Emergence of fractional quantum mechanics in condensed matter physics

被引：0

作者：

Dartora, C.A. ^{[1
]}

Zanella, Fernando ^{[1
]}

Cabrera, G.G. ^{[2
]}

机构：

[1] Electrical Engineering Department, Federal University of Paraná (UFPR), Curitiba,PR, Brazil

[2] Institute of Physics Gleb Wataghin, State University of Campinas (UNICAMP), Campinas,SP, Brazil

来源：

Physics Letters, Section A: General, Atomic and Solid State Physics | 2021年 / 415卷

关键词：

Condensed matter physics - Calculations - Quantum theory - Dispersions - Vanadium compounds;

D O I：

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学科分类号：

摘要：

Condensed matter provides a fertile ground for the emergence of exotic phenomena. For instance, polymers typically lack long range order and crystalline symmetry, leading to difficulties in establishing a general theory to describe the properties of these materials. They exhibit memory, some extent of self-similarity and non-locality effects, which are better described by fractional calculus. In this letter we demonstrate the emergence of an effective Hamiltonian possessing fractional dispersion taking as the starting point a tight-binding model in which the hopping parameters from next-nearest neighbours cannot be neglected. Our model was applied to describe the Pauli paramagnetism in a system with fractional dispersion, the magnetic susceptibility of vanadyl acetate and the electronic transport as a function of temperature in conductive polymers, displaying good agreement between theory and experimental data. © 2021 Elsevier B.V.

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