Shape effect on information theoretic measures of quantum heterostructures

Abstract

Theoretic measures of information entropies like Shannon entropy and Fisher information are studied for multiple quantum well systems (MQWS). The effect of shape and number of wells in the MQWS is explored in detail. The shapes taken are: rectangular, parabolic and V-shape. Onicescu energy is an important tool to study the information content stored in the system, which is also found to depend on shape and number of wells of heterostructures. Statistical measure of complexity also shows noticeable dependence on these parameters.

Two‐dimensional confined hydrogen: An entropy and complexity approach

“…The idea of two-and multidimensional spherical confinement of atoms has been used not only to simulate the effect of high pressure on the static dipole polarizability in hydrogen [18] but also to model a great deal of nanotechnological objects such as quantum dots, quantum wells and quantum wires [19,20], atoms and molecules embedded in nanocavities as for example in fullerenes, zeolites cages and helium droplets [4,6,7,[21][22][23], dilute bosonic and fermionic systems in magnetic traps of extremely low temperatures [24][25][26] and a variety of quantum-information elements [27,28]. This has provoked a fast development of a density functional theory of independent particles moving in multidimensional central potentials with various analytical forms (see e.g., [5][6][7][29][30][31]).…”

“…Most efforts have been centered around the spectroscopic properties and some density-functional descriptors of physical and chemical quantities for the ground state of spherically confined atoms [4,6,7]. However, not so much is known about the information-theoretic measures of the multidimensional confined systems except for a few recent entropy-like [20,[32][33][34][35][36][37][38][39][40] and complexity-like [33,41] results of the three-dimensional confined hydrogenic atom. The aim of this work is to cover this informational lack by means of the determination of the confinement dependence of some entropy (Shannon, Fisher) and complexity (Fisher-Shannon, LMC and LMC-Rényi) measures for the 1s, 2s, 2p and 3d quantum states of the two-dimensional confined hydrogenic atom (2D-CHA, in short) [42][43][44][45][46] in both position and momentum spaces.…”

“…The Fisher information, which is a gradient functional of ρ( r), measures the pointwise concentration of the electronic probability cloud all over the region wherein the electron moves. These entropic quantities are (i) closely related to fundamental and/or experimentally measurable quantities of electronic systems, (ii) satisfy sharp uncertainty relationships [49,50,54], (iii) the basic variables of two extremization procedures (the maximum entropy method and the principle of extreme physical information, respectively), (iv) indicators of the most distinctive nonlinear phenomena (avoided crossings) encountered in atomic and molecular spectra under external fields [55,56], and (v) identifiers of the shape effect of quantum heterostructures [20], among many other properties.…”

Crámer‐Raocomplexity of the confined two‐dimensional hydrogen

“…This atom is the prototype that has been used to interpret numerous phenomena and systems in surface chemistry, [22][23][24] semiconductors (see, eg, Li et al [25] ), quantum dots, [26,27] atoms and molecules embedded in nanocavities (eg, fullerenes, helium droplets, …), [18,19,21,[28][29][30] dilute bosonic and fermionic systems in magnetic traps of extremely low temperatures, [31][32][33] and a variety of quantuminformation elements. [34,35] Up until now, contrary to the stationary states of the confined 3D-HA, where both the (energy-dependent) spectroscopic and the (eigenfunction-dependent) information-theoretic properties have received much attention, [27,[36][37][38][39][40][41][42][43][44][45] the knowledge of these properties for the confined 2D-HA is quite scarce. [46][47][48][49][50] Just recently, the authors have determined [51] the entropy-like (Shannon, Fisher) and complexity-like (Fisher-Shannon, LMC) measures for a few low-lying stationary states of the confined 2D-HA.…”

Crámer-Rao complexity of the two-dimensional confined hydrogen

“…This atom is the prototype which has been used to interpret numerous phenomena and systems in surface chemistry [22][23][24], semiconductors (see e.g., [25]), quantum dots [26,27], atoms and molecules embedded in nanocavities (e.g., fullerenes, helium droplets,...) [18,19,21,28,30,31], dilute bosonic and fermionic systems in magnetic traps of extremely low temperatures [32,34,35] and a variety of quantum-information elements [36,37]. Up until now, contrary to the stationary states of the confined 3D-HA where both the (energy-dependent) spectroscopic and the (eigenfunction-dependent) information-theoretic properties have received much attention [27,[38][39][40][41][42][43][44][45][46][47], the knowledge of these properties for the confined 2D-HA is quite scarce [48-50, 52, 53]. Just recently, the authors have determined [54] the entropy-like (Shannon, Fisher) and complexity-like (Fisher-Shannon, LMC) measures for a few low-lying stationary states of the confined 2D-HA.…”