Transmission through locally periodic potentials in space-fractional quantum mechanics

Tare, Jeffrey D.; Esguerra, Jose Perico

doi:10.1016/j.physa.2014.03.084

Cited by 25 publications

(19 citation statements)

References 16 publications

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“…Based on this outstanding idea, intense investigations have been carried out in different fields of studies, for example, energy band structure for the periodic potential, position‐dependent mass fractional Schrödinger equation, fractional quantum oscillator, nuclear dynamics of the H 2 + molecular ion, propagation dynamics of a light beam, spatial soliton propagation, solitons in the fractional Schrödinger equation with parity‐time‐symmetric lattice potential, gap solitons, Rabi oscillations in a fractional Schrödinger equation, self‐focusing, and wave collapse, elliptic solitons, light propagation in honeycomb lattice, and so on. These studies are based on the different methods such as domain decomposition method, energy conservative difference scheme, conservative finite element method, fractional Fan subequation method, split‐step Fourier spectral method, transfer‐matrix method, and so on.…”

Section: Introductionmentioning

confidence: 99%

Quantum information entropies of multiple quantum well systems in fractional Schrödinger equations

Solaimani

Dong

2019

Int J of Quantum Chemistry

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In this work, we study the position and momentum information entropies of multiple quantum well systems in fractional Schrödinger equations, which, to the best of our knowledge, have not so far been studied. Through a confining potential, their shape and number of wells (NOW) can be controlled by using a few tuning parameters; we present some interesting quantum effects that only appear in the fractional Schrödinger equation systems. One of the parameters denoted by the Ld can affect the position and momentum probability densities if the system is fractional (1 < α < 2). We find that the position (momentum) probability density tends to be more severely localized (delocalized) in more fractional systems (ie, in smaller values of α). Affecting the Ld on the position and momentum probability densities is a quantum effect that only appears in the fractional Schrödinger equations. Finally, we show that the Beckner Bialynicki‐Birula‐Mycieslki (BBM) inequality in the fractional Schrödinger equation is still satisfied by changing the confining potential amplitude Vconf, the NOW, the fractional parameter α, and the confining potential parameter Ld.

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Section: Introductionmentioning

confidence: 99%

Quantum information entropies of multiple quantum well systems in fractional Schrödinger equations

Solaimani

Dong

2019

Int J of Quantum Chemistry

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“…For a rectangular barrier the expression of reflection and transmission coefficients of a particle are calculated by Guo et al [5]. The formulation developed by Griffith et al [24] for the scattering coefficients of a periodic system are used in [25] to study the transmission from Dirac comb and periodic rectangular barrier in space fractional quantum mechanics.…”

Section: Introductionmentioning

confidence: 99%

Tunneling time in space fractional quantum mechanics

Hasan

Mandal

2018

Physics Letters A

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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.Comment: 13 pages, 2 Figures, Published online in Physics Letter

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“…where height of the potential ζ is a complex number. Following [52] the transfer matrix M = m 11 m 12 m 21 m 22 (8) for this potential in space fractional quantum mechanics has following elements: The diagonal elements,…”

Section: Scattering Features Of Complex Delta Potential In Sfqmmentioning

confidence: 99%

“…The tunneling problem of SFQM have been solved for various potential configuration by many authors [46,51,52]. However to the best of our knowledge the study of SFQM has not been extended for non-Hermitian potential which accounts for gain and loss configuration.…”

Section: Introductionmentioning

confidence: 99%

New scattering features in non-Hermitian space fractional quantum mechanics

Hasan

Mandal

2018

Annals of Physics

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The spectral singularity (SS) and coherent perfect absorption (CPA) have been extensively studied over the last one and half decade for different non-Hermitian potentials in non-Hermitian standard quantum mechanics (SQM) governed by Schrodinger equation. In the present work we explore these scattering features in the domain of non-Hermitian space fractional quantum mechanics (SFQM) governed by fractional Schrodinger equation which is characterized by Levy index α (1 < α ≤ 2). We observe that non-Hermitian SFQM systems have more flexibility for SS and CPA and display some new features of scattering. For the delta potential V (x) = −iρδ(x − x 0 ), ρ > 0, the SS energy, E ss , is blue or red shifted with decreasing α depending the strength of the potential. For complex rectangular barrier in non-Hermitian SQM, it is known that the reflection and transmission amplitudes are oscillatory near the spectral singular point. It is found that these oscillations eventually develop SS in non-Hermitian SFQM. The similar features is also reported for the case of CPA phenomena from complex rectangular barrier in non-Hermitian SFQM. These observations suggest a deeper relation between scattering features of non-Hermitian SQM and non-Hermitian SFQM.

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Transmission through locally periodic potentials in space-fractional quantum mechanics

Cited by 25 publications

References 16 publications

Quantum information entropies of multiple quantum well systems in fractional Schrödinger equations

Quantum information entropies of multiple quantum well systems in fractional Schrödinger equations

Tunneling time in space fractional quantum mechanics

New scattering features in non-Hermitian space fractional quantum mechanics

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