Quantization of Foster mesoscopic circuit and DC – pumped Josephson parametric amplifier

This research paper presents a novel quantum theory for mesoscopic LC circuits by utilizing a product-like fractal measure to account for anisotropy in materials. The author develops a mathematical framework where electrical components like inductance and capacitance are position-dependent, leading to the derivation of a specific Schrödinger equation and energy spectrum. Key contributions include the definition of new creation and annihilation operators tailored for fractal-based oscillators. The study specifically applies this formalism to the quantization of Foster circuits and DC-pumped Josephson parametric amplifiers. A significant finding is that the energy expectation value remains finite and time-independent at high temperatures, offering a more stable result than previous literature. Ultimately, the work suggests that fractal geometry provides a robust lens for understanding charge carrier dynamics in nanoscale electronics and semiconductors.
This briefing document synthesizes the findings of the research paper "Quantization of Foster mesoscopic circuit and DC–pumped Josephson parametric amplifier from fractal measure arguments." The research addresses the lack of a quantum mechanical description for position-dependent charge (PDC) in materials, specifically within semiconductor devices.Utilizing the Li and Ostoja-Starzewski approach (LOSA) of product-like fractal measures, the study proposes a new quantum theory for mesoscopic LC circuits. Key developments include the derivation of the Schrödinger equation for circuits with position-dependent components and the analysis of discrete energy spectrums. The study's most significant outcome is the identification of a finite, time-independent energy expectation value at very high temperatures , contradicting previous literature that suggested time-dependency. These findings have critical implications for nanotechnology, mesoscopic physics, and the engineering of nanoelectronic components like Josephson parametric amplifiers.

Rami Ahmad El-Nabulsi, “Quantization of Foster mesoscopic circuit and DC–pumped Josephson parametric amplifier from fractal measure arguments,” Physica E: Low-dimensional Systems and Nanostructures, Volume 133, 2021, 114845, ISSN 1386-9477, https://doi.org/10.1016/j.physe.2021.114845

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