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Fractal and Fractional

Fractional Dynamics of Information Entropy in Quantum Wire System Under Rashba Interaction

Rabie I. Mohamed, Ramy M. Hafez, Atef F. Hashem, Mahmoud Abdel‐Aty

Published Nov 17, 2025• 0 citations
Publisher

Abstract

We present a theoretical examination of the fractional dynamics of information entropy within a semiconductor nanowire system influenced by Rashba spin–orbit interaction and external magnetic fields. Moreover, we determine the fractional nanowire state through the analytical solution of the fractional Schrödinger equation, considering various initial states of the nanowire system. Our research emphasizes the impact of the fractional order and the interaction parameters on the behavior of information entropy. Our findings reveal that the temporal behavior of information entropy is highly sensitive to any variations in the magnetic field length, the Rashba spin–orbit interaction, and the fractional order parameter. The results demonstrate that these parameters are pivotal in determining the coherence and correlation properties of the nanowire system. Therefore, precise control of these factors paves the way for enhancing entanglement performance and facilitating information transfer in spintronic and quantum communication applications.

DOI
10.3390/fractalfract9110741

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We analyze the dynamics of squeezing in a ballistic quantum wire with Rashba spin-orbit interaction in the presence of both strong and weak magnetic fields and for different initial states of the system. Compared to the more standard measure of squeezing based on variances, we show that entropy squeezing is a more sensitive measure. Our results show that there is a strong relationship between the spin-orbit interaction and the strength of entropy squeezing. Furthermore, there is a relationship between the initial state and the number of squeezed components. This allows new knobs to control the strength and the component of entropy squeezing in a nanowire system.
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In this paper we study the entanglement dynamics of spin–subband states for an electron in a quasi-one-dimensional Rashba quantum loop, in a strong perpendicular magnetic field, explicitly including the confining potential and the Rashba spin–orbit coupling into the entropy, which is a measure of entanglement, as a function of time. Our results indicate that the entanglement between the spin states and the structural subbands undergoes periodic oscillations. Furthermore, it is shown that the period of oscillations strongly depends upon the Rashba coupling, while the amplitudes may be optimized by making proper choices of the external magnetic field. It is also shown that the maxima of entanglement, in the long run, oscillate under periodic envelopes, whose characteristics depend upon the magnetic field. Our results, thereby, provide means of controlling the degree of entanglement by adjusting these agents.
This investigation delves into the dynamics of quantum correlations and coherence within a two-dimensional electron gas (2DEG) system, taking into account the influence of Rashba spin–orbit coupling (SOC). We utilize metrics such as logarithmic negativity ([Formula: see text]), local quantum uncertainty (LQU ([Formula: see text])), and relative entropy of coherence ([Formula: see text]) to specifically assess these quantum resources among electron spins within non-interacting electron gases. Our study investigates how the separation distance (R) between electrons and the intensity of Rashba SOC ([Formula: see text]), impact the behavior of quantum properties within the 2DEG system. We find that specific strengths of Rashba SOC can effectively regulate quantum correlations and coherence within this system. Particularly significant is our observation that optimal quantum indicators emerge when electron proximity is minimized, underscoring the substantial influence of electron distance on quantum characteristics. Conversely, as electron separation increases, these quantum metrics diminish. Therefore, by adjusting the Rashba parameter, we can enhance the resilience of these quantum measurements against increasing electron separations, providing valuable insights into the potential for controlling and manipulating quantum behavior in similar 2DEG systems.
A new analytical description is obtained for a ballistic quantum wire under Rashba spin–orbit mechanism with a magnetic field. The system is also analyzed for two different cases, one with and the other without an external electric field. The measurement-induced nonlocality based on trace norm (trace-norm MIN) and concurrence are employed in order to witness different quantum correlations of the electron-harmonic system beyond quantum entanglement. The robustness and stability of the initial maximal correlation are explored. It is shown that the generation and enhancement of quantum correlations can be controlled for particular external electric fields. Furthermore, this study shows that the correlations of trace-norm MIN always present independently of the existence of the magnetic field and the external electric field. The external electric field reduces the effect of the interaction of the electron-harmonic system; therefore, it leads to the conservation of the initial quantum correlations.