Non‐Hermitian Hartman Effect

Abstract

The Hartman effect refers to the rather paradoxical result that the time spent by a quantum mechanical particle or a photon to tunnel through an opaque potential barrier becomes independent of barrier width for long barriers. Such an effect, which has been observed in different physical settings, raised a lively debate and some controversies, owing to the correct definition and interpretation of tunneling times and the apparent superluminal transmission. A rather open question is whether (and under which conditions) the Hartman effect persists for inelastic scattering, that is, when the potential becomes non-Hermitian and the scattering matrix is not unitary. Here, tunneling through a heterojunction barrier in the tight-binding picture is considered, where the barrier consists of a generally non-Hermitian finite-sized lattice attached to two semi-infinite nearest-neighbor Hermitian lattice leads. A simple and general condition is derived for the persistence of the Hartman effect in non-Hermitian barriers, showing that it can be found rather generally when non-Hermiticity arises from nonreciprocal couplings, that is, when the barrier displays the non-Hermitian skin effect, without any special symmetry in the system.

Effect of the Rashba interaction on the tunneling time and Hartman effect in an 8-Pmmn borophene superlattice

“…Indeed, Hartman found that, for opaque barriers the group delay time decays exponentially by increasing the width of barriers and for sufficiently large width of the barrier reaches a constant value [38]. In recent decades, tunneling time and Hartman effect have been considered widely both theoretically and experimentally [39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55]. The Hartman effect in a monolayer graphene-based single and double potential barriers was described by Wu et al [40].…”

Tunneling from general Smith–Volterra–Cantor potential

“…Driven by its theoretical significance and potential practical applications, extensive investigations have explored how matter waves propagate through various potential distributions [7,8]. Such efforts span a diverse array of quantum mechanical domains, including non-Hermitian quantum mechanics (NHQM) [9][10][11][12], space-fractional quantum mechanics (SFQM) [13][14][15][16][17][18], and quaternionic quantum mechanics (QQM) [19][20][21][22][23][24][25]. With an array of contributions over the past century, quantum tunneling and the associated analytical calculations of scattering coefficients continue to be a focal point of quantum research [1][2][3][4][5][6][7][8][26][27][28][29][30].…”

Superluminality in parity-time symmetric Bragg gratings

“…We believe that addressing these open questions and proposing potential mathematical approaches should consider non-Hermitian quantum theory[40,[55][56][57]. Literature on non-Hermitian Hartman effects[58,59…”