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pro vyhledávání: '"Drouot, Alexis"'
We show that if a topological insulator is truncated along a curve that separates the plane in two sufficiently large regions, then the edge system admits absolutely continuous spectrum. Our approach combines a recent version of the bulk-edge corresp
Externí odkaz:
http://arxiv.org/abs/2410.02157
Autor:
Drouot, Alexis, Lyman, Curtiss
In this paper, we develop a systematic framework to study the dispersion surfaces of Schr\"odinger operators $ -\Delta + V$, where the potential $V \in C^\infty(\mathbb{R}^n,\mathbb{R})$ is periodic with respect to a lattice $\Lambda \subset \mathbb{
Externí odkaz:
http://arxiv.org/abs/2410.02092
Autor:
Drouot, Alexis, Zhu, Xiaowen
The bulk-edge correspondence is a condensed matter theorem that relates the conductance of a Hall insulator in a half-plane to that of its (straight) boundary. In this work, we extend this result to domains with curved boundaries. Under mild geometri
Externí odkaz:
http://arxiv.org/abs/2408.07950
Autor:
Drouot, Alexis, Zhu, Xiaowen
We prove that that if the boundary of a topological insulator divides the plane in two regions containing arbitrarily large balls, then it acts as a conductor. Conversely, we show that topological insulators that fit within strips do not need to admi
Externí odkaz:
http://arxiv.org/abs/2311.00918
Autor:
Drouot, Alexis
We study solutions of $2 \times 2$ systems $(h D_t + \mathcal{D}) \Psi_t = 0$ on $\mathbb{R}^2$ in the semiclassical regime $h \rightarrow 0$. Our Dirac operator $\mathcal{D}$ is a standard model for interfaces between topological insulators: it repr
Externí odkaz:
http://arxiv.org/abs/2206.08238
We study the propagation of wavepackets along curved interfaces between topological, magnetic materials. Our Hamiltonian is a massive Dirac operator with a magnetic potential. We construct semiclassical wavepackets propagating along the curved interf
Externí odkaz:
http://arxiv.org/abs/2201.07133
Autor:
Bal, Guillaume, Becker, Simon, Drouot, Alexis, Kammerer, Clotilde Fermanian, Lu, Jianfeng, Watson, Alexander
We study the propagation of wavepackets along weakly curved interfaces between topologically distinct media. Our Hamiltonian is an adiabatic modulation of Dirac operators omnipresent in the topological insulators literature. Using explicit formulas f
Externí odkaz:
http://arxiv.org/abs/2106.00729
Autor:
Drouot, Alexis
We show that generically, the degeneracies of a family of Hermitian matrices depending on three parameters have a conical structure. Our result applies to the study of topological phases of matter. It implies that adiabatic deformations of two-dimens
Externí odkaz:
http://arxiv.org/abs/2004.07068
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Autor:
Drouot, Alexis
The bulk-edge correspondence predicts that interfaces between topological insulators support robust currents. We prove this principle for PDEs that are periodic away from an interface. Our approach relies on semiclassical methods. It suggests novel p
Externí odkaz:
http://arxiv.org/abs/1909.10474