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The Quantum Potential: The Missing Interaction in the Density Maximum of He4 at the Lambda Point

Received: 21 November 2013     Published: 10 December 2013
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Abstract

The lambda point in liquid He4 is a well established phenomenon acknowledged as an example of Bose-Einstain condensation. This is generally accepted, but there are serious discrepancies between the theory and experimental results, namely the lower value of the transition temperature T and the negative value of dT /dP. These discrepancies can be explained in term of the quantum stochastic hydrodynamic analogy (SQHA). The SQHA shows that at the He4IHe4II superfluid transition the quantum coherence length c becomes of order of the distance up to which the wave function of a couple of He4 atoms extends itself. In this case, the He42 state is quantum and the quantum pseudo-potential brings a repulsive interaction that leads to the negative dT /dP behavior. This fact overcomes the difficulty to explain the phenomenon by introducing a Hamiltonian inter-atomic repulsive potential that would obstacle the gas-liquid transition.

Published in American Journal of Physical Chemistry (Volume 2, Issue 6)
DOI 10.11648/j.ajpc.20130206.12
Page(s) 122-131
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This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2013. Published by Science Publishing Group

Keywords

Lambda Point, Liquid He4, Maximum Density, Low Temperature Critical Dynamics, Ballistic to Diffusive Transition, Anomalous Transport

References
[1] F. London, Nature 141 (1938) 643.
[2] P. Papon, J. Leblon, P.H.E. Meijer, The Physics of Phase Transition, Springer-Verlagh, Berlin, 2002.
[3] A. M. Guenault, Statistical Physics, Kluwer Academic, Dordrecht, 1995.
[4] R.P. Feynman, Phys. Rev, 91 (1953) 1291.
[5] S.T. Butler, M.H. Friedman, Phys. Rev. 98 (1955) 287.
[6] ibid [5] p. 294.
[7] D. ter Haar, Phys. Rev. 95 (1954) 895.
[8] F.A: Deeney, J.P.O’Leary, P. O’Sullivan, Phys. Lett. A 358 (2006) 53.
[9] Weiner, J.H., Statistical Mechanics of Elasticity (John Wiley & Sons, New York, 1983), p. 317.
[10] P.Chiarelli, "Can fluctuating quantum states acquire the classical behavior on large scale?" J. Adv. Phys. 2013; 2, 139-163 ; arXiv: 1107.4198 [quantum-phys] 2012.
[11] Ibid [9] p. 315.
[12] Ibid [9] p. 406.
[13] Y. B. Rumer, M. S. Ryvkin, Thermodynamics, Statistical Physics, and Kinetics (Mir Publishers, Moscow, 1980), p. 333.
[14] ibid [13] p. 334.
[15] ibid [13] p. 56.
[16] J. B. Anderson, C. A. Traynor and B. M. Boghosian, J. Chem. Phys. 99 (1), 345 (1993).
[17] R.A. Aziz and M.A. Slaman, Metrologia 27, 211 (1990).
[18] Teragon Research 2518 26th Avenue San Francisco, CA 94116, http://www.trgn.com/database/cryogen.html;
[19] S. Noegi and G.D. Mahan, arXiv:0909.3078v1 (2009).
[20] R. J. Donnelly and C. F. Barenghi, "The observed properties of liquid Helium at the saturated vapor pressure"; http://darkwing.uoregon.edu/~rjd/vapor1.htm.
[21] ibid [13] p. 325.
[22] ibid [13] p. 260.
[23] F. A. Deeney, J.P O'Leary, 2012; Eur. J. Phys. 33 677 doi:10.1088/0143-0807/33/3/677;
[24] Chiarelli, P.," Quantum to Classical Transition in the Stochastic Hydrodynamic Analogy: The Explanation of the Lindemann Relation and the Analogies Between the Maximum of Density at He Lambda Point and that One at Water-Ice Phase Transition", Physical Review & Research International, 2013; 3(4): 348-66.
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    Piero Chiarelli. (2013). The Quantum Potential: The Missing Interaction in the Density Maximum of He4 at the Lambda Point. American Journal of Physical Chemistry, 2(6), 122-131. https://doi.org/10.11648/j.ajpc.20130206.12

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    ACS Style

    Piero Chiarelli. The Quantum Potential: The Missing Interaction in the Density Maximum of He4 at the Lambda Point. Am. J. Phys. Chem. 2013, 2(6), 122-131. doi: 10.11648/j.ajpc.20130206.12

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    AMA Style

    Piero Chiarelli. The Quantum Potential: The Missing Interaction in the Density Maximum of He4 at the Lambda Point. Am J Phys Chem. 2013;2(6):122-131. doi: 10.11648/j.ajpc.20130206.12

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  • @article{10.11648/j.ajpc.20130206.12,
      author = {Piero Chiarelli},
      title = {The Quantum Potential: The Missing Interaction in the Density Maximum of He4 at the Lambda Point},
      journal = {American Journal of Physical Chemistry},
      volume = {2},
      number = {6},
      pages = {122-131},
      doi = {10.11648/j.ajpc.20130206.12},
      url = {https://doi.org/10.11648/j.ajpc.20130206.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajpc.20130206.12},
      abstract = {The lambda point in liquid He4 is a well established phenomenon acknowledged as an example of Bose-Einstain condensation. This is generally accepted, but there are serious discrepancies between the theory and experimental results, namely the lower value of the transition temperature T and the negative value of dT /dP. These discrepancies can be explained in term of the quantum stochastic hydrodynamic analogy (SQHA). The SQHA shows that at the He4IHe4II superfluid transition the quantum coherence length c becomes of order of the distance up to which the wave function of a couple of He4 atoms extends itself. In this case, the He42 state is quantum and the quantum pseudo-potential brings a repulsive interaction that leads to the negative dT /dP behavior. This fact overcomes the difficulty to explain the phenomenon by introducing a Hamiltonian inter-atomic repulsive potential that would obstacle the gas-liquid transition.},
     year = {2013}
    }
    

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    T2  - American Journal of Physical Chemistry
    JF  - American Journal of Physical Chemistry
    JO  - American Journal of Physical Chemistry
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    AB  - The lambda point in liquid He4 is a well established phenomenon acknowledged as an example of Bose-Einstain condensation. This is generally accepted, but there are serious discrepancies between the theory and experimental results, namely the lower value of the transition temperature T and the negative value of dT /dP. These discrepancies can be explained in term of the quantum stochastic hydrodynamic analogy (SQHA). The SQHA shows that at the He4IHe4II superfluid transition the quantum coherence length c becomes of order of the distance up to which the wave function of a couple of He4 atoms extends itself. In this case, the He42 state is quantum and the quantum pseudo-potential brings a repulsive interaction that leads to the negative dT /dP behavior. This fact overcomes the difficulty to explain the phenomenon by introducing a Hamiltonian inter-atomic repulsive potential that would obstacle the gas-liquid transition.
    VL  - 2
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Author Information
  • National Council of Research of Italy, Interdepartmental Center “E.Piaggio” University of Pisa, Area of Pisa, 56124 Pisa, Moruzzi 1, Italy

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