Unitary evolution for a two-level quantum system in fractional-time scenario

Cius, D.; Menon, L.; Santos, Maike A. F. dos; Castro, A. S. M. de; Andrade, Fabiano M.

doi:10.1103/physreve.106.054126

Cited by 5 publications

(1 citation statement)

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“…Other applications of fractional calculus are found in Refs. [20][21][22][23][24][25][26] and the references therein. These fractional operators, and the processes connected to them, have been widely analyzed in several fields, particularly in quantum mechanics, as a fundamental physics theory that describes the physical properties of nature in lighting on a subatomic and atomic level.…”

Section: Introductionmentioning

confidence: 99%

Anomalous Relaxation and Three-Level System: A Fractional Schrödinger Equation Approach

et al. 2023

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We investigate a three-level system in the context of the fractional Schrödinger equation by considering fractional differential operators in time and space, which promote anomalous relaxations and spreading of the wave packet. We first consider the three-level system omitting the kinetic term, i.e., taking into account only the transition among the levels, to analyze the effect of the fractional time derivative. Afterward, we incorporate a kinetic term and the fractional derivative in space to analyze simultaneous wave packet transition and spreading among the levels. For these cases, we obtain analytical and numerical solutions. Our results show a wide variety of behaviors connected to the fractional operators, such as the non-conservation of probability and the anomalous spread of the wave packet.

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