Quantum Markov Semigroups of Low Density Limit: the Generic Case

We investigate the structure of quantum Markov generators that describe the reduced dynamics of a test particle interacting with a dilute Bose gas in the low density limit. These generators, called low density limit type generators (LDL), differ from the weak coupling limit type generators (WCL) studied in [4, 5] because of the presence of the T-operator that describes the change in momentum of the gas particle due to collisions with the test particle. We propose a general definition of Markov generator of stochastic limit type that includes (almost) all generators arising in the stochastic limit approach and we prove that the associated semigroups as well as their invariant states (or weights) have a very special structure which extends the explicit representation for the generic quantum Markov semigroups of weak coupling limit type, due to Accardi, Hachicha and Ouerdiane [7]. We also investigate the structure of invariant states and give conditions on the T - operator for the existence of a unique invariant state and of equilibrium states.

On the Critical Speed, Supercritical Bifurcation, and Stability Problems of Certain Type of High-Speed Rail Vehicle

Recently, Chinese engineers have proposed a simple way to find the vehicles’ critical speed, which is similar to the ramping method. In this article, through an example of vehicle of supercritical properties, it is proved that the new easier way is not scientifically justified and should not be used in engineering practice. In addition, the ramping way also yields inaccurate critical speed. Then one abnormal vibration phenomenon which appears on Beijing-Shanghai high-speed line is studied. The results demonstrate that it is car body hunting but not bogie hunting. Finally, through the computation and comparison of the lateral ride indices under different conditions, one stability problem about stochastic limit cycle banding is tentatively discussed.