Role of PT-symmetry in understanding Hartman effect

Hasan, Mohammad M.; Singh, Vibhav Narayan; Mandal, Bhabani Prasad

doi:10.1140/epjp/s13360-020-00664-6

Cited by 9 publications

(12 citation statements)

References 45 publications

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“…This condition can be satisfied when the intra‐ and inter‐dimer hopping amplitudes t 1, 2 , ρ 1, 2 are real and the on‐site potential energies are either real or satisfy the condition

\Delta _{\rm A}=\Delta _{\rm B}^*

, which basically corresponds PT symmetry in the system. Hence, like in continuous models of the NH Hartman effect, [ 49,50 ] PT symmetry ensures the independence of the tunneling phase time on barrier width for long barriers. However, the NH Hartman effect can be observed even without any complex on‐site potential, for example by assuming

\Delta _{\rm A}=\Delta _{\rm B}=0

, as a result of nonreciprocal hopping in the lattice.…”

Section: Illustrative Examples and Numerical Simulationsmentioning

confidence: 99%

Non‐Hermitian Hartman Effect

Longhi

2022

Annalen der Physik

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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.

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“…This condition can be satisfied when the intra‐ and inter‐dimer hopping amplitudes t 1, 2 , ρ 1, 2 are real and the on‐site potential energies are either real or satisfy the condition

\Delta _{\rm A}=\Delta _{\rm B}^*

\Delta _{\rm A}=\Delta _{\rm B}=0

, as a result of nonreciprocal hopping in the lattice.…”

Section: Illustrative Examples and Numerical Simulationsmentioning

confidence: 99%

Non‐Hermitian Hartman Effect

Longhi

2022

Annalen der Physik

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“…From the knowledge of transfer matrix of a 'unit cell' potential, one can find the transfer matrix for the corresponding locally periodic potential consisting N such cells [28]. Using the approach outlined in [28,29], we obtain the following transfer matrix for the layered P T -symmetric system,…”

Section: Transfer Matrixmentioning

confidence: 99%

Locally finite free space as limiting case of PT-symmetric medium

Hasan¹,

Umar²,

Mandal³

2022

Preprint

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We explicitly prove that the transfer matrix of a finite layered P T -symmetric system of fix length L consisting of N units of the potential system '+iV ' and '−iV ' of equal thickness becomes a unit matrix in the limit N → ∞. This result is true for waves of arbitrary wave vector k. This shows that in this limit, the transmission coefficient is always unity while the reflection amplitude is zero for all waves traversing this length L. Therefore, a free space of finite length L can be represented as a P T -symmetric medium.

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“…This condition can be satisfied when the intra-and inter-dimer hopping amplitudes t 1,2 , ρ 1,2 are real and the on-site potential energies are either real or satisfy the condition ∆ A = ∆ * B , which basically corresponds PT symmetry in the system. Hence, like in continuous models of the NH Hartman effect [49,50], PT symmetry ensures the inde-pendence of the tunneling phase time on barrier width for long barriers. However, the NH Hartman effect can be observed even without any complex on-site potential, for example by assuming ∆ A = ∆ B = 0, as a result of nonreciprocal hopping in the lattice.…”

Section: The Non-hermitian Rice-mele Modelmentioning

confidence: 99%

“…For recent works discussing the various controversies and interpretations of the Hartman effect see, for example, the review article [15] and the more recent works [17,22,35,43]. Most of previous results on the Hartman effect, with the exception of few works [44][45][46][47][48][49][50], concern with non-dissipative (Hermitian) systems, where the dynamics conserves the norm of the wave function and the scattering matrix is unitary. However, in dissipative (open) quantum systems as well as in a variety of classical platforms such as photonic systems, mechanical metamaterials and topolectrical systems, scattering phenomena are described by effective non-Hermitian (NH) Hamiltonians, displaying non-unitary dynamics and possible singularities in the spectrum (see e.g.…”

Section: Introductionmentioning

confidence: 99%

“…In particular, the use of synthetic lattices in frequency domain [81]can realize rather arbitrary single-band NH Hamiltonians with tailored non-reciprocal hopping displaying arbitrary topological winding numbers. The impact of inelastic scattering on the tunneling times and Hartman effect has been investigated in few models [44,45,[47][48][49][50], where non-Hermiticity was introduced via a complex potential term in the Hamiltonian. A general result is that, for a sufficiently strong absorption, the Hartman effect is washed out and the tunneling time turns out to depend on barrier width [44,45,47]; such a result is in agreement with some early observations on photon tunneling in microwave experiments [45].…”

Section: Introductionmentioning

confidence: 99%

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Non-Hermitian Hartman effect

Longhi¹

2022

Preprint

View full text Add to dashboard Cite

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, i.e. when the potential becomes non-Hermitian and the scattering matrix is not unitary. Here we consider tunneling through a heterojunction barrier in the tight-binding picture, where the barrier consists of a generally non-Hermitian finite-sized lattice attached to two semi-infinite nearestneighbor Hermitian lattice leads. We derive a simple and general condition for the persistence of the Hartman effect in non-Hermitian barriers, showing that it can be found rather generally when non-Hermiticity arises from non-reciprocal couplings, i.e. when the barrier displays the non-Hermitian skin effect, without any special symmetry in the system.

show abstract

Role of PT-symmetry in understanding Hartman effect

Cited by 9 publications

References 45 publications

Non‐Hermitian Hartman Effect

Non‐Hermitian Hartman Effect

Locally finite free space as limiting case of PT-symmetric medium

Non-Hermitian Hartman effect

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