All Title Author
Keywords Abstract


On the Quantum Zeno Effect and Time Series Related to Quantum Measurements

DOI: 10.4236/am.2013.410A3008, PP. 61-69

Keywords: Quantum Zeno Effect, Quantum Measurements, Time Series

Full-Text   Cite this paper   Add to My Lib

Abstract:

Our main aim is to prove a more general version of the quantum Zeno effect. Then we discuss some examples of the quantum Zeno effect. Furthermore, we discuss a possibility that based on the quantum Zeno effect and certain experiments one could check whether, from the statistical point of view, a concrete system behaves like a quantum system. The more general version of quantum Zeno effect can be helpful to prove that the brain acts like in a quantum system. The proof of our main result is based on certain formulas describing probability distributions of time series related to quantum measurements.

References

[1]  E. C. G. Sudarshan and B. Misra, “The Zeno’s Paradox in Quantum Theory,” Journal of Mathematical Physics, Vol. 18, No. 4, 1977, pp. 756-763.
[2]  T. Nakanishi, K. Yamane and M. Kitano, “AbsorptionFree Optical Control of Spin Systems: The Quantum Zeno Effect in Optical Pumping,” Physical Review A, Vol. 65, No. 1, 2001, Article ID: 013404.
http://dx.doi.org/10.1103/PhysRevA.65.013404
[3]  P. Facchi, D. A. Lidar and S. Pascazio, “Unification of Dynamical Decoupling and the Quantum Zeno Effect,” Physical Review A, Vol. 69, No. 3, 2004, Article ID: 032314.
http://dx.doi.org/10.1103/PhysRevA.69.032314
[4]  A. Degasperis, L. Fonda and G. C. Ghirardi, “Does the Lifetime of an Unstable System Depend on the Measuring Apparatus?” Il Nuovo Cimento A Series 11, Vol. 21, No. 3, 1974, pp. 471-484.
http://dx.doi.org/10.1007/BF02731351
[5]  C. Teuscher and D. Hofstadter, “Alan Turing: Life and Legacy of a Great Thinker,” Springer, Berlin, Heidelberg, 2004.
http://dx.doi.org/10.1007/978-3-662-05642-4
[6]  J. von Neumann, “Mathematische Grundlagen der Quantenmechanik,” Springer, Berlin, Heidelberg, 1932.
[7]  K.-H. Fichtner and L. Fichtner, “Bosons and a quantum model of the brain, Jenaer Schriften zur Mathematik und Informatik,” Math/Inf/08/05, Faculty of Mathematics and Informatics, FSU Jena, Jena, 2005, 27 p.
[8]  K.-H. Fichtner and L. Fichtner, “Quantum Models of Brain Activities I—Recognition of Signals,” In: J. C. Garcia, R. Quezada and S. B. Sontz, Eds., Quantum Probability and Related topics, XXIII of QP-PQ: Quantum Probability and White Noise Analysis, World Scientific, New Jersey, London, Singapore, 2008, pp. 135-144.
[9]  K.-H. Fichtner, L. Fichtner, W. Freudenberg and M. Ohya, “On a Mathematical Model of Brain Activities,” Quantum Theory, Reconsideration of Foundations-4, 962 of AIP Conference Proceedings, American Institute of Physics, Melville, New York, 2007, pp. 85-90.
[10]  K.-H. Fichtner, L. Fichtner, W. Freudenberg and M. Ohya, “On a Quantum Model of the Recognition Process,” In: L. Accardi, W. Freudenberg and M. Ohya, Eds., Quantum Bio-Informatics, XXI of QP-PQ: Quantum Probability and White Noise Analysis, World Scientific, New Jersey, London, Singapore, 2008, pp. 64-84.
[11]  K.-H. Fichtner, L. Fichtner, W. Freudenberg and M. Ohya, “On a Quantum Model of the Brain Activities,” In: L. Accardi, W. Freudenberg and M. Ohya, Eds., Quantum Bio-Informatics III, XXVI of QP-PQ: Quantum Probability and White Noise Analysis, World Scientific, New Jersey, London, Singapore, 2010, pp. 81-92.
[12]  K.-H. Fichtner, L. Fichtner, W. Freudenberg and M. Ohya, “Quantum Models of the Recognition Process—On a Convergence Theorem,” Open Systems and Information Dynamics, Vol. 17, No. 2, 2010, pp. 161-187.
http://dx.doi.org/10.1142/S1230161210000114
[13]  K.-H. Fichtner, L. Fichtner, W. Freudenberg and M. Ohya, “Self-Collapses of Quantum Systems and Brain Activities,” In: L. Accardi, W. Freudenberg and M. Ohya, Eds., Quantum Bio-Informatics IV, XXVIII of QP-PQ: Quantum Probability and White Noise Analysis, World Scientific, New Jersey, London, Singapore, 2011, pp. 101-115.
[14]  K.-H. Fichtner, L. Fichtner, K. Inoue and M. Ohya, “Internal Noise Caused by the Memory,” Open Systems and Information Dynamics, Vol. 18, No. 4, 2011, pp. 405-422.
http://dx.doi.org/10.1142/S1230161211000285
[15]  K.-H. Fichtner, K. Inoue and M. Ohya, “On a Quantum Model of Brain Activities—Distribution of the Outcomes of EEG-Measurements and Random Point Fields,” Open Systems and Information Dynamics, Vol. 19, No. 4, 2012, Article ID: 1250025.
[16]  J. M. Schwartz, H. P. Stapp and M. Beauregard, “Quantum Physics in Neuroscience and Psychology: A Neurophysical Model of Mind-Brain Interaction,” Philosophical Transactions of the Royal Society of London B, Vol. 360, No. 1458, 2005, pp. 1309-1327.
http://dx.doi.org/10.1098/rstb.2004.1598
[17]  R. Penrose, “The Emperor’s New Mind: Concerning Computers, Minds and The Laws of Physics,” Oxford University Press, Oxford, 1989.
[18]  S. Hameroff and R. Penrose, “Orchestrated Objective Reduction of Quantum Coherence N Brain Microtubules: The ‘Orch OR’ Model Forconsciousness,” Mathematics and Computer Simulation, Vol. 40, No. 3-4, 1996, pp. 453-480. http://dx.doi.org/10.1016/0378-4754(96)80476-9
[19]  R. Hari and O. V. Lounasmaa, “Neuromagnetism: Tracking the Dynamics of the Brain,” Physics World, Vol. 13, 2000, pp. 33-38.
[20]  W. Tirsch, “Biomedizinische Relevanz der quantitativen EEG Analyse,” LMU München, München, 2009.
[21]  K.-H. Fichtner, “Time Series Related to Quantum Measurements and the Quantum Zenon Effect,” Jenaer Schriften zur Mathematik und Informatik, Math/Inf/02/ 2012, Faculty of Mathematics and Informatics, FSU Jena, Jena, 2012, 15 p.
[22]  M. Asano, M. Ohya, Y. Tanaka, A. Khrennikov and I. Basieva, “Quantum Like Representation of Baysian Updating,” American Institute of Physics, Vol. 1327, No. 1, 2011, pp. 57-62.
[23]  M. Asano, I. Basieva, A. Khrennikov, M. Ohya and I. Yamato, “A General Quantum Information Model for the Contextual Dependent Systems Breaking the Classical Probability Law,” ArXiv:1105.4769v1(quant-ph), 21 May 2011.

Full-Text

comments powered by Disqus