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MON: Monday Contributed Sessions

MON 23: Poster Session: Fundamental Aspects and Model Systems

MON 23.55: Poster

Montag, 8. September 2025, 18:30–20:30, ZHG Foyer 1. OG

Geometrically Constrained Quantum Dynamics: A Numerical Study on a Comb — •Ognen Kapetanoski and Irina Petreska — Ss. Cyril and Methodius University in Skopje, Faculty of Natural Sciences and Mathematics, Institute of Physics, Skopje, Macedonia

We investigate the quantum dynamics of a particle constrained by a two-dimensional comb-like geometry using the time-dependent Schrödinger equation. This structure consists of a backbone and branching fingers, which models transport phenomena in heterogeneous and anisotropic media. Geometric constraints are implemented by implementing a Dirac delta function into the kinetic energy operator, approximated by a Gaussian. Spatial discretization is done using a finite-difference scheme and time evolution is computed with a fourth-order Runge-Kutta method. We compare Gaussian and comb-like wave functions to study how initial conditions affect the evolution of the probability density. The comb-like initial state shows strong localization near the backbone in early stages of time evolution. At later times, this localization disappears and the resulting probability distribution becomes similar to that of the Gaussian case. Numerical results are compared with analytical solutions, showing excellent agreement for short to intermediate time intervals. This method allows quantum transport modeling in finite domains and complex initial conditions where analytical solutions do not exist.
[1] O. Kapetanoski and I. Petreska, Phys. Scr. 100, 025254 (2025).

Keywords: Schrödinger equation; comb model; numerical methods; quantum dynamics; geometric constraints