |
Year of Completion: | 2000 |
Year of first Publication: | 2000 |
Publishing Institution: | 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: | Kaiserslautern - 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 |