Nonlinear Liouville Equation and Information Soliton


In this work, some types of nonlinear Liouville equation (NLE) and nonlinear Master equations (NME) are studied. We found that the nonlinear terms in the equation can resist state of system damping so that an information solitonic structure appears. Furthermore, the power in the non-linear term is independent of limitation of the solution. This characteristic offers a possibility to construct complicated information solitons from some simple solutions, which allow one to solve complicated NLE or NME. The results obtained in this work may provide an innovated channel for the quantum information transmission over far distance against dissipation and decoherence, and also open a constructive way to resist age decaying of system by designing adjusted field interaction with the system nonlinearly.

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Qiao, B. (2015) Nonlinear Liouville Equation and Information Soliton. Journal of Modern Physics, 6, 2058-2069. doi: 10.4236/jmp.2015.614212.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Simon, D.R. (1997) SIAM Journal on Computing, 26, 1474.
[2] Shor, P.W. (1997) SIAM Journal on Computing, 26, 1484.
[3] Wiesner, S. (1983) Sigact News, 15, 78.
[4] Bennett, C., Bessette, F., Brassard, G., Salvail, L. and Smolin, J. (1992) Journal of Cryptology, 5, 3.
[5] Shor, P.W. (1994) Proceedings of the 35th Annual Symposium on Foundations of Computer Science, Santa Fe, 124.
[6] Deutch, D. (1985) Proceedings of the Royal Society of London A, 425, 73.
[7] Qiao, B., Song, K.Z. and Ruda, H.E. (2013) Journal of Modern Physics, 4, 49-55.
[8] Qiao, B., Fang, J.Q. and Ruda, H.E. (2012) Journal of Modern Physics, 3, 1070-1080.
[9] Grover, L. (1995) A Fast Quantum Mechanical Algorithm for Data Base Search. Proceedings of the 28th Annual ACM Symposium on the Theory of Computation, ACM Press, New York, 212.
[10] Tomonaga, S. (1946) Progress of Theoretical Physics, 1, 27.
[11] Breuer, H.P. (2002) The Theory of Quantum Open Systems. Oxford University Press, New York.
[12] Schweber, S.S. (1948) An Introduction to Relativistic Quantum Field Theory. Row, Peterson and Company, Evanston.
[13] Schwinger, J. (1948) Physical Review, 74, 1439-1461.
[14] Prugovecki, E. (1995) Principles of Quantum General Relativity. World Scientific Publishing, Co. Pte. Ltd., Singapore.
[15] Giulini, D., Kiefer, C. and Lämmerzahl, C. (2003) Quantum Gravity: From Theory to Experimental Search. Springer-Verlag, New York.
[16] Qiao, B. and Song, K.Z. (2013) Journal of Modern Physics, 4, 923-929.
[17] Pang, X.-F. and Feng, Y.-P. (2005) Quantum Mechanics in Nonlinear Systems. World Scientific Publishing, Co. Pte. Ltd., Singapore.
[18] Eu, B.C. (1998) Nonequilibrium Statistical Mechanics (Ensemble Method). Kluwer Academic Publishers, Dordrecht, Boston and London.
[19] Fan, S.Y. (2010) Quantum Decoherent Entangled States in Open System. Shanghai Jiao Tong University Press, Shanghai. (In Chinese)
[20] Takahashi, Y. and Umezawa, H. (1957) Collective Phenomena, 2, 55.
[21] Umezawa, H. (1993) Advanced Field Theory-Micro, and Thermal Physics. AIP, New York.
[22] Chrusciński, D., Kossakowski, A. and Pascazio, S. (2010) Physical Review A, 81, Article ID: 032101.
[23] Brown, D.W. and Lindenberg, K. (1998) Physica D, 113, 267-275.
[24] Gisin, N. and Rigo, M. (1995) Journal of Physics A, 28, 7375-7390.
[25] Prigogine, I. and Nicolis, G. (1977) Self-Organization in Non-Equilibrium Systems. Wiley, New York.
[26] Prigogine, I. (1980) From Being to Becoming. W.H. Freeman, San Francisco.

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