# Dynamical analysis of the buildup process near resonance

**Authors:** Jorge Villavicencio, Roberto Romo  
**arXiv:** [quant-ph/0011032](https://arxiv.org/abs/quant-ph/0011032)  
**Date:** 2000-11-09  
**Summary page:** https://www.summarizepaper.com/fr/arxiv-id/quant-ph--0011032v1/

## Abstract

The time evolution of the buildup process inside a double-barrier system for off-resonance incidence energies is studied by considering the analytic solution of the time dependent Schr\"{o}dinger equation with cutoff plane wave initial conditions. We show that the buildup process exhibits invariances under arbitrary changes on the system parameters, which can be successfully described by a simple and easy-to-use one-level formula. We find that the buildup of the off-resonant probability density is characterized by an oscillatory pattern modulated by the resonant case which governs the duration of the transient regime. This is evidence that off-resonant and resonant tunneling are two correlated processes, whose transient regime is characterized by the same transient time constant of two lifetimes.