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Modern Physics Letters A

Quantum information entropy and squeezing of 𝒫𝒯-symmetric potential

Aarti Sharma, Pooja Thakur, Girish Kumar, Anil Kumar

Published Mar 8, 2021• 2 citations
Publisher

Abstract

The information theoretic concepts are crucial to study the quantum mechanical systems. In this paper, the information densities of [Formula: see text]-symmetric potential have been demonstrated and their properties deeply analyzed. The position space and momentum space information entropy is obtained and Bialynicki-Birula–Mycielski inequality is saturated for different parameters of the potential. Some interesting features of information entropy have been discussed. The variation in these entropies is described which gets saturated for specific values of the parameter. These have also been analyzed for the [Formula: see text]-symmetry breaking case. Further, the entropy squeezing phenomenon has been investigated in position space as well as momentum space. Interestingly, [Formula: see text] phase transition conjectures the entropy squeezing in position space and momentum space.

DOI
10.1142/s0217732321500656

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The information theoretic concepts are crucial to study the quantum mechanical systems. In this paper, the information densities of [Formula: see text]-symmetric potential have been demonstrated and their properties deeply analyzed. The position space and momentum space information entropy is obtained and Bialynicki-Birula–Mycielski inequality is saturated for different parameters of the potential. Some interesting features of information entropy have been discussed. The variation in these entropies is described which gets saturated for specific values of the parameter. These have also been analyzed for the [Formula: see text]-symmetry breaking case. Further, the entropy squeezing phenomenon has been investigated in position space as well as momentum space. Interestingly, [Formula: see text] phase transition conjectures the entropy squeezing in position space and momentum space.
Abstract In this article, some information theoretic concepts are analyzed for modified Hylleraas plus exponential Rosen Morse potential in position and momentum space. The angular and radial contributions of the information density are graphically demonstrated for different states. The entropy densities have asymmetric shape which depends on the values of quantum numbers. The information entropy is analytically obtained for ground state of the potential whereas the numerical calculations have been performed for the higher states and Bialynicki‐Birula and Mycielski inequality is tested for various states using different parameters of the potential. It is shown that the information entropy is reduced, both in position and momentum space, for careful selection of some parameters. Further, it is found that there exist eigenstates exhibiting squeezing in information entropy of modified Hylleraas plus exponential Rosen Morse and Eckart potential. Interestingly, in case of Eckart potential, the squeezed states are obtained in position as well as momentum space and are attempted to saturate for some values of the parameters.
Abstract In this work, the position and momentum space information densities of the Eckart potential are graphically demonstrated and their properties are studied. The position space information densities have quite an asymmetric shape depending on the values of quantum numbers. The information entropy is obtained and Bialynicki‐Birula and Mycielski inequality is numerically saturated for some parameters of the potential. It is shown that the inequality is saturated with increasing potential depth.
The exact solutions to the Schrödinger equation with a hyperbolic potential are obtained. The position S x and momentum S p Shannon information entropies for the low-lying states are calculated. Some interesting features of the information entropy densities and as well as the probability densities and are demonstrated. We find that the choices of the values for those parameters have to satisfy the condition on . We also notice that the and are symmetric to the momentum p and the or is equal or greater than 1 at some positions r or momentum p . In addition, the Bialynicki-Birula–Mycielski inequality is tested from different cases and found to hold for these cases.
Shannon entropy for lower position and momentum eigenstates of Pöschl—Teller-like potential is evaluated. Based on the entropy densities demonstrated graphically, we note that the wave through of the position information entropy density ρ( x ) moves right when the potential parameter V 1 increases and its amplitude decreases. However, its wave through moves left with the increase in the potential parameter | V 2 |. Concerning the momentum information entropy density ρ( p ), we observe that its amplitude increases with increasing potential parameter V 1 , but its amplitude decreases with increasing | V 2 |. The Bialynicki—Birula—Mycielski (BBM) inequality has also been tested for a number of states. Moreover, there exist eigenstates that exhibit squeezing in the momentum information entropy. Finally, we note that position information entropy increases with V 1 , but decreases with | V 2 |. However, the variation of momentum information entropy is contrary to that of the position information entropy.