School of Systems Science
Beijing Normal University
Tel: +86-10-58807876(O), +86-18610014018(M)
E-mail: Jinshanw@bnu.edu.cn
Physics is all about interaction. By calculating indirect interaction from direct interactions, via such as Green’s function, physics, epsecially the field of statistical physics, establishs bridges between macroscopic behaviors and microscopic structures of systems. In fact, more generally, the idea and techniques of the combination of direct and indirect interactions, which we call relational thinking or lynkagem can be applied to systems beyond physical ones and it serves as the basic ways of thinking of systems science. It is natrually cross-disciplinary. We have applid this idea and related techniques to studies in physics, economics, scientometrics, language and learning, and the studies of systemmic safety, for instance
It is one of my research pursuits and dreams to extend the above thinking mode and analysis method to other fields, so that as many researchers and research questions as possible can adopt it.
Recently, based on our previous work of learning Chinese characters over the Chinese character network, and the concept of meaningful learning and concept maps of experts in education, especially David Ausubel and Joseph Novak, we have established the "Institute of Educationa System Science" (IESS) in the School of Systems Science at Beijing Normal University. We hope that the institute will carry out systematic and scientific educational research aimed at "helping teachers to teach better and helping students to learn better".
In my Ph. D. work at UBC I aimed to establish a theoretical framework for finding the non-equilibrium stationary states of quantum systems starting mostly from first principles. Approaches exist for this problem such as the Landauer-Buttiker formula and the non-equilibrium Green's function method. We decided to use the open-system scenario, which is not widely used because of the difficulty in solving the resulting open-system master equation. Using direct methods, one needs to solve an eigenvalue problem of size 4N where N is the size of the system measured in qubits. We first searched for efficient methods to solve this problem and then applications of this framework on physical models. The following lists several projects I have worked on.
I found that the answer is very non-trivial: a probability distribution over the strategy space, which is the description of a general strategy in classical game theory, is no longer capable of describing games with quantum objects. A density matrix over a basis of the strategy space has to be used. The same transition happens from Classical Mechanics to Quantum Mechanics. A probability distribution is replaced by a density matrix, which allows superpositions while the former allows only probability summations.
On one hand there is a theorem stating that all convex theories, which includes quantum mechanics, can be embedded into a classical probability theory with constraints (see for example, A. S. Holevo, Probabilistic and Statistical Aspects of Quantum Theory). On the other hand, Bell's inequality rules out all local hidden variable theories. The constrained classical theory has to be non-local. Of course many believe that physical theory should be local, but some are still willing to sacrifice locality. I investigated the question of what are the necessary intuitions, including for example the sense of locality, one has to give up in order to have such a classical theory for quantum systems. I found that there are many other unacceptable features of the classical theory by explicitly constructing such a theory for systems of one spin half and two spin halfs. Those unwanted features make the theory even harder to understand than the usual quantum mechanics.