## 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 $$\xi \to 0$$.

### Weitere Dienste

Verfasserangaben: Nirmalendu Chaudhuri, Andreas Unterreiter urn:nbn:de:hbz:386-kluedo-10481 Berichte der Arbeitsgruppe Technomathematik (AGTM Report) (230) Preprint Englisch 2000 2000 Technische Universität Kaiserslautern 16.08.2000 charged fluids; mixture of quantum fluids and classical fluids; semi-classical limits; thermal equilibrium state Fachbereich Mathematik 5 Naturwissenschaften und Mathematik / 510 Mathematik 35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Bxx Qualitative properties of solutions / 35B45 A priori estimates Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011