Scholarlink

<p>This paper delves into the analytical study of two significant nonlinear fractional-order models in the Liouville-Caputo sense, which play a crucial role in the mathematical formulation of quantum field theory, particularly in describing anomalous diffusion and nonlocal interactions. The two models considered are the fractional-order massive Thirring model (FMTM) and the fractional-order Kundu-Eckhaus equation (FKEE). These models provide insights into natural events, such as the stability and dynamics of quantum solitons, rogue waves, and coherent quantum states in coupled quantum fields. Fractional orders in the FKEE highlight their impact on wave dispersion and memory effects, influencing the propagation and stability of quantum solitons. Similarly, the FMTM captures the intricate interplay between linear and nonlinear interactions, showcasing oscillatory behavior and emergent coherence in quantum systems. Using the Fractional Reduced Differential Transform Method (FRDTM), semi-analytical approximations are derived for both models, demonstrating the method’s efficacy in reducing computational complexity while maintaining high accuracy. The study emphasizes the role of fractional-order Liouville-Caputo derivative in encapsulating nonlocality and time-dependent memory effects, offering a deeper understanding of complex quantum dynamics and their applications in advanced optical systems, plasma physics, and quantum information science.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Analytical Study of Models in Quantum Field Theory: Fractional Kundu-Eckhaus and Massive Thirring Equations

  • 期刊论文

  • 发表日期：

    2025年6月12日

查看全文
  • Mohammad Izadi,
  • Yogeshwari F. Patel

摘要

This paper delves into the analytical study of two significant nonlinear fractional-order models in the Liouville-Caputo sense, which play a crucial role in the mathematical formulation of quantum field theory, particularly in describing anomalous diffusion and nonlocal interactions. The two models considered are the fractional-order massive Thirring model (FMTM) and the fractional-order Kundu-Eckhaus equation (FKEE). These models provide insights into natural events, such as the stability and dynamics of quantum solitons, rogue waves, and coherent quantum states in coupled quantum fields. Fractional orders in the FKEE highlight their impact on wave dispersion and memory effects, influencing the propagation and stability of quantum solitons. Similarly, the FMTM captures the intricate interplay between linear and nonlinear interactions, showcasing oscillatory behavior and emergent coherence in quantum systems. Using the Fractional Reduced Differential Transform Method (FRDTM), semi-analytical approximations are derived for both models, demonstrating the method’s efficacy in reducing computational complexity while maintaining high accuracy. The study emphasizes the role of fractional-order Liouville-Caputo derivative in encapsulating nonlocality and time-dependent memory effects, offering a deeper understanding of complex quantum dynamics and their applications in advanced optical systems, plasma physics, and quantum information science.