Quantum Graphs : Physics of Quantum Singularity (8-1)
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Summary and Prospects
In this lecture, we have seen that there are a family of point interactions generated by quantum mechanical anomaly that has no correspondance in classical analogue which exists only in the form of inpenetrable wall. The nontrivial geometrical structure describing this family of point interactions results in several very intriguing features in the quantum systems with point interactions. Moreover, it has been revealed that in dealing with singular object of point-like potential, we had to abondon usually unquestioned assumptions of quantum physics and return to the question von Neumann had asked; what is the minimal requirement sastidfied by quantum state?
Here, we also would like to attract the readers attention to the pedagogical value of the system under study. All students of quantum physics can reacall having faced the steep gap in mathematical and physical sophistication in the learning process between the elementary quantum mechanics and quantum field theory. Having an example of a technically simple quantum system posessing advanced topological aspects of quantum field theory would no doubt let us go some way to mitigate that gap.
If we can once estabish a way to experimentally controll the system that amounts to the desired transport in parameter space, we shall learn to activate a part of the quantum mystery in the real-world experiment. It could then be said that what we are observing now is the transformation process of the quantum mechnaics of 20th century that has been a science of the description of exising being to that of 21st centur that is the art of designing realizable quantum intrigues.
Lastly, we leave the interested readers with materials for further studies.
Reviews for general readership
[1] T. Cheon, Bessatsu Suuri Kagaku, Apr., 2000, pp 140-150.
[2] I. Tsutsui, Suuri Kagaku, Jul. 2001, pp 12-19.
Original Papers
T. Cheon and T. Shigehara, Phys. Rev. Lett. 82 (1999) 2539-2542.
T. Fulop and I. Tsutsui, Phys. Lett. A264 (2000) 366-374.
T. Cheon, T. Fulop and I. Tsutsui, Ann. of Phys. 294 (2001) 1-23.
I. Tsutsui, T. Fulop and T. Cheon, J. Math. Phys.42 (2001) 5687-5697.
P. Hejcik and T. Cheon, Phys. Lett. A356 (2006) 290-293.
Websites
http://www.mech.kochi-tech.ac.jp/cheon/ That is here!
http://research.kek.jp/people/itsutsui/ This is by Dr. Izumi Tsutsui at KEK.
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