2009/05/25 by J. Martorell, D. W. L. Sprung, W. van Dijk +1
Computer Science · Mathematics · Physics and Astronomy · #Amplitude #Condensed matter physics #Constant (computer programming) #Context (archaeology) #Coupling (piping) #Coupling constant #Exponential decay #Exponential function #Materials science #Mathematical analysis #Mathematics #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Phase (matter) #Physics #Quantum chaos and dynamical systems #Quantum electrodynamics #Quantum mechanics #State (computer science) #Time constant #quant-ph
paper · pdf · doi:10.1103/physreva.79.062104
12 pages, 10 figures, accepted by Phys. Rev. A
arxiv created 2009/05/25 · openalex publication_date 2009/06/08 · arxiv updated 2015/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Initial switching refers to the way in which the decay of an initially confined state begins, as the barrier isolating it from the exterior is relaxed. We study these effects in the context of Longhi's version of the Fano-Anderson model. Most authors assume the sudden approximation where the coupling is turned on instantaneously. We consider a finite rise time T both numerically and analytically. When the coupling is ramped up linearly over a switching time T, we show that the asymptotic survival amplitude acquires a phase T and is modulated by a factor (sin T)/T. Several other results relating to the solution of the model are obtained. All site amplitudes have the same decay constant during the exponential decay regime. In the asymptotic regime, the amplitude and phase of decay oscillations depend on the initial-switching profile, but the period does not.