2011/07/21 by Hajime Isimori, Isimori, Hajime
Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.1107.4329
openalex publication_date 2011/07/21 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We propose new equations of motion under the theory of the Brownian motion to connect the states of quantum, diffusion, soliton, and periodic localization. The new equations are nothing but the classical equations of motion with two additional terms and the one of them can be regarded as the the quantum potential. By choosing a parameter space, various important states are obtained. Further, the equations contain other interesting phenomena such as general dynamics of diffusion process, collapse of the soliton, the nonlinear extension of the Schrdinger equation, and the dynamics of phase transition.