Before revision: We investigate the relevance between quantum open systems and stock markets. A Quantum Brownian motion model is proposed for studying the interaction between the Brownian system and the reservoir, i. e., the stock index and the entire stock market. Based on the model, we investigate the Shanghai Stock Exchange of China from perspective of quantum statistics, and thereby examine the behaviors of the stock index violating the efficient market hypothesis, such as fat-tail phenomena and non-Markovian features.
After revision: It is believed by the majority today that the efficient market hypothesis is imperfect because of market irrationality. Using the physical concepts and mathematical structures of quantum mechanics, we construct an econophysics framework for the stock market, based on which we analogously map massive numbers of single stocks into a reservoir consisting of many quantum harmonic oscillators and their stock index into a typical quantum open system--a quantum Brownian particle. In particular, the irrationality of stock transactions is quantitatively considered as the Planck constant within Heisenberg's uncertainty relationship of quantum mechanics in an analogous manner. We analyze real stock data of Shanghai Stock Exchange of China from perspective of quantum statistics, and thereby examine the behaviors of the stock index violating the efficient market hypothesis, such as fat-tail phenomena and non-Markovian features.