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Physics Letters A

Derivation of a non-linear schrödinger equation describing possible vacuum dissipative effects

P. N. Kaloyerou, Jean Pierre Vigier

Published Jul 1, 1988• 9 citations
Publisher
DOI
10.1016/0375-9601(88)90606-8

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In this paper, we examine the time-fractional Schrödinger equation from the perspective of non-Markovian dynamics in dissipative systems. First, we determine the range of the fractional derivative's order by examining the memory properties of the time-fractional Schrödinger equation. Next, we employ the Jaynes-Cummings model to identify the appropriate mathematical form of the imaginary unit. Finally, we use the refined equation to study quantum teleportation under amplitude damping noise. It was found that the time-fractional Schrödinger equation without fractional operations on the imaginary unit i might be more suitable for describing non-Markovian dynamics in dissipative systems. Our research may provide a new perspective on the time-fractional Schrödinger equation, contributing to a deeper understanding and further development of time-fractional quantum mechanics.