This paper applies Zipf rank approach to measure how long it will take for the individual economy to reach the final state of equilibrium by using local-level data of China's urban areas. The indicators, the gross domestic product (GDP) per capita and the market capitalization (MCAP per capita of 150 major cities in China are used for analyzing their convergence. Besides, the power law relationship is examined for GDP and MCAP. Our findings show that, compared to the classical approaches:β-convergence and σ-convergence, the Zipf ranking predicts that, in approximately 16 years, all the major cities in China will reach comparable values of GDP per capita. However,the MCAP per capita tends to follow the periodic fluctuation of the economic cycle, while the mean-log derivation (MLD) confirms the results of our study. Moreover, GDP per capita and MCAP per capita follow a power law with an average value of α = 0.41 which is higher than α= 0.38 obtained based on a large number of countries around the world.

The linearized Hamiltonian model is proposed to extend the London Interbank Offered Rate (LIBOR) Market Model (LMM). Firstly, we studied the Hamiltonian of LMM in the framework of quantum finance, and the nontrivial upper triangle form of LIBOR drift is derived. The linearized Hamiltonian is derived to improve the explanatory capability of the model for market data. Our approach uses one more parameter to explain the initial condition and the model can be used to calibrate LIBORs with extremely high accuracy. Furthermore, the market time index is required for applying the model to multi-LIBOR, and the results imply that the LIBOR future time lattice becomes shorter as one goes from near future to distant future.