Study On Energy Disspative Process In Finete Muti-Degree Of Freedom System With Power Spectrum Analysis

It's a fundamental problem in statistical physics to study the dynamical behavior of different degree of freedom (DOF) in the energy dissipative process of finite coupled multi-DOF system. This is also an important topic in some fields such as nuclear physics, biophysics etc.. With some widely admitted theories and numerical simulation consulted, dynamical features of the energy dissipative process in finite coupled multi-DOF Hamiltonian system is explored in this dissertation by nonlinear dynamical analyzing methods. There are certain meanings in mis work for thoroughly understanding the nonlinear dynamical course of different DOFs related to energy dissipation.It is studied that how the power spectrum of moment pit) in the motion of relevant DOF changes with time and the number of irrelevant DOFs. The work discusses the comparison between the power spectrum of moment p(t) in the motion of irrelevant DOFs before the coupling interaction between subsystems activated and that after the coupling interaction activated, as well as the difference between the power spectrum of moment pit) in the motion of irrelevant DOFs and that with different number of irrelevant DOFs. It is found that in energy dissipative process, the distribution of spectral density about the motion of relevant DOF remarkably extends to either lower or higher frequency. The more irrelevant DOFs are, the much broader the distribution expands. In the power spectrum about relevant DOF, higher frequency components are weakened as time evolves but there are no remarkable changes for lowercomponents. Finally, the motion of relevant DOF runs to chaos with the effects from a chaotic environment. With the interaction from relevant system, the chaotic feature in the motion of all DOFs contained in irrelevant system is accordingly enhanced after the coupling interaction activated. As far as the whole system concerned, feature of quasi-periodic motion as well as feature of chaos is partially kept during an interval shortly after the coupling interaction between subsystems activated. In addition, by the variance of q(i) related to different DOF, an acute contracting-expanding behavior in the probable distribution area of the track about different DOF is observed during the interval shortly after the coupling interaction activatedThe dissertation consists of 5 sections.The background and progress for study on the problems about finite multi-DOF coupled system are introduced in Section 1, which ends with a brief summary of this work. Section 2 quotes some useful nonlinear dynamical analyzing methods. The theory of coupled-master equation derived by time-dependent projection operator is recapitulated in Section 3. With a reliable numerical simulation consulted, the dynamical features in the motion of relevant or irrelevant DOF are discussed. The last section gives a summary of the conclusions from this work.