Universität zu Köln

Braukhoff, Marcel and Juengel, Ansgar (2018). Energy-transport systems for optical lattices: Derivation, analysis, simulation. Math. Models Meth. Appl. Sci., 28 (3). S. 579 - 615. SINGAPORE: WORLD SCIENTIFIC PUBL CO PTE LTD. ISSN 1793-6314

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Abstract

Energy-transport equations for the transport of fermions in optical lattices are formally derived from a Boltzmann transport equation with a periodic lattice potential in the diffusive limit. The limit model possesses a formal gradient-flow structure like in the case of the energy-transport equations for semiconductors. At the zeroth-order high-temperature limit, the energy-transport equations reduce to the whole-space logarithmic diffusion equation which has some unphysical properties. Therefore, the first-order expansion is derived and analyzed. The existence of weak solutions to the time-discretized system for the particle and energy densities with periodic boundary conditions is proved. The difficulties are the nonstandard degeneracy and the quadratic gradient term. The main tool of the proof is a result on the strong convergence of the gradients of the approximate solutions. Numerical simulations in one-space dimension show that the particle density converges to a constant steady state if the initial energy density is sufficiently large, otherwise the particle density converges to a nonconstant steady state.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Braukhoff, Marcel UNSPECIFIED UNSPECIFIED UNSPECIFIED Juengel, Ansgar UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-195427
DOI:	10.1142/S021820251850015X
Journal or Publication Title:	Math. Models Meth. Appl. Sci.
Volume:	28
Number:	3
Page Range:	S. 579 - 615
Date:	2018
Publisher:	WORLD SCIENTIFIC PUBL CO PTE LTD
Place of Publication:	SINGAPORE
ISSN:	1793-6314
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language DEGENERATE COERCIVITY; PARABOLIC EQUATIONS; EXISTENCE ANALYSIS; MODEL; THERMODYNAMICS Multiple languages Mathematics, Applied Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/19542