Displaying similar documents to “A Quantum Corrected Poisson-Nernst-Planck Model for Biological Ion Channels”

Relaxation-time limits of global solutions in full quantum hydrodynamic model for semiconductors

Sungjin Ra, Hakho Hong (2024)

Applications of Mathematics

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This paper is concerned with the global well-posedness and relaxation-time limits for the solutions in the full quantum hydrodynamic model, which can be used to analyze the thermal and quantum influences on the transport of carriers in semiconductor devices. For the Cauchy problem in ℝ 3 , we prove the global existence, uniqueness and exponential decay estimate of smooth solutions, when the initial data are small perturbations of an equilibrium state. Moreover, we show that the solutions...

Hybrid fluid-quantum coupling for the simulation of the transport of partially quantized particles in a DG-MOSFET

C. Jourdana, N. Vauchelet (2015)

Nanoscale Systems: Mathematical Modeling, Theory and Applications

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This paper is devoted to numerical simulations of electronic transport in nanoscale semiconductor devices forwhich charged carriers are extremely confined in one direction. In such devices, like DG-MOSFETs, the subband decomposition method is used to reduce the dimensionality of the problem. In the transversal direction electrons are confined and described by a statistical mixture of eigenstates of the Schrödinger operator. In the longitudinal direction, the device is decomposed into...

Two Hartree-Fock models for the vacuum polarization

Philippe Gravejat, Christian Hainzl, Mathieu Lewin, Éric Séré (2012)

Journées Équations aux dérivées partielles

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We review recent results about the derivation and the analysis of two Hartree-Fock-type models for the polarization of vacuum. We pay particular attention to the variational construction of a self-consistent polarized vacuum, and to the physical agreement between our non-perturbative construction and the perturbative description provided by Quantum Electrodynamics.

Poisson boundaries of discrete quantum groups

Reiji Tomatsu (2010)

Banach Center Publications

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This is a survey article about a theory of a Poisson boundary associated with a discrete quantum group. The main problem of the theory, that is, the identification problem is explained and solved for some examples.