Tunneling time in space fractional quantum mechanics

Highlights: • In space fraction quantum mechanics (SFQM) Brownian paths are replaced by Levy flight paths. • We study Hartman effect (saturation of tunneling time) in SFQM. • Hartman effect is not present in SFQM. • Location of the maximum in tunneling time is obtained in the parameter space. • Hartman effect is restored in the limit SFQM to usual QM. - Abstract: We calculate the time taken by a wave packet to travel through a classically forbidden region of space in space fractional quantum mechanics. We obtain the close form expression of tunneling time from a rectangular barrier by stationary phase method. We show that tunneling time depends upon the width b of the barrier for $b\to \infty$ and therefore Hartman effect doesn't exist in space fractional quantum mechanics. Interestingly we found that the tunneling time monotonically reduces with increasing b. The tunneling time is smaller in space fractional quantum mechanics as compared to the case of standard quantum mechanics. We recover the Hartman effect of standard quantum mechanics as a special case of space fractional quantum mechanics.