Fractional Schrödinger equation and time dependent potentials

Gabrick, Enrique C.; Sayari, E.; Castro, A. S. M. de; Trobia, J.; Batista, A.M.; Lenzi, E. K.

doi:10.1016/j.cnsns.2023.107275

Cited by 8 publications

(2 citation statements)

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“…A particular case was considered in Ref. [52] for a two-level system. This system of linear differential equations can be analyzed from analytical and numerical points of view.…”

Section: Schrödinger Equation Without Kinetic Termsmentioning

confidence: 99%

“…Equations ( 1) and (3) are possible extensions and have been considered in many situations, such as optical solitons [50], resonant mode conversions [51], and two-level systems [52] as an extension of Rabi's model. However, note that when a Wick rotation is performed, the imaginary unit is increased to the same power as the time coordinates considered for Equation (1).…”

Section: Introductionmentioning

confidence: 99%

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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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“…A particular case was considered in Ref. [52] for a two-level system. This system of linear differential equations can be analyzed from analytical and numerical points of view.…”

Section: Schrödinger Equation Without Kinetic Termsmentioning

confidence: 99%