2024/10/14 by Pei Wang, Wang, Pei
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2410.10164
openalex publication_date 2024/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We develop a theory of random non-Hermitian action that, after quantization, describes the stochastic nonlinear dynamics of quantum states in Hilbert space. Focusing on fermionic fields, we propose both canonical quantization and path integral quantization, demonstrating that these two approaches are equivalent. Using this formalism, we investigate the evolution of a single-particle Gaussian wave packet under the influence of non-Hermiticity and randomness. Our results show that specific types of non-Hermiticity lead to wave packet localization, while randomness affects the central position of the wave packet, causing the variance of its distribution to increase with the strength of the randomness.