New scattering features in non-Hermitian space fractional quantum mechanics

Hasan, Mohammad M.; Mandal, Bhabani Prasad

doi:10.1016/j.aop.2018.07.008

Cited by 15 publications

(7 citation statements)

References 49 publications

(36 reference statements)

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“…Others notable features are invisibility [21,22,23] and reciprocity [24]. CPA and SS have also been studied in the context of non-Hermitian space fractional quantum mechanics [25]. Phenomena of SS have also been studied in the domain of quaternionic quantum mechanics [26].…”

Section: Introductionmentioning

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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Section: Introductionmentioning

confidence: 99%

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

Hasan¹,

Umar²,

Mandal³

2022

Preprint

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“…Because of this exciting realization the research in non-Hermitian systems have received a huge boost over the past two decades [37]. P T symmetric non-Hermitian systems have found numerous applications in various branches of physics and interdisciplinary ares [38][39][40][41][42][43][44][45][46][47][48][49] and some of the predictions of non-Hermitian theories are experimentally observed [50][51][52][53]. Another important aspects is that such PT symmetric non-Hermitian systems generally exhibit a phase transition ( or more appropriately a P T breaking transition ) that separates two parametric regions (i) region of the unbroken P T symmetry in which the entire spectrum is real and eigenstates of the system respects P T symmetry and (ii) a region of broken P T symmetry in which the whole spectrum (or a part of it) appears as complex conjugate pairs and eigenstates of the Hamiltonian do not respect P T symmetry [54][55][56][57][58][59][60].…”

Section: Introductionmentioning

confidence: 99%

Eigenstate entanglement entropy in $PT$ invariant non-Hermitian system

Modak,

Mandal

2021

Preprint

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Much has been learned about universal properties of the eigenstate entanglement entropy for onedimensional lattice models, which is described by a Hermitian Hamiltonian. While very less of it has been understood for non-Hermitian systems. In the present work we study a non-Hermitian, noninteracting model of fermions which is invariant under combined P T transformation. Our models show a phase transition from P T unbroken phase to broken phase as we tune the hermiticity breaking parameter. Entanglement entropy of such systems can be defined in two different ways, depending on whether we consider only right (or equivalently only left) eigenstates or a combination of both left and right eigenstates which form a complete set of bi-orthonormal eigenstates. We demonstrate that the entanglement entropy of the ground state and also of the typical excited states show some unique features in both of these phases of the system. Most strikingly, entanglement entropy obtained taking a combination of both left and right eigenstates shows an exponential divergence with system size at the transition point. While in the P T -unbroken phase, the entanglement entropy obtained from only the right (or equivalently left) eigenstates shows identical behavior as of an equivalent Hermitian system which is connected to the non-Hermitian system by a similarity transformation.

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“…Others notable features are invisibility [44,45,46] and reciprocity [47]. Recently CPA and SS have also been studied in the context of non-Hermitian fractional quantum mechanics [48].…”

Section: Introductionmentioning

confidence: 99%

Hartman effect from layered PT-symmetric system

Hasan

Mandal

2020

Eur. Phys. J. Plus

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The time taken by a wave packet to cross through a finite layered P T -symmetric system is calculated by stationary phase method. We consider the P T -symmetric system of fix spatial length L consisting of N units of the potential system '+iV ' and '−iV ' of equal width 'b' such that L = 2N b. In the limit of large 'b', the tunneling time is found to be independent of L and therefore the layered P T -symmetric system display the Hartman effect. The interesting limit of N → ∞ such that L remains finite is investigated analytically. In this limit the tunneling time matches with the time taken to cross an empty space of length L. The result of this limiting case N → ∞ also shows the consistency of phase space method of calculating the tunneling time despite the existence of controversial Hartman effect. The reason of Hartman effect is unknown to present day however the other definitions of tunneling time that indicate a delay which depends upon the length of traversing region have been effectively ruled out by recent attosecond measurements.

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New scattering features in non-Hermitian space fractional quantum mechanics

Cited by 15 publications

References 49 publications

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

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

Eigenstate entanglement entropy in $PT$ invariant non-Hermitian system

Hartman effect from layered PT-symmetric system

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