Shannon and Fisher Entropy for a New Class of Single Hyperbolic Potentials in Fractional Schrödinger Equation

IF 2.3 3区 化学 Q3 CHEMISTRY, PHYSICAL
R. Santana-Carrillo, D. Maya-Franco, Guo-Hua Sun, Shi-Hai Dong
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Abstract

We investigate the quantum information entropy for a class of single hyperbolic potentials within the context of the fractional Schrödinger equation (FSE). We find that as the derivative variable n $$ n $$ decreases, the position entropy density function ρ ( x ) $$ \rho (x) $$ becomes more localized, and its peak heightens. However, there are differences in the degree of localization between the position entropy density functions for each hyperbolic potential, which can be attributed to the varying sizes of the potentials. Conversely, in momentum space, the momentum entropy density function ρ ( p ) $$ \rho (p) $$ becomes more delocalized, and its peak lowers as the derivative variable n $$ n $$ decreases for both hyperbolic potentials studied. Our analysis also examines the BBM inequality, demonstrating that it is satisfied for different values of the potential depths. Finally, we explore the Fisher entropy and observe that it increases in position space while decreasing in momentum space as the depth of the wells increases. Our findings provide new insights into the behavior of quantum systems governed by hyperbolic potentials within the fractional Schrödinger framework. The observed localization effects in position space, delocalization in momentum space, and the validation of the BBM inequality highlight the role of fractional derivatives in modifying quantum entropy measures. These results deepen our understanding of quantum information entropy in non-local quantum systems. They may have implications for fields such as quantum transport in disordered media, semiconductor physics, and the study of anomalous diffusion processes in quantum mechanics.

Abstract Image

分数阶Schrödinger方程中一类新的单双曲势的Shannon和Fisher熵
我们研究了分数阶Schrödinger方程(FSE)下一类单双曲势的量子信息熵。我们发现,随着导数变量n $$ n $$的减小,位置熵密度函数ρ (x) $$ \rho (x) $$变得更加局域化,其峰值增大。然而,每个双曲势的位置熵密度函数之间的局域化程度存在差异,这可归因于势的大小不同。相反,在动量空间中,动量熵密度函数ρ (p) $$ \rho (p) $$变得更加离域,并且随着所研究的双曲势的导数变量n $$ n $$的减小,其峰值降低。我们的分析还检验了BBM不等式,证明它对不同的潜在深度值都是满足的。最后,我们研究了Fisher熵,并观察到随着井深的增加,它在位置空间增加,而在动量空间减少。我们的发现为分数Schrödinger框架内由双曲势控制的量子系统的行为提供了新的见解。观察到的位置空间的局域效应、动量空间的非局域效应以及BBM不等式的验证,突出了分数阶导数在修正量子熵测度中的作用。这些结果加深了我们对非局域量子系统中量子信息熵的理解。它们可能对诸如无序介质中的量子输运、半导体物理以及量子力学中异常扩散过程的研究等领域具有启示意义。
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来源期刊
International Journal of Quantum Chemistry
International Journal of Quantum Chemistry 化学-数学跨学科应用
CiteScore
4.70
自引率
4.50%
发文量
185
审稿时长
2 months
期刊介绍: Since its first formulation quantum chemistry has provided the conceptual and terminological framework necessary to understand atoms, molecules and the condensed matter. Over the past decades synergistic advances in the methodological developments, software and hardware have transformed quantum chemistry in a truly interdisciplinary science that has expanded beyond its traditional core of molecular sciences to fields as diverse as chemistry and catalysis, biophysics, nanotechnology and material science.
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