# Tunneling time from locally periodic potential in space fractional quantum mechanics

## TL;DR

This paper derives an explicit formula for tunneling time in space fractional quantum mechanics through locally periodic potentials, revealing that tunneling time decreases with barrier width and number, unlike in standard quantum mechanics.

## Contribution

It introduces a closed-form expression for tunneling time in SFQM for locally periodic potentials and demonstrates the absence of the Hartman effect in this framework.

## Key findings

- Tunneling time depends on barrier width and separation in SFQM.
- Tunneling time is smaller for large barriers in SFQM compared to single barriers.
- Increasing the number of barriers reduces tunneling time in SFQM.

## Abstract

We calculate the time taken by a wave packet to travel through a classically forbidden locally periodic rectangular potential in space fractional quantum mechanics (SFQM). We obtain the close form expression of tunneling time from such a potential by stationary phase method. We show that tunneling time depends upon the width $b$ of the single barrier and separation $L$ between the barriers in the limit $b \to \infty$ and therefore generalized Hartman effect doesn't exist in SFQM. We observe that in SFQM, the tunneling time for large $b$ in the case of locally periodic potential is smaller than the tunneling from a single barrier of the same width $b$. It is further shown that with the increase in barrier numbers, the tunneling time reduces in SFQM in the limit of large $b$.