Quantum resonances and time decay for a double-barrier model

TL;DR

This paper analyzes the time decay and quantum resonances in a one-dimensional double-barrier quantum system modeled by two repulsive Dirac deltas, providing explicit expressions for the dominant terms of the system's evolution.

Contribution

It offers an explicit analytical description of quantum resonances and time decay in a simplified double-barrier model using the theory of quantum resonances.

Findings

Explicit expression for dominant terms of quantum evolution

Analysis of quantum resonances in a double-barrier system

Insights into time decay behavior of the model

Abstract

Here we consider the time evolution of a one-dimensional quantum system with a double barrier given by a couple of two repulsive Dirac's deltas. In such a "pedagogical" model we give, by means of the theory of quantum resonances, the explicit expression of the dominant terms of $<\psi, e^{-it H} \phi >$, where $H$ is the double-barrier Hamiltonian operator and where $\psi$ and $\phi$ are two test functions.