Résonances en limite semi-classique

Helffer, Bernard; Sjöstrand, Johannes

doi:10.24033/msmf.327

Cited by 149 publications

(315 citation statements)

References 0 publications

Supporting

Mentioning

305

Contrasting

Unclassified

Order By: Relevance

“…This approach can be viewed as an application of the semi-classical method (see e.g. [48], [47], [1], [68]) which has been illustrated in the nonlinear case in the work by Grenier [45]. The QDD 2 model turns out to be identical with the classical CDD model corrected by the Bohm potential [42].…”

Section: Statement Of the Resultsmentioning

confidence: 99%

Quantum Energy-Transport and Drift-Diffusion Models

2005

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

Section: Statement Of the Resultsmentioning

confidence: 99%

Quantum Energy-Transport and Drift-Diffusion Models

2005

View full text Add to dashboard Cite

show abstract

“…The step ∆ k has to be chosen small enough in order to catch the resonances which produce very stiff spectral quantities when h > 0 is small. Actually, it is known (see for example [19,20,38]) that this slope is of order e C/h . The stiffness of this spectral quantities is a first test to check that the asymptotic model for h → 0 is relevant.…”

Section: Generalized Eigenfunctionsmentioning

confidence: 99%

Computing the steady states for an asymptotic model of quantum transport in resonant heterostructures

Bonnaillie‐Noël

Nier

Patel

2006

Journal of Computational Physics

View full text Add to dashboard Cite

In this article we propose a rapid method to compute the steady states, including bifurcation diagrams, of resonant tunneling heterostructures in the far from equilibrium regime. Those calculations are made on a simplified model which takes into account the characteristic quantities which arise from an accurate asymptotic analysis of the nonlinear Schrödinger-Poisson system. After a summary of the former theoretical results, the asymptotical model is explicitly adapted to physically realistic situations and numerical results are shown in various cases.MSC : 34L25, 34L30, 34L40, 65L10, 65Z05, 82D37

show abstract

“…In the following, P denotes be the parity operator: Pu(t) = u(−t); from (3.13), we get 15) where, according to the notation introduced in (3.1), F 0 is the standard Fourier transform. Thus, 1 {x≤a} φ b is estimated by…”

Section: Generalized Eigenfunctions Expansionmentioning

confidence: 99%

“…It can be adapted to the particular case of H θ (V), by noticing that: H θ (V) = Q θ,3θ (V). 15) and assume |θ j | < δ, j = 1, 2, with δ > 0 small enough. Then −iQ θ1,θ2 (V) generates a strongly continuous group of bounded operators on L 2 (R), e −itQ θ 1 ,θ 2 (V) t∈R .…”

Section: Schrödinger Operators With Non-mixed Interface Conditionsmentioning

confidence: 99%

Wave operators, similarity and dynamics for a class of Schrödinger operators with generic non-mixed interface conditions in 1D

Mantile

2013

Journal of Mathematical Physics

View full text Add to dashboard Cite

We consider a simple modification of the 1D-Laplacian where non-mixed interface conditions occur at the boundaries of a finite interval. It has recently been shown that Schrödinger operators having this form allow a new approach to the transverse quantum transport through resonant heterostructures. In this perspective, it is important to control the deformations effects introduced on the spectrum and on the time propagator by this class of non-selfadjont perturbations. In order to obtain uniform-in-time estimates of the perturbed semigroup, our strategy consists in constructing stationary waves operators allowing to intertwine the modified non-selfadjoint Schrödinger operator with a 'physical' Hamiltonian. For small values of a deformation parameter 'θ', this yields a dynamical comparison between the two models showing that the distance between the corresponding semigroups is dominated by |θ| uniformly in time in the L 2 -operator norm.

show abstract

Résonances en limite semi-classique

Cited by 149 publications

References 0 publications

Quantum Energy-Transport and Drift-Diffusion Models

Quantum Energy-Transport and Drift-Diffusion Models

Computing the steady states for an asymptotic model of quantum transport in resonant heterostructures

Wave operators, similarity and dynamics for a class of Schrödinger operators with generic non-mixed interface conditions in 1D

Contact Info

Product

Resources

About