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Advances in Condensed Matter Physics
Volume 2018 (2018), Article ID 1618252, 7 pages
https://doi.org/10.1155/2018/1618252
Research Article

Gravitation at the Josephson Junction

Department of Condensed Matter Physics, Sofia University, 5 Boul. J. Bourchier, 1164 Sofia, Bulgaria

Correspondence should be addressed to Victor Atanasov

Received 3 November 2017; Accepted 21 December 2017; Published 1 February 2018

Academic Editor: Jörg Fink

Copyright © 2018 Victor Atanasov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. B. P. Abbott and LIGO Scientific Collaboration and Virgo Collaboration, “Observation of gravitational waves from a binary black hole merger,” Physical Review Letters, vol. 116, no. 6, p. 061102, 2016. View at Google Scholar
  2. B. P. Abbott and LIGO Scientific Collaboration and Virgo Collaboration, “GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral,” Physical Review Letters, vol. 119, Article ID 161101, 2017. View at Google Scholar
  3. H. Ohanian, Gravitation and Spacetime, p. 271, 1st edition, 1976.
  4. S. Carroll, “Spacetime and Geometry,” p. 144, 2004.
  5. A. Einstein, “Die Grundlage der allgemeinen Relativitätstheorie,” Annalen der Physik (Leipzig), vol. 49, p. 769, 1916. View at Google Scholar
  6. H. Shima, H. Yoshioka, and J. Onoe, “Geometry-driven shift in the Tomonaga-Luttinger exponent of deformed cylinders,” Physical Review B: Condensed Matter and Materials Physics, vol. 79, no. 20, Article ID 201401(R), 2009. View at Publisher · View at Google Scholar
  7. J. Onoe, T. Ito, H. Shima, H. Yoshioka, and S.-I. Kimura, “Observation of Riemannian geometric effects on electronic states,” EPL (Europhysics Letters), vol. 98, no. 2, Article ID 27001, 2012. View at Publisher · View at Google Scholar · View at Scopus
  8. B. Leaf, “Momentum operators for curvilinear coordinate systems,” American Journal of Physics, vol. 47, p. 811, 1979. View at Publisher · View at Google Scholar
  9. Q. H. Liu, J. Zhang, D. K. Lian, L. D. Hu, and Z. Li, “Generalized centripetal force law and quantization of motion constrained on 2D surfaces,” Physica E: Low-dimensional Systems and Nanostructures, vol. 87, pp. 123–128, 2017. View at Publisher · View at Google Scholar · View at Scopus
  10. B. De Witt, “Point transformations in quantum mechanics,” Physical Review, vol. 85, p. 635, 1952. View at Google Scholar
  11. P. J. Camp and J. L. Safko, “Quantization conditions in curved spacetime and uncertainty-driven inflation,” International Journal of Theoretical Physics, vol. 39, no. 6, pp. 1643–1668, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  12. N. D. Birrell and P. C. W. Davies, Quantum Fields in Curved Space, Cambridge University Press, Cambridge, UK, 1982. View at MathSciNet
  13. S. Hollands and R. M. Wald, “Quantum fields in curved spacetime,” Physics Reports, vol. 574, pp. 1–35, 2015. View at Publisher · View at Google Scholar · View at Scopus
  14. R. M. Wald, Quantum field theory in Curved Spacetime and Black Hole Thermodynamics, University of Chicago Press, Chicago, Ill, USA, 1994.
  15. H. Jensen and H. Koppe, “Quantum mechanics with constraints,” Annals of Physics, vol. 63, no. 2, pp. 586–591, 1971. View at Publisher · View at Google Scholar · View at Scopus
  16. L. C. da Silva, C. C. Bastos, and F. G. Ribeiro, “Quantum mechanics of a constrained particle and the problem of prescribed geometry-induced potential,” Annals of Physics, vol. 379, pp. 13–33, 2017. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. R. C. da Costa, “Quantum mechanics of a constrained particle,” Physical Review. A. General Physics. Third Series, vol. 23, no. 4, pp. 1982–1987, 1981. View at Publisher · View at Google Scholar · View at MathSciNet
  18. F. T. Brandt and J. A. Sánchez-Monroy, “Quantum dynamics of spinless particles on a brane coupled to a bulk gauge field,” Classical and Quantum Gravity, vol. 34, no. 7, p. 075010, 2017. View at Google Scholar · View at MathSciNet
  19. N. Ogawa, K. Fujii, and A. Kobushukin, “Quantum mechanics in Riemannian manifold,” Progress of Theoretical and Experimental Physics, vol. 83, no. 5, pp. 894–905, 1990. View at Publisher · View at Google Scholar · View at MathSciNet
  20. J. Goldstone and R. L. Jaffe, “Bound states in twisting tubes,” Physical Review B: Condensed Matter and Materials Physics, vol. 45, no. 24, pp. 14100–14107, 1992. View at Publisher · View at Google Scholar · View at Scopus
  21. G.-H. Liang, Y.-L. Wang, L. Du, H. Jiang, G.-Z. Kang, and H.-S. Zong, “Coherent electron transport in a helical nanotube,” Physica E: Low-dimensional Systems and Nanostructures, vol. 83, pp. 246–255, 2016. View at Publisher · View at Google Scholar · View at Scopus
  22. P. Duclos, P. Exner, and D. Krejcirik, “Bound states in curved quantum layers,” Communications in Mathematical Physics, vol. 223, no. 1, pp. 13–28, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  23. P. C. Schuster and R. L. Jaffe, “Quantum mechanics on manifolds embedded in Euclidean space,” Annals of Physics, vol. 307, no. 1, pp. 132–143, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  24. R. Pincak and J. Smotlacha, “The chiral massive fermions in the graphitic wormhole,” Quantum Matter, vol. 5, p. 107, 2016. View at Publisher · View at Google Scholar
  25. G. G. Naumis, “Electronic and optical properties of strained graphene and other strained 2D materials: a review,” Reports on Progress in Physics, vol. 80, p. 096501, 2017. View at Google Scholar
  26. U. Muller, C. Schubert, and A. E. M. van de Ven, “A closed formula for the Riemann normal coordinate expansion,” General Relativity and Gravitation, vol. 31, no. 11, pp. 1759–1768, 1999. View at Publisher · View at Google Scholar · View at MathSciNet
  27. G. Herglotz, “Über die Bestimmung eines Linienelementes in Normalkoordinaten aus dem Riemannschen Krümmungstensor,” Mathematische Annalen, vol. 93, p. 46, 1925. View at Google Scholar
  28. R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics, Volume III, Addison-Wesley, Reading, Mass, USA, 1963.
  29. D. Bohm, “A Suggested Interpretation of the Quantum Theory in Terms of “Hidden” Variables. I,” Physical Review A: Atomic, Molecular and Optical Physics, vol. 85, p. 166, 1952. View at Google Scholar
  30. D. Bohm, “A Suggested Interpretation of the Quantum Theory in Terms of “Hidden” Variables. II,” Physical Review A: Atomic, Molecular and Optical Physics, vol. 85, p. 180, 1952. View at Google Scholar
  31. F. London, “On the problem of the molecular theory of superconductivity,” Physical Review A: Atomic, Molecular and Optical Physics, vol. 74, no. 5, pp. 562–573, 1948. View at Publisher · View at Google Scholar · View at Scopus
  32. J. Bardeen, L. N. Cooper, and J. R. Schrieffer, “Theory of superconductivity,” Physical Review Letters, vol. 108, pp. 1175–1204, 1957. View at Publisher · View at Google Scholar · View at MathSciNet
  33. R. G. Sharma, “A Review of Theories of Superconductivity,” in Superconductivity, vol. 214 of Springer Series in Materials Science, pp. 109–133, Springer International Publishing, Cham, Switzerland, 2015. View at Publisher · View at Google Scholar
  34. L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields, Pergamon, Oxford, UK, 1975. View at MathSciNet
  35. V. Atanasov, “The geometric field (gravity) as an electro-chemical potential in a Ginzburg-Landau theory of superconductivity,” Physica B: Condensed Matter, vol. 517, pp. 53–58, 2017. View at Publisher · View at Google Scholar · View at Scopus
  36. V. Atanasov, “Gravity at a quantum condensate,” Journal of the Physical Society of Japan, vol. 86, p. 074004, 2017. View at Google Scholar
  37. D. K. Ross, “The London equations for superconductors in a gravitational field,” Journal of Physics A: Mathematical and General, vol. 16, no. 6, pp. 1331–1335, 1983. View at Publisher · View at Google Scholar · View at MathSciNet
  38. M. Liu, “Rotating superconductors and the frame-independent London equation,” Physical Review Letters, vol. 81, p. 3223, 1998. View at Google Scholar
  39. E. M. Lifshitz and L. P. Pitaevskii, “Statistical Physics, Part 2: Theory of the Condensed State,” in Butterworth-Heinemann, vol. 9, Part 2, Theory of the Condensed State, 1st edition, 1980. View at Google Scholar
  40. D. Giulini, Canonical Gravity, and 16th Saalburg Summer School, Fundamentals and New Methods in Theoretical Physics, Wolfersdorf, Germany, 2010.