Schrodinger-Langevin Equation and Ion Transport atNano Scale

ABSTRACT

Schrodinger-Langevin equation has been constructed for the ion-transport for K-ion channel. The stability of the solutions of this equation has been discussed under various physical situations. This will shed new light on the ion transport at nano-scale as well as the possibility of ion trapping and quantum information processing.

Schrodinger-Langevin equation has been constructed for the ion-transport for K-ion channel. The stability of the solutions of this equation has been discussed under various physical situations. This will shed new light on the ion transport at nano-scale as well as the possibility of ion trapping and quantum information processing.

KEYWORDS

Schrodinger-Langevin Equation, Stochastic Mechanics, Lyapunov Stability, Ion Transport at Nano Scale

Schrodinger-Langevin Equation, Stochastic Mechanics, Lyapunov Stability, Ion Transport at Nano Scale

Cite this paper

nullS. Bhattacharya, S. Dutta and S. Roy, "Schrodinger-Langevin Equation and Ion Transport atNano Scale,"*Journal of Modern Physics*, Vol. 2 No. 4, 2011, pp. 231-235. doi: 10.4236/jmp.2011.24032.

nullS. Bhattacharya, S. Dutta and S. Roy, "Schrodinger-Langevin Equation and Ion Transport atNano Scale,"

References

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[2] S. Chandrasekhar, “Stochastic Problems in Physics and Astronomy,” Reviews of Modern Physics, Vol. 43, No. 1, 1943, pp 1-89. Hdoi:10.1103/RevModPhys.15.1

[3] J. Messer, “On the Theory of Quantum Mechanical Langevin Systems,” Princeton University Press, Princeton, 1975.

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[6] N. Edward, “Quantum Fluctuations,” Princeton University Press, Princeton, New Jersey, 1985.

[7] L. K. Yu, “Contribution to Plasma Physics,”Introduction in Quantum Theory of Open Systems, Vol. 37, No. 2-3, 1997, pp. 157-166.

[8] H. P. Breuer and F. Petruccione, “Concepts and Methods in the Theory of Open Quantum Systems,” ar-Xiv-ph/ 0302047, 2003.

[9] K. S. Bo-Sture, “Stochastic Mechanics and Dissipative Forces,” Journal of Mathematical Physics, Vol. 18, No. 2, 1977, pp. 308-311.

[10] K. Yasue, “Quantum Mechanics of Non-Conservative Systems,” Annals of Physics, Vol. 114, No.1-2, 1978, pp. 479-496. Hdoi:10.1016/0003-4916(78)90279-8

[11] M. D. Kostin, “On the Schr?dinger-Langevin Equation ”, Journal of Chemical Physics, Vol. 57, No. 9, 1972, pp. 3589-3591. Hdoi:10.1063/1.1678812

[12] P. Van and T. Fül?p, “Stability of Stationary Solutions of the Schr?dinger-Langevin Equation,” arXiv:quant-ph/030 4190v3, 2004.

[13] S. Roy and R. Llinás, “Relevance of Quantum Mechanics on Some Asoect of Ion Channel Function,” C. R. Biologies, Vol. 332, No. 6, 2009 , pp. 517-522.

[14] Y. Zhou, J. H. Morais-Cabral, A. Kaufman and R. Mackinnon, “Chemistry of Ion Coordination and Hydration Revealed by the K+ Selectivity Filter,” Nature, Vol. 414, No. 6859, 2001, pp. 43-48. Hdoi:10.1038/35102009

[15] S. Roy, I. Mitra and R. Llinás, “Non-Markovian Noise Mediated through Anomalous Diffusion within Ion Channels,” Physical Review E, Vol. 78, No. 4, 2008, pp. 041920- 041929. Hdoi:10.1103/PhysRevE.78.041920H

[1] E. B. Davies, “Quantum Theory of Open Systems,” Academic Press, London, 1976.

[2] S. Chandrasekhar, “Stochastic Problems in Physics and Astronomy,” Reviews of Modern Physics, Vol. 43, No. 1, 1943, pp 1-89. Hdoi:10.1103/RevModPhys.15.1

[3] J. Messer, “On the Theory of Quantum Mechanical Langevin Systems,” Princeton University Press, Princeton, 1975.

[4] U. Weiss, “Quantum Dissipative Systems,” World Scientific Publishing Co. Pvt. Ltd, Singapore, 2008.

[5] H. P. Breuer and F. Petruccione, “The Theory of Open Quantum Systems,” Oxford University Press, Inc., NY, 2003.

[6] N. Edward, “Quantum Fluctuations,” Princeton University Press, Princeton, New Jersey, 1985.

[7] L. K. Yu, “Contribution to Plasma Physics,”Introduction in Quantum Theory of Open Systems, Vol. 37, No. 2-3, 1997, pp. 157-166.

[8] H. P. Breuer and F. Petruccione, “Concepts and Methods in the Theory of Open Quantum Systems,” ar-Xiv-ph/ 0302047, 2003.

[9] K. S. Bo-Sture, “Stochastic Mechanics and Dissipative Forces,” Journal of Mathematical Physics, Vol. 18, No. 2, 1977, pp. 308-311.

[10] K. Yasue, “Quantum Mechanics of Non-Conservative Systems,” Annals of Physics, Vol. 114, No.1-2, 1978, pp. 479-496. Hdoi:10.1016/0003-4916(78)90279-8

[11] M. D. Kostin, “On the Schr?dinger-Langevin Equation ”, Journal of Chemical Physics, Vol. 57, No. 9, 1972, pp. 3589-3591. Hdoi:10.1063/1.1678812

[12] P. Van and T. Fül?p, “Stability of Stationary Solutions of the Schr?dinger-Langevin Equation,” arXiv:quant-ph/030 4190v3, 2004.

[13] S. Roy and R. Llinás, “Relevance of Quantum Mechanics on Some Asoect of Ion Channel Function,” C. R. Biologies, Vol. 332, No. 6, 2009 , pp. 517-522.

[14] Y. Zhou, J. H. Morais-Cabral, A. Kaufman and R. Mackinnon, “Chemistry of Ion Coordination and Hydration Revealed by the K+ Selectivity Filter,” Nature, Vol. 414, No. 6859, 2001, pp. 43-48. Hdoi:10.1038/35102009

[15] S. Roy, I. Mitra and R. Llinás, “Non-Markovian Noise Mediated through Anomalous Diffusion within Ion Channels,” Physical Review E, Vol. 78, No. 4, 2008, pp. 041920- 041929. Hdoi:10.1103/PhysRevE.78.041920H