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A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
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Quantum Information Entropy for Another Class of New Proposed Hyperbolic Potentials.
R Santana-Carrillo1, Roberto de J León-Montiel2, Guo-Hua Sun1
1Centro de Investigación en Computación, Instituto Politécnico Nacional, UPALM, Mexico City 07738, Mexico.
Entropy (Basel, Switzerland)
|September 28, 2023
Summary
This study explores Shannon entropy in hyperbolic potentials, finding single-well potentials localize wave functions more than double-well ones. Entropies satisfy the BBM inequality across potential depths.
Area of Science:
- Quantum Mechanics
- Mathematical Physics
Background:
- Shannon entropy quantifies uncertainty in quantum systems.
- Hyperbolic potentials are relevant in various physical models.
- Understanding entropy-wave function localization is key.
Purpose of the Study:
- Investigate Shannon entropy for four novel hyperbolic potentials.
- Analyze position and momentum entropies.
- Examine the Bialynicki-Birula and Mycielski (BBM) inequality.
Main Methods:
- Calculated position and momentum entropies for hyperbolic potentials.
- Studied wave function localization.
- Assessed entropy behavior with varying potential depths (u¯).
Main Results:
- Single-well potentials (U0,3) show greater wave function localization than double-well (U1,2).
- Position entropy density is more localized for single-well potentials; momentum density is more delocalized.
- Double-well potentials exhibit the inverse localization behavior.
- Shannon entropies satisfy the BBM inequality for all tested depths.
- Sum of position and momentum entropies increases with u¯ for U1,2,3, but decreases for U0.
- Fisher entropy (F¯x) increases with u¯, while F¯p decreases.
Conclusions:
- Hyperbolic potential depth influences wave function localization and entropy distribution.
- The BBM inequality holds for these potentials.
- Entropy behavior varies distinctly between single- and double-well potentials.
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