Bereiche | Tage | Auswahl | Suche | Aktualisierungen | Downloads | Hilfe
AKPIK: Arbeitskreis Physik, moderne Informationstechnologie und Künstliche Intelligenz
AKPIK 5: Poster
AKPIK 5.12: Poster
Donnerstag, 12. März 2026, 15:00–16:30, P5
Non-unitary time evolution via the Chebyshev expansion method — •Aron Hollo1,2, Daniel Varjas3,4,5, Cosma Fulga3,4, Laszlo Oroszlany1,2, and Viktor Konye3,4,6 — 1Department of Physics of Complex Systems, Eötvös Loránd University, Budapest, Hungary — 2Wigner Research Centre for Physics, Budapest, Hungary — 3Institute for Theoretical Solid State Physics, IFW Dresden, Dresden, Germany — 4Würzburg-Dresden Cluster of Excellence ct.qmat, Germany — 5Department of Theoretical Physics, Budapest University of Technology and Economics, Budapest, Hungary — 6Institute for Theoretical Physics Amsterdam, University of Amsterdam, Amsterdam, The Netherlands
The Chebyshev expansion method is a highly efficient technique for computing the time evolution of quantum states in Hermitian systems with bounded spectra. In the physics literature, its applicability is often assumed to be restricted to real spectra within the interval [-1,1], limiting its use for non-Hermitian dynamics.
Here, we show that this restriction is not fundamental. The Chebyshev expansion of the exponential function remains mathematically valid over the entire complex plane and can therefore be applied to arbitrary non-Hermitian matrices. The apparent breakdown of the method outside the conventional spectral bounds is traced back to numerical rounding errors rather than to a failure of the expansion. By deriving an analytic upper bound for the accumulated rounding error, we obtain a practical criterion for selecting safe time steps based on the spectral radius of the Hamiltonian.
Keywords: non-Hermitian dynamics; Chebyshev expansion; time evolution; numerical methods; Hatano–Nelson model