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Chaotic Systems Part 5

Tham khảo tài liệu 'chaotic systems part 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Microscopic Theory of Transport Phenomenon in Hamiltonian Chaotic Systems 89 of the n-th pseudo-particle at time t whose time dependence is described by the canonical equations of motion given by qi dH dpi dH p1 - di i 1 Nd q d H TCT d p dH p - 88 We use the fourth order simplectic Runge-Kutta algorithm 75 76 for integrating the canonical equations of motion and Np is chosen to be 10 000. In our study the coupling strength parameter is chosen as A 0.002. 3.2.2 Energy dissipation and equipartition We have discussed a microscopic dynamical system with three degrees of freedom in Sec. 3.1.3 3.1.4 and 3.1.5 and shown that the dephasing mechanism induced by fluctuation mechanism turned out to be responsible for the energy transfer from collective subsystem to environment 30 . In that case as we shown the fluctuation-dissipation relation does not hold and there is substantial difference in the microscopic behaviors between the microscopic dynamical simulation based on the Liouville equation and the phenomenological transport equation even if these two descriptions provide almost same macroscopic behaviors. Namely the collective distribution function organized by the Liouville equation evolves into the whole ring shape with staying almost the same initial energy region of the phase space while the solution of the Langevin equation evolves to a round shape whose collective energy is ranging from the initial value to zero. For answering the questions as how to understand the above stated differences and in what condition where the microscopic descriptions by the Langevin equation and by the Liouville equation give the same results and in what physical situation where the fluctuation-dissipation theorem comes true a naturally extension of our work 30 is to considered the effects of the number of degrees of freedom in intrinsic subsystem because no matter how our simulated dissipation phenomenon is obtained by a simplest system which is composed of only three degrees of .