Research
#Publications
1.
A Real-Space Formulation of the Zak Phase via Weyl m-Functions
Habib Ammari, Clemens Thalhammer
Journal of Physics A: Mathematical and Theoretical (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.
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
3.
Competing Edge and Bulk Localization in Nonreciprocal Disordered Systems
Habib Ammari, Silvio Barandun, Clemens Thalhammer, Alexander Uhlmann
Multiscale Modeling & Simulation (2026)
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
4.
Spectra and Pseudo-spectra of Tridiagonal k-Toeplitz Matrices and the Topological Origin 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
#Preprints
1.
High-frequency spectral asymptotics and homogenization for quasiperiodic operators
Elena Cherkaev, Bryn Davies, Sébastien Guenneau, Clemens Thalhammer, Niklas Wellander
preprint (2026)
We study the spectral asymptotics of elliptic operators with quasiperiodic coefficients, establishing homogenization results in the low-frequency regime and characterising bulk and boundary layer spectra in the high-frequency regime.
homogenization spectral theory quasiperiodic operators two-scale convergence
2.
Perturbative Approach to Nonlinear Capacitance Matrix Formulations
Habib Ammari, Clemens Thalhammer
preprint (2026)
We develop a perturbative theory for nonlinear Helmholtz systems on high-contrast inclusions, establishing a rigorous two-way correspondence between continuous subwavelength solitons and a finite discrete nonlinear capacitance system.
nonlinear waves subwavelength resonators capacitance matrix solitons
3.
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 dynamical systems