Research
#Publications
2.
Spectral and pseudo-spectral analysis of tridiagonal k-Toeplitz matrices: mathematical origins of the non-Hermitian skin effect
Habib Ammari, Silvio Barandun, Yannick De Bruijn, Ping Liu, Clemens Thalhammer
Journal of Physics A: Mathematical and Theoretical (2025)
We investigate the spectral properties of tridiagonal k-Toeplitz matrices and reveal the topological origins of the non-Hermitian skin effect, providing new insights into non-Hermitian quantum mechanics and condensed matter physics.
non-hermitian physics spectral theory topological physics
1.
Convergence of supercell and superspace methods for computing spectra of quasiperiodic operators
Bryn Davies, Clemens Thalhammer
Proceedings of the Royal Society A (2025)
We analyze the convergence properties of supercell and superspace computational methods for determining the spectral properties of quasiperiodic operators, providing rigorous mathematical foundations for numerical approaches in quasicrystal physics.
spectral theory computational methods quasicrystals
#Preprints
3.
A Real-Space Formulation of the Zak Phase via Weyl m-Functions
Habib Ammari, Clemens Thalhammer
preprint (2026)
We develop a real-space approach to computing the Zak phase using Weyl m-functions, providing new insights into the topological characterization of one-dimensional periodic systems.
zak phase weyl m-functions topological phases
2.
Uniform Hyperbolicity, Bandgaps and Edge Modes in Aperiodic Systems of Subwavelength Resonators
Habib Ammari, Clemens Thalhammer, Alexander Uhlmann
preprint (2025)
We investigate the spectral properties of aperiodic systems of subwavelength resonators, establishing conditions for uniform hyperbolicity and analyzing the emergence of bandgaps and edge modes in these complex metamaterial structures.
aperiodic systems metamaterials subwavelength resonators edge modes bandgap engineering uniform hyperbolicity
1.
Competing edge and bulk localisation in non-reciprocal disordered systems
Habib Ammari, Silvio Barandun, Clemens Thalhammer, Alexander Uhlmann
preprint (2025)
We investigate the interplay between edge and bulk localisation phenomena in non-reciprocal disordered systems, revealing competing mechanisms that determine the nature of wave propagation in these complex media.
mathematical physics disorder localisation non-reciprocal systems edge states