Zobrazeno 1 - 10
of 128
pro vyhledávání: '"Gontier, David"'
Autor:
Gontier, David
Publikováno v:
Comptes Rendus. Mathématique, Vol 359, Iss 8, Pp 949-958 (2021)
We consider a semi-periodic two-dimensional Schrödinger operator which is cut at an angle. When the cut is commensurate with the periodic lattice, the spectrum of the operator has the band-gap Bloch structure. We prove that in the incommensurable ca
Externí odkaz:
https://doaj.org/article/3c6e798698a34a829be15f399967e50f
We study one- and two-dimensional periodic tight-binding models under the presence of a potential that grows to infinity in one direction, hence preventing the particles to escape in this direction (the soft wall). We prove that a spectral flow appea
Externí odkaz:
http://arxiv.org/abs/2403.02462
We review thermodynamic limits and scaling limits of electronic structure models for condensed matter. We discuss several mathematical ways to implement these limits in three models of increasing chemical complexity and mathematical difficulty: (1) T
Externí odkaz:
http://arxiv.org/abs/2309.05118
In this paper we consider stationary states of the SSH model for infinite polyacetylene chains that are homoclinic or heteroclinic connections between two-periodic dimerized states. We prove that such connections converge exponentially fast to the co
Externí odkaz:
http://arxiv.org/abs/2308.00145
This paper studies DFT models for homogeneous 2D materials in 3D space, under a constant perpendicular magnetic field. We show how to reduce the three--dimensional energy functional to a one--dimensional one, similarly as in our previous work. This i
Externí odkaz:
http://arxiv.org/abs/2212.00448
Publikováno v:
Annales Henri Poincar\'e 24 (2023), no. 11, pp. 3945--3966
We consider the Peierls model for closed polyactetylene chains with an even number of carbon atoms as well as infinite chains, in the presence of temperature. We prove the existence of a critical temperature below which the chain is dimerized, and ab
Externí odkaz:
http://arxiv.org/abs/2211.09588
We estimate the lowest eigenvalue in the gap of the essential spectrum of a Dirac operator with mass in terms of a Lebesgue norm of the potential. Such a bound is the counterpart for Dirac operators of the Keller estimates for the Schr\"odinger opera
Externí odkaz:
http://arxiv.org/abs/2210.03091
Publikováno v:
Phys. Rev. B 107, 155403, published 5 April 2023
We provide a formal derivation of a reduced model for twisted bilayer graphene (TBG) from Density Functional Theory. Our derivation is based on a variational approximation of the TBG Kohn-Sham Hamiltonian and asymptotic limit techniques. In contrast
Externí odkaz:
http://arxiv.org/abs/2206.05685
Publikováno v:
J. Math. Phys. 63, 041902 (2022)
We review Kitaev's celebrated "periodic table" for topological phases of condensed matter, which identifies ground states (Fermi projections) of gapped periodic quantum systems up to continuous deformations. We study families of projections which dep
Externí odkaz:
http://arxiv.org/abs/2201.01576
We consider the homogenization at second-order in $\varepsilon$ of $\mathbb{L}$-periodic Schr\"odinger operators with rapidly oscillating potentials of the form $H^\varepsilon =-\Delta + \varepsilon^{-1} v(x,\varepsilon^{-1}x ) + W(x)$ on $L^2(\mathb
Externí odkaz:
http://arxiv.org/abs/2112.12008