Work

Survival Probability in Waveguides with Delta Barriers: A Study of Tunneling and Resonances

Year: 2026

Type: article

Abstract: We study resonances and time decay in a quantum waveguide with two semitransparent barriers. The model is first analyzed as a one-dimensional Schrödinger operator with two delta interactions and then extended to a two-dimensional strip, where transverse Dirichlet modes reduce the problem, channel by channel, to the one-dimensional setting. We derive explicit scattering amplitudes and characterize resonance poles by analytic continuation. In the strong-barrier regime ρ=α−1→0+, the real parts of the resonances approach the eigenvalues of the decoupled cavity, while the imaginary parts are negative and of order α−2, so the lifetimes grow like α2. We also study the time evolution on short, intermediate, and long time scales: the survival probability is quadratic at short times, in accordance with the quantum Zeno effect; the intermediate regime is resonance-dominated and approximately exponential; and the long-time behavior is governed by the low-energy threshold and becomes algebraic. Numerical simulations complement the analysis by confirming these regimes and by showing the breakdown of exponential decay. They also provide an empirical fit for the breakdown time tbr in terms of the barrier strength α and the distance d1 between the barriers.

Source: Symmetry

DOI: 10.3390/sym18091436

Authors: Wiktor Wolak, João G. M. Silva, Sylwia Kondej, Kacper Ślipko

Institution: University of Zielona Góra

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funder: Polska Akademia Nauk