Research Of Strongly Correlated Quantum Networks

Complex networks are an emerging discipline to study the complex systems in recent years and has received widespread attention of domestic and foreign scholars, and become a research hotspot. Complex network can be seen everywhere, we live in a world that is filled with the networks, such as the Internet, wireless communication networks, power networks, social networks, financial and commercial networks, etc. Studying the networks can change our lives. The past 20 years, Physics has been studying complex networks, the first method is using statistical elastic wave and quantum elastic wave, which satisfy some equation, research the features of the electronic wave function of complex netwoks, and the method is widely used in quantum Chaos, Anderson localization and other research areas, which reveal a new chapter of the quantum network. The work of this thesis is based on complex network theory and methods to study a type of strongly correlated quantum network. Through the establishment of Anderson s-d mixing model and using Green's function method to perform analytic calculations to the model, and thus get the energy spectrum for the strongly correlated quantum network; from this we study the dynamical property of the network, and find the degree distribution of the network is related to the spectrum of the energy, which reveals how they are mutual interacted and influenced. This allows us to get a formalism of the topological parameters with dynamical properties for the network. At the same time, we also made use of non-equilibrium statistical ensemble method to explore the strongly correlated quantum network. This method is also establishing a Hubbard model which is similar to the Anderson s-d mixing model, and the use of sub-dynamic projection operator techniques, as well as still adopt the Green's function method to analyze the entropy of the strongly correlated quantum network based on this model, revealing the the relationship between the complex entropy of the system and the local magnetic moment on the network nodes and explaining the dynamical characteristics of the strongly correlated quantum network. Both methods can help us well to understanding the quantum networks, which give us some reference value to buid some quantum devices.