On the Minimal Energy State of a Mixture of Charged Classical and Quantum Fluids

Chaudhuri, N and Unterreiter, A (2002) On the Minimal Energy State of a Mixture of Charged Classical and Quantum Fluids. In: ZAMM, 82 (9). pp. 587-597.

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Abstract

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 Planck's constants of holes, \xi , is significantly smaller than the scaled Planck's constant of electrons. By setting formally \xi = 0 a well-posed differentialalgebraic 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 \rightarrow 0. In particular the ground state energies of the quantum systems converge to the ground state energy of the differential-algebraic system as \xi \rightarrow 0.

Item Type: Journal Article The copyright belongs to WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. thermal equilibrium state;charged fluids;mixture quantum fluids;classical fluids;semi classical limits Division of Physical & Mathematical Sciences > Mathematics 09 Jan 2006 19 Sep 2010 04:22 http://eprints.iisc.ernet.in/id/eprint/4859