By Grégoire Allaire, Anton Arnold, Pierre Degond, Thomas Y. Hou, Ben Abdallah Naoufel, Giovanni Frosali
ISBN-10: 3540795731
ISBN-13: 9783540795735
ISBN-10: 354079574X
ISBN-13: 9783540795742
The CIME summer season college held in Cetraro, Italy, in 2006 addressed researchers drawn to the mathematical learn of quantum shipping versions.
In this quantity, as a result of the above pointed out summer time college, 4 best experts current varied elements of quantum shipping modelling. Allaire introduces the periodic homogenization concept, with a specific emphasis on functions to the Schrödinger equation. Arnold makes a speciality of a number of quantum evolution equations which are used for quantum semiconductor gadget simulations. Degond offers quantum hydrodynamic and diffusion versions ranging from the entropy minimization precept. Hou presents the state of the art survey of the multiscale research, modelling and simulation of shipping phenomena.
The quantity comprises actual expositions of the most facets of quantum delivery modelling and offers an outstanding foundation for researchers during this field.
Read Online or Download Quantum Transport: Modelling, Analysis and Asymptotics — Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy September 11–16, 2006 PDF
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Extra info for Quantum Transport: Modelling, Analysis and Asymptotics — Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy September 11–16, 2006
Example text
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6. By changing the main assumption on the Bloch spectrum it is possible to obtain a fourth order homogenized equation instead of the usual Schr¨ odinger equation. Specifically, if we consider i 2 ∂u − div A x ∇u + −2 x x (79) (i) λn (θn ) is a simple eigenvalue, (ii) ∇θ λn (θn ) = 0, ∇θ ∇θ λn (θn ) = 0, ∇θ ∇θ ∇θ λn (θn ) = 0, (80) c + 2 u = 0, ∂t d x, and if we make the following assumption, instead of (62), then, for the same type of initial data (66), we can prove that the solution of (79) can be written as u (t, x) = ei λn (θ n )t 4 e2iπ θ n ·x x ψn ( , θn )v(t, x) + r (t, x), (81) + 2 N + 2 N where r converges strongly to 0 in L∞ loc R ; L (R ) and v ∈ C R ; L (R ) is the solution of the fourth-order homogenized problem 30 G.
Quantum Transport: Modelling, Analysis and Asymptotics — Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy September 11–16, 2006 by Grégoire Allaire, Anton Arnold, Pierre Degond, Thomas Y. Hou, Ben Abdallah Naoufel, Giovanni Frosali
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