# 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/en/arxiv-id/quant-ph--0011032v1/

## Key points

- Villavicencio and Romo investigate the time evolution of the buildup process inside a double-barrier system for off-resonance incidence energies
- They consider the analytic solution of the time-dependent Schrödinger equation with cutoff plane wave initial conditions to study this phenomenon
- 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
- The buildup of off-resonant probability density is characterized by an oscillatory pattern modulated by the resonant case, which governs the duration of the transient regime
- Off-resonant and resonant tunneling are two correlated processes whose transient regime is characterized by the same transient time constant of two lifetimes
- This study provides valuable insights into how double-barrier systems behave under different conditions, shedding light on important phenomena such as tunneling and quantum mechanics
- The authors' findings could have implications for a range of fields including materials science, electronics, and quantum computing.

## Summary

In their paper "Dynamical analysis of the Buildup Process near Resonance," Jorge Villavicencio and Roberto Romo investigate the time evolution of the buildup process inside a double-barrier system for off-resonance incidence energies. They consider the analytic solution of the time-dependent Schrödinger equation with cutoff plane wave initial conditions to study this phenomenon. The authors find 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. The authors also observe that the buildup of off-resonant probability density is characterized by an oscillatory pattern modulated by the resonant case, which governs the duration of the transient regime. This finding suggests that off-resonant and resonant tunneling are two correlated processes whose transient regime is characterized by the same transient time constant of two lifetimes. Overall, this study provides valuable insights into how double-barrier systems behave under different conditions, shedding light on important phenomena such as tunneling and quantum mechanics. The authors' findings could have implications for a range of fields including materials science, electronics, and quantum computing.