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

Piero Chiarelli

doi:doi:10.11648/j.ajpc.20130206.12

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

Piero Chiarelli

Published in American Journal of Physical Chemistry (Volume 2, Issue 6)

Received: 21 November 2013 Accepted: 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
Creative Commons	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), 2024. 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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TY  - JOUR
T1  - The Quantum Potential: The Missing Interaction in the Density Maximum of He4 at the Lambda Point
AU  - Piero Chiarelli
Y1  - 2013/12/10
PY  - 2013
N1  - https://doi.org/10.11648/j.ajpc.20130206.12
DO  - 10.11648/j.ajpc.20130206.12
T2  - American Journal of Physical Chemistry
JF  - American Journal of Physical Chemistry
JO  - American Journal of Physical Chemistry
SP  - 122
EP  - 131
PB  - Science Publishing Group
SN  - 2327-2449
UR  - https://doi.org/10.11648/j.ajpc.20130206.12
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
IS  - 6
ER  -

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Author Information

Piero Chiarelli

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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APA Style

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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
T1  - The Quantum Potential: The Missing Interaction in the Density Maximum of He4 at the Lambda Point
AU  - Piero Chiarelli
Y1  - 2013/12/10
PY  - 2013
N1  - https://doi.org/10.11648/j.ajpc.20130206.12
DO  - 10.11648/j.ajpc.20130206.12
T2  - American Journal of Physical Chemistry
JF  - American Journal of Physical Chemistry
JO  - American Journal of Physical Chemistry
SP  - 122
EP  - 131
PB  - Science Publishing Group
SN  - 2327-2449
UR  - https://doi.org/10.11648/j.ajpc.20130206.12
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
IS  - 6
ER  -

Copy | Download