A Note on quantum moment hydrodynamics and the entropy principle

Degond, Pierre; Ringhofer, Christian

doi:10.1016/s1631-073x(02)02595-5

Cited by 77 publications

(172 citation statements)

References 13 publications

Supporting

Mentioning

169

Contrasting

Unclassified

Order By: Relevance

“…The general guidelines can be found in [32,33]. This approach has been followed in [34] (see also [35] and references therein). However, one has to deal with operatorial equations which are very complex and therefore hard to be solved numerically.…”

Section: Quantum Corrections To the Semiclassical Modelsmentioning

confidence: 99%

Exploitation of the Maximum Entropy Principle in Mathematical Modeling of Charge Transport in Semiconductors

Mascali

Romano

2017

Entropy

View full text Add to dashboard Cite

Abstract:In the last two decades, the Maximum Entropy Principle (MEP) has been successfully employed to construct macroscopic models able to describe the charge and heat transport in semiconductor devices. These models are obtained, starting from the Boltzmann transport equations, for the charge and the phonon distribution functions, by taking-as macroscopic variables-suitable moments of the distributions and exploiting MEP in order to close the evolution equations for the chosen moments. Important results have also been obtained for the description of charge transport in devices made both of elemental and compound semiconductors, in cases where charge confinement is present and the carrier flow is two-or one-dimensional.

show abstract

Section: Quantum Corrections To the Semiclassical Modelsmentioning

confidence: 99%

Exploitation of the Maximum Entropy Principle in Mathematical Modeling of Charge Transport in Semiconductors

Mascali

Romano

2017

Entropy

View full text Add to dashboard Cite

show abstract

“…In this paper, we shall use our previous works [27] (see also [28]) and [29]. In [27], we propose to define quantum local equilibria (or quantum Maxwellians) as minimizers of the quantum entropy functional, subject to given local moment constraints (such as local density, momentum and energy). As opposed to global equilibria, whose definitions are standard (see e.g.…”

Section: The Wigner-bgk Modelmentioning

confidence: 99%

“…It uses an earlier work [27], [28] where quantum equilibria (or quantum Maxwellians) are defined as minimizers of the quantum entropy, subject to local constraints of, say, given mass and energy. By local constraints, we mean that we enforce, not only that the total number of particles and the total energy of the system is fixed, like in usual quantum statistical mechanics approaches [8], but that the local density and energy at any given point x are given functions.…”

Section: Introductionmentioning

confidence: 99%

“…The reader will find in [42], [41], [46], [43], [32], [38], [39], [40] a sample of recent works on quantum hydrodynamic models. The entropy minimization principle which is the core of the present work has previously been used to derive quantum hydrodynamic models in [27] and [28]. A different, but related approach, can be found in [55], [58], [71].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Quantum Energy-Transport and Drift-Diffusion Models

2005

Self Cite

View full text Add to dashboard Cite

We show that Quantum Energy-Transport and Quantum Drift-Diffusion models can be derived through diffusion limits of a collisional Wigner equation. The collision operator relaxes to an equilibrium defined through the entropy minimization principle. Both models are shown to be entropic and exhibit fluxes which are related with the state variables through spatially non-local relations. Thanks to an expansion of these models, 2 perturbations of the Classical Energy-Transport and Drift-Diffusion models are found. In the DriftDiffusion case, the quantum correction is the Bohm potential and the model is still entropic. In the Energy-Transport case however, the quantum correction is a rather complex expression and the model cannot be proven entropic.

show abstract

“…This form is also similar to the one recently obtained in [20] for a fully quantum drift-diffusion (QDD) model. This model was derived in [14] by following the strategy of quantum moments developed in [13] (see also the review paper [15]). It consists of a three-dimensional drift-diffusion equation involving a quantum chemical potential that depends on the density in a non-local way, via the resolution of a quasistatic auxiliary quantum problem.…”

Section: Notations and Strategy Of The Proofmentioning

confidence: 99%

Diffusive Transport of Partially Quantized Particles: Existence, Uniqueness and Long-Time Behaviour

Abdallah¹,

Méhats²,

Vauchelet³

2006

Proceedings of the Edinburgh Mathematical Society

View full text Add to dashboard Cite

A self-consistent model for charged particles, accounting for quantum confinement, diffusive transport and electrostatic interaction is considered. The electrostatic potential is a solution of a threedimensional Poisson equation with the particle density as the source term. This density is the product of a two-dimensional surface density and that of a one-dimensional mixed quantum state. The surface density is the solution of a drift-diffusion equation with an effective surface potential deduced from the fully three-dimensional one and which involves the diagonalization of a one-dimensional Schrödinger operator. The overall problem is viewed as a two-dimensional drift-diffusion equation coupled to a Schrödinger-Poisson system. The latter is proven to be well posed by a convex minimization technique. A relative entropy and an a priori L 2 estimate provide sufficient bounds to prove existence and uniqueness of a global-in-time solution. In the case of thermodynamic equilibrium boundary data, a unique stationary solution is proven to exist. The relative entropy allows us to prove the convergence of the transient solution towards it as time grows to infinity. Finally, the low-order approximation of the relative entropy is used to prove that this convergence is exponential in time.

show abstract

A Note on quantum moment hydrodynamics and the entropy principle

Cited by 77 publications

References 13 publications

Exploitation of the Maximum Entropy Principle in Mathematical Modeling of Charge Transport in Semiconductors

Exploitation of the Maximum Entropy Principle in Mathematical Modeling of Charge Transport in Semiconductors

Quantum Energy-Transport and Drift-Diffusion Models

Diffusive Transport of Partially Quantized Particles: Existence, Uniqueness and Long-Time Behaviour

Contact Info

Product

Resources

About