Information entropy and level-spacing distribution based signatures of quantum chaos in electron doped 2D single carrier quantum dots

Hazra, Ram Kuntal; Ghosh, Manas; Bhattacharyya, S. P.

doi:10.1016/j.cplett.2008.05.095

Cited by 12 publications

(8 citation statements)

References 15 publications

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“…During the last few decades, the Shannon entropies have been analytically calculated for low-lying states of some quantum systems with potentials such as the Morse potential, [2,3] harmonic oscillator, [4,5] the Pöschl-Teller potential, [2,6] modified Yukawa potential, [7] and the Rosen-Morse potential. [8] On the other hand, the Shannon entropies for other complicated quantum systems such as the position-dependent mass Schrödinger equation with null potential, [9] quantum dots, [10] double-well potential, [11] finite well, [12] and infinite circular well [13] have also been investigated. Relevant studies about this topic were also conducted in Refs.…”

Section: Introductionmentioning

confidence: 99%

“…And we also have studied the miniband formation scenario in GaN/AlN constant total effective length multiple quantum dots. [29] It should be recognized that the above-mentioned studies of the Shannon entropy focus on the soluble quantum systems, [2][3][4][5][6][7][8][9][10][11][12][13] which means that the solutions of those quantum systems are analytical and consequently the wave function in momentum space can be calculated by the Fourier transform. In the present work, we study the quantum information entropies for rectangular multiple quantum well systems with a constant total length, in which the solution cannot be obtained analytically.…”

Section: Introductionmentioning

confidence: 99%

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Shannon information entropies for rectangular multiple quantum well systems with constant total lengths*

2018

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We first study the Shannon information entropies of constant total length multiple quantum well systems and then explore the effects of the number of wells and confining potential depth on position and momentum information entropy density as well as the corresponding Shannon entropy. We find that for small full width at half maximum (FWHM) of the position entropy density, the FWHM of the momentum entropy density is large and vice versa. By increasing the confined potential depth, the FWHM of the position entropy density decreases while the FWHM of the momentum entropy density increases. By increasing the potential depth, the frequency of the position entropy density oscillation within the quantum barrier decreases while that of the position entropy density oscillation within the quantum well increases. By increasing the number of wells, the frequency of the position entropy density oscillation decreases inside the barriers while it increases inside the quantum well. As an example, we might localize the ground state as well as the position entropy densities of the 1st, 2nd, and 6th excited states for a four-well quantum system. Also, we verify the Bialynicki–Birula–Mycieslki (BBM) inequality.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Shannon information entropies for rectangular multiple quantum well systems with constant total lengths*

2018

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“…Such Gaussian potentials can be assumed to simulate nanocrystals fabricated by means of colloidal chemical synthesis [36][37][38]. It needs to be mentioned here that in addition to the Gaussian type of potential to represent the impurity, there are also exponential types of potential for the same purpose [39,40].…”

Section: Methodsmentioning

confidence: 99%

Impurity strength and impurity domain modulated frequency‐dependent linear and second non‐linear response properties of doped quantum dots

Datta¹,

Ghosh

2011

Physica Status Solidi (b)

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We explore the pattern of frequency-dependent linear and second non-linear optical responses of repulsive impurity doped quantum dots harmonically confined in two dimensions. The dopant impurity potential chosen assumes a Gaussian form and it is doped into an on-center location. The quantum dot is subject to a periodically oscillating external electric field. For some fixed values of transverse magnetic field strength (v c ) and harmonic confinement potential (v 0 ), the influence of impurity strength (V 0 ) and impurity domain (j) on the diagonal components of the frequency-dependent linear (a xx and a yy ) and second non-linear (g xxxx and g yyyy ) responses of the dot are computed through a linear variational route. The investigations reveal that the optical responses undergo enhancement with increase in both V 0 and j values. However, in the limitingly small dopant strength regime one observes a drop in the optical responses with increase in V 0 . A time-average rate of energy transfer to the system is often invoked to support the findings.

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“…Quantum information entropy has been studied widely since Shannon proposed the classical concept in 1948 [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 ]. This is because the Shannon entropy as a measure of uncertainty is a generalization to the traditional Heisenberg relation.…”

Section: Introductionmentioning

confidence: 99%

Quantum Information Entropy of Hyperbolic Potentials in Fractional Schrödinger Equation

Santana-Carrillo

González-Flores

Magaña-Espinal

et al. 2022

Entropy

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In this work we have studied the Shannon information entropy for two hyperbolic single-well potentials in the fractional Schrödinger equation (the fractional derivative number (0<n≤2) by calculating position and momentum entropy. We find that the wave function will move towards the origin as the fractional derivative number n decreases and the position entropy density becomes more severely localized in more fractional system, i.e., for smaller values of n, but the momentum probability density becomes more delocalized. And then we study the Beckner Bialynicki-Birula–Mycieslki (BBM) inequality and notice that the Shannon entropies still satisfy this inequality for different depth u even though this inequality decreases (or increases) gradually as the depth u of the hyperbolic potential U1 (or U2) increases. Finally, we also carry out the Fisher entropy and observe that the Fisher entropy increases as the depth u of the potential wells increases, while the fractional derivative number n decreases.

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Information entropy and level-spacing distribution based signatures of quantum chaos in electron doped 2D single carrier quantum dots

Cited by 12 publications

References 15 publications

Shannon information entropies for rectangular multiple quantum well systems with constant total lengths*

Shannon information entropies for rectangular multiple quantum well systems with constant total lengths*

Impurity strength and impurity domain modulated frequency‐dependent linear and second non‐linear response properties of doped quantum dots

Quantum Information Entropy of Hyperbolic Potentials in Fractional Schrödinger Equation

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