Department of Systems Science
Beijing Normal University
Tel: +86-10-58807876(O), +86-18610014018(M)
- 2011, PH.D. in Condensed Matter Physics, Department of Physics & Astronomy, University of British Columbia (UBC)
- 2003-2004, one year in a PH.D. program in Simon Fraser University (SFU), and then transferred to UBC
- 2006, M.Sc. in Condensed Matter Physics, Department of Physics & Astronomy, UBC
- 2002, M.Sc. in Statistical Physics, Physics Department, Beijing Normal University(BNU)
- 1999, B.S. in Physics, Department of Physics, BNU
- 2011-, Associate Professor, Department of Systems Science, BNU, Beijing, China
- 2004-2011, Teaching Assistant, Department of Physics & Astronomy, UBC
- 2003-2004, Teaching Assistant, Department of Physics, SFU
- 2002-2003, Lecturer and Research Associate, Department of Systems Science, BNU
- 2012 Spring, Physics and Mathematics in Studies of Complexity II, graduate course, Department of Systems Science, BNU.
- 2011 Fall, Physics and Mathematics in Studies of Complexity I, graduate course, Department of Systems Science, BNU.
- 2011- , Non-equilibrium statistical physics and Quantum transport project, PI, funded partially by National Natural Science Foundation of China.
- 2011- , Network-based learning strategies of Chinese characters, PI, not yet funded by any agencies.
- 2012- , Study concept mapping technology and generate collections of concept maps, PI, funded partially by university research fund from BNU.
- 2003, Math Model, undergraduate course, Department of Systems Science, BNU.
- 2002, Econophysics, a course for graduate students, Department of Systems Science, BNU, 2002,9-2003,1. I designed and established this course from scratch. A review paper ( in the publication list) on Econophysics prepared for the class was post on arXiv. Since then many have used it as an introductory material for the subject.
- 2002-2003, under Prof. Zengru Di’s supervision, lead a team working on empirical studies of and modelling weighted complex networks
- 2002-2003, help Prof. Zengru Di to organize a proposal for National Fund of Natural Science in China, The statistical properties of firm sizes and its theoretical model, funded at 2003,9.
- 2004-2011, as a graduate student in Prof. Mona Berciu’s group, working on various projects related to quantum transport
- 1999-2002, as a graduate student (master) in Prof. Zhanru Yang’s group, during the later years of and one year after my graduation (2001-2003), I lead a team working on physical models on complex networks
Skills in numerical computation
- High-performance computational software: BLAS, Lapack, Petsc, Slepc, gsl, xmds
- Programming language: C, Java, Linux shell script
- University Graduate Fellowship (UGF) from UBC, 2006-2009
- Graduate Fellowship from SFU, spring 2004
- Canron Limited – Sidney Hong Memorial Grad Scholarship, Spring 2004
- Westak International Sales Inc. Grad Scholarship in Expert Systems, Spring 2004
- Scholarship for Excellent Graduate Students from BNU, 2000
- Award for excellent undergraduate students from BNU, 1998
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.
- Using a BBGKY-like method for solving the open-system master equation  the task of solving an eigenvalue problem of size 4N becomes a problem of solving a linear system of size N2 by converting the open-system master equation into linear equations of Green’s functions. The equations of different Green’s functions (single-particle ones, tow-particle ones and so on) are coupled. The cluster expansion, originally used for the equilibrium BBGKY method, is used to truncate the coupled equation. The accuracy of this method is around 2%.
- The second order form of the BBGKY-like method requires solving a linear system of size N4 but improves accuracy even further. Such a form also gives the two-particle correlated Green’s functions beyond the Hartree-Fock approximation. Manuscript in preparation.
- A coherent-state representation approach was also explored to solve the above problem of size 4N by simulating a stochastic differential equation with 2N complex variables by converting the open-system master equation into a generalized Fokker-Planck equation. Analytical expression of the non-equilibrium stationary states are derived for some systems. The accuracy of this method is around 6%. Manuscript in preparation.
- We also found in study of the Kubo formula for open systems  that in order to study transport one has to take into account the coupling from the central system to the baths explicitly. In using the usual Kubo formula in transport studies, one assume the central system is a closed system.
- Using direct methods we studied thermal transport of spin chains and analyzed systems up to N=10. Connections between integrability and anomalous transport, which is widely believed by physicists and has been demonstrated by studies based on the usual Kubo formula, is challenged by our results.
This series of works started in late 2002 when I was employed as a research associate for Prof. Zengru Di at BNU after I got my M.Sc. Degree in statistical physics from BNU. Many thanks to Prof. Zengru Di, Prof. Yougui Wang and Prof. Zhangang, Han for offering me a position usually requiring a PH.D. Degree. The focus of my research on weighted networks has been the basic statistical features of static weighted networks, their evolution and also some more advanced structure in those networks.
- Empirical study of weighted networks[11,12]: We collected almost all papers published on Econophysics up to date (back then), compiled a weighted network and studies its basic statistical properties.
- Evolutionary model for weighted networks [3,7,9]: Inspired by social networks and the above weighted networks of econophysicists, a new model of weighted networks was proposed. It is based on local rules, which means that nodes in the network only need to know limited information about their neighbors and at most their next neighbors. That is in this model a data centers providing global information is not required. We went one step further and conjectured that the well-known mechanism of global preferential attachment (that the richest gets richer while the poorest gets poorer) can be an emergent phenomenon rooted from local rules. We tested and confirmed this conjecture on our own model and several others.
Quantum Game Theory
In physicists’ terminologies, classical games can be regarded as games based on classical objects. The state of the object changes according to players’ choice of strategies. These strategies are described by operators acting on the object to modify its state. The final state of the object determines the payoff for every player. The coin flipping games is a perfect example of this picture. The coin is a classical two-state system, which is denoted by physicists as a mixture state of “heads” and “tails”. Flipping and non-flipping correspond respectively to the Pauli matrixand identity matrix. A natural question then arises of what happens if the classical coin is replaced by a quantum spin.
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.
Partially inspired by the above work on quantum game theory, I was motivated to study the difference between a probability distribution and a density matrix. Can the former be converted to the later equivalently or vice versa? Luckily I found that the same question has been asked and investigated by physicists on the question of validity of hidden variable theory. In a hidden variable theory, there is no superposition principle, but classical probability summations are allowed. In a sense, the hidden variable theory is searching for a map from a density matrix to a classical probability distribution.
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 beyond locality one has to give up in order to have such a classical theory for quantum systems. I found 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.
- 1. Jinshan Wu and Mona Berciu, Heat transport in quantum spin chains: the relevance of integrability, Phys. Rev. B 83, 214416 (2011).
- 2. Jinshan Wu and Mona Berciu, Kubo formula for open finite-size systems, Europhysics Letters, 92(2010), 30003.
- 3. Jinshan Wu, Non-equilibrium stationary states from the equation of motion of open systems, New Journal of Physics, 12(2010), 083042.
- 4. Menghui Li, Liang Gao, Ying Fan, Jinshan Wu and Zengru Di, Emergence of global preferential attachment from local interaction, New Journal of Physics, 12(2010), 043029
- 5. Yanqing Hu, Jinshan Wu and Zengru Di, Enhance the efficiency of heuristic algorithms for maximizing the modularity Q, Europhysics Letters, 85(2009), 18009
- 6. Ying Fan, Menghui Li, Peng Zhang, Jinshan Wu and Zengru Di, The effect of weight on community structure of networks, Physica A, 378(2007), 583-590.
- 7. Ying Fan, Menghui Li, Peng Zhang, Jinshan Wu and Zengru Di, Accuracy and precision of methods for community identification in weighted networks, Physica A, 377(2007), 363-372.
- 8. Menghui Li, Jinshan Wu, Dahui Wang, Tao Zhou, Zengru Di and Ying Fan, Evolving model of weighted networks inspired by scientific collaboration networks, Physica A, 375(2007), 355-364.
- 9. Menghui Li, Ying Fan, Dahui Wang, Daqing Li, Jinshan Wu and Zengru Di, Small-world effect induced by weight randomization on regular networks, Physics Letters A, 364(2007), 488-493.
- 10. Menghui Li, Dahui Wang, Ying Fan, Zengru Di and Jinshan Wu, Modelling weighted networks using connection count, New Journal of Physics, 8(2006), 72.
- 11. Peng Zhang, Menghui Li, Jinshan Wu, Zengru Di and Ying Fan, The analysis and dissimilarity comparison of community structure, Physica A, 367(2006), 577-585.
- 12. Menghui Li, Ying Fan, Jiawei Chen, Liang Gao, Zengru Di and Jinshan Wu, Weighted networks of scientific communication: the measurement and topological role of weight, Physica A, 350(2005), 643-656.
- 13. Ying Fan, Menghui Li, Zengru Di, Jiawei Cheng, Liang Gao, and Jinshan Wu, Networks of Econophysicists, International Journal of Modern Physics B, Vol. 18, Nos. 17-19 (2004) 2505-2511.
- 14. Jingzhou Liu, Jinshan Wu and Z. R. Yang, The spread of infectious disease on complex networks with household-structure, Physica A, 341(2004), 273-280.
- 15. Jinshan Wu and Zengru Di, Complex networks in statistical physics, Progress in Physics (Chinese), 24-1(2004), 18-46.
- 16. Jinshan Wu, Zengru Di and Zhanru Yang, Division of labor as the result of phase transition, Physica A, 323(2003), 663-676.
- 17. Jinshan Wu, Jingdong Bao and Zhanru Yang, Improved Metropolis method for systems with discrete states, Chinese Journal of Computational Physics, 19-2(2002), 103-107.
- 18. Jinshan Wu and Shouyong Pei, Could a Classical Probability Theory Describe Quantum Systems?, arXiv:quant-ph/0503093.
- 19. Yougui Wang, Jinshan Wu and Zengru Di, Physics of Econophysics, arXiv:cond-mat/0401025.
- 20. Jinshan Wu, A series of papers on Game Theory: A new mathematical representation of Game Theory I, II arXiv:quant-ph/0404159, arXiv:quant-ph/0405183.
- Talk at APS March Meeting 2009, Heat transport in quantum spin chains: the relevance of integrability, March, 2009
- Invited talk at Beijing Normal University, games on quantum objects, Aug. 2007
- A presentation file for a talk on Quantum Games in Math@SFU, for non-physicists
- an outline for a talk on Quantum Games in Phas@UBC, for physicists
- A talk on Quantum Games for “Complex systems forum in Shanghai” (PDF, in Chinese)
- A presentation on quantum games in the “Internaltional conference on Econophysics in Shanghai”(PDF, in English)
- A lecture note (in PDF, in Chinese) for “BNU summer school on Complex Systems” : Games on Quantum Objects: from the viewpoint of a second-year undergraduate