International Journal of Theoretical Physics

, Volume 37, Issue 8, pp 2153–2186 | Cite as

Quantization by Parts, Maximal Symmetric Operators, and Quantum Circuits

  • K. Kong Wan
  • R. H. Fountain


In the context of a generalized quantum theorywhich admits maximal symmetric operators as observables,we discuss a quantization scheme which cansystematically deal with what may be called quantumcircuits. The scheme, known as the method of quantizationby parts, has recently been applied to obtain a newderivation of the Josephson equation for thesupercurrent through a Josephson junction in asuperconducting circuit. This paper presents an application ofthis scheme to several circuit configurations, namely,from one branch to many-branch circuits. We also proposean experimental test on whether the condensate is always in a pure state, using a three-branchY-shape circuit.


Field Theory Elementary Particle Quantum Field Theory Experimental Test Pure State 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Akhiezer, N. I., and Glazman, I. M. (1963). Theory of Linear Operators in Hilbert Space, Vol. 2, Ungar, New York.Google Scholar
  2. Blank, J., Exner, P., and Havlicek, M. (1994). Hilbert Space Operators in Quantum Physics, American Institute of Physics, New York.Google Scholar
  3. Busch, P., Grabowski, M., and Lahti, P. (1995). Operational Quantum Physics, Springer-Verlag, Berlin.Google Scholar
  4. Devoret, M. H., Esteve, D., and Urbina, U. (1992). Nature, 360, 547.Google Scholar
  5. Exner, P., and Seba, P. (1987). Journal of Mathemtical Physics, 28, 386.Google Scholar
  6. Exner, P., and Seba, P. (1989a). Reports on Mathematical Physics, 28, 7.Google Scholar
  7. Exner, P., and Seba, P. (1989b). Quantum junctions and the self-adjoint extensions theory, in Applications of Self-Adjoint Extensions in Quantum Physics, P. Exner and P. Seba, eds., Springer-Verlag, Berlin.Google Scholar
  8. Exner, P., Seba, P., and Stovicek, P. (1989). Quantum waveguides, in Applications of Self-Adjoint Extensions in Quantum Physics, P. Exner and P. Seba, eds., Springer-Verlag, Berlin.Google Scholar
  9. Fano, G. (1971). Mathematical Methods of Quantum Mechanics, McGraw-Hill, New York.Google Scholar
  10. Feynman, R. P. (1965). The Feynman Lectures of Physics, Vol. III, Addison-Wesley, Reading, Massachusetts, Section 21-9.Google Scholar
  11. Feynman, R. P. (1972). Statistical Mechanics, Benjamin, Reading, Massachusetts, p. 304.Google Scholar
  12. Gough, C. E. (1991). In High Temperature Superconductivity: Proceedings of the 39th Scottish Universities Summer School in Physics, St Andrews, June 1991, D. P. Tunstall and W. Barford, eds., Hilger, Bristol, England, p. 50.Google Scholar
  13. Harrison, F. E. and Wan, K. K. (1997). Journal of Physics A 30, 4731-4755.Google Scholar
  14. Hudson, V., and Pym, S. J. (1980). Applications of Functional Analysis and Operator Theory, Academic Press, London, p. 269.Google Scholar
  15. Josephson, B. D. (1962). Physics Letters 1, 251.Google Scholar
  16. Mandl, F. (1992). Quantum Mechanics, Wiley, New York, Section 2.2.Google Scholar
  17. Reed, M., and Simon, B. (1975). Fourier Analysis, Selfadjointness, Academic Press, New York, pp. 144-145.Google Scholar
  18. Richtmyer, R. D. (1978). Principles of Advanced Mathematical Physics, Vol. 1, Springer-Verlag, New York.Google Scholar
  19. Rose-Innes, A. C., and Rhoderick, E. H. (1969). Introduction to Superconductivity, Pergamon Press, Oxford.Google Scholar
  20. Schroeck, E. F., Jr. (1996). Quantum Mechanics on Phase Space, Kluwer, Dordrecht.Google Scholar
  21. Selleri, F., and Tarozzi, F. (1981). Nuovo Cimento, 4(2).Google Scholar
  22. Tilley, D. R., and Tilley, J. (1990). Superfluidity and Superconductivity, Hilger, Bristol, England, pp. 38-39.Google Scholar
  23. Wan, K. K., and Fountain, R. H. (1996). Foundations of Physics, 26, 1165.Google Scholar
  24. Wan, K. K., and Harrison, F. E. (1993). Physics Letters A, 174, 1.Google Scholar
  25. Wan, K. K., and McLean, D. R. (1984). Journal of Physics A 17, 835, 2363.Google Scholar
  26. Wan K. K., Fountain, R. H., and Tao, Z. Y. (1995). Journal of Physics A 28, 2379.Google Scholar
  27. Weidman, J. (1980). Linear Operators in Hilbert Spaces, Springer-Verlag, New York.Google Scholar
  28. Wheeler, J. A., and Zurek, W. H., eds. (1983). Quantum Theory and Measurement, Princeton University Pres., Princeton, New Jersey.Google Scholar
  29. Wollman, D. A., et al., (1993). Physics Review Letters, 71, 2134.Google Scholar

Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • K. Kong Wan
  • R. H. Fountain

There are no affiliations available

Personalised recommendations