Abstract
The detection of the number of extra–compact dimensions contained in some gravitational models is analyzed resorting to the discontinuity of the specific heat at the critical temperature of a Bose–Einstein condensate. It is shown that the function relating the number of particles and this discontinuity defines a segment of a straight line whose slope depends upon the number of extra–compact dimensions. The experimental feasibility of the proposal is also considered.
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References
Amelino-Camelia, G.: Quantum-Spacetime Phenomenology. Living Rev. Relativ. 16, 5 (2013)
Stachel, J.: The Early History of Quantum Gravity (1916–1940). In: Iyer, B.R., Bhawal, B. (eds.) Black Holes, Gravitational Radiation and the Universe: Essays in Honour of C. V. Vishveshwara, pp. 525–535. Kluwer, Boston (1999)
Amelino–Camelia, G.: Are we at the dawn of quantum, gravity phenomenology? In: Kowalski–Glikman, G. (ed.) Proceedings of the XXXV International Winter School on Theoretical Physics, Polanica, Poland, pp. 1–44. Springer, Berlin (2000)
Kane, G.: How could (should) we make contact between string/M theory and our four-dimensional world? In: Acharya, B., Kane, G., Kumar, P. (eds.) Perspectives on String Phenomenology, World Scientific Publishing Co., pp. 325–350. Singapore (2015)
Zwiebach, B.: A First Course in String Theory. Cambridge University Press, Cambridge (2009)
Griffin, A., Nikuni, T., Zaremba, E.: Bose-Condensed Gases at Finite Temperatures. Cambridge University Press, Cambridge (2009)
Landsberg, P.T.: Thermodynamics and Statistical Mechanics. Dover Publications Inc., New York (1990)
Andrews, M., et al.: Propagation of sound in a Bose-Einstein Condensate. Phys. Rev. Lett. 79, 553 (1997)
Amelino-Camelia, G., Loret, N., Mandanici, G., Mercati, F.: Gravity in quantum space-time. Int. J. Mod. Phys. D 19, 2385 (2010)
Schiff, L.I.: Quantum Mechanics. McGraw-Hill, New York (1968)
Pethick, C.J., Smith, H.: Bose-Einstein Condensation in Dilute Gases. Cambridge University Press, Cambridge (2008)
Stoof, H.T.C., Dickercheid, D.B.M., Gubbles, K.: Ultra-Cold Quantum Fields. Springer, Dordrecht (2009)
Ueda, M.: Fundamentals and New Frontiers of Bose-Einstein Condensation. World Scientific, Singapore (2010)
Pathria, R.K.: Statistical Mechanics. Butterworth–Heinemann, Oxford (1996)
Pitaevskii, L., Stringari, S.: Bose-Einstein Condensation. Oxford Science Publications, Oxford (2003)
Mullin, W.J.: Bose-Einstein condensation in a harmonic trap. J. Low Temp. Phys. 106, 615–641 (1997)
Lieb, E.H., Seiringer, R., Solovej, J.P., Yngvason, J.: The Mathematics of the Bose Gas and its Condensation. Birkhšäuser-Verlag, Berlin (2005)
Noziéres, P., Pine, D.: The Theory of Quantum Liquids, vol. II. Westview Press, Boulder (1999)
Ensher, J.R., et al.: Bose-Einstein condensation in a dilute gas: Measurement of ground-state occupation. Phys. Rev. Lett. 77, 4984–4987 (1996)
Hull, R.A., Wilkinson, K.R., Wilks, J.: Using Na J-crystal Scintillation counters for y-ray energy discrimination. Proc. Phys. Soc. A 64, 379–388 (1951)
Myatt, C.J.: Ph.D. thesis, University of Colorado (1997)
Chapovsky, P.L.: Bose-Einstein condensation of rubidium atoms. JETP Lett. 95, 132–136 (2012)
Cornish, S.L., Cassettari, D.: Recent progress in Bose-Einstein condensation experiments. Philos. Trans. R. Soc. A 361, 2699–2713 (2003)
Donley, E.A., et al.: Dynamics of collapsing and exploding Bose-Einstein condensates. Nature 412, 295–299 (2001)
Berlinsky, A.J., Harris, A.B.: Statistical Mechanics. An Introductory Graduate Course. Springer, Berlin (2019)
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H. R. acknowledges CONACyT grant No. 596978 and S. G. the received UAM grant.
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Gutiérrez, S., Camacho, A. & Ríos, H. Ultra–Cold Many–Body Systems and Phenomenology of Gravity Theories with Compact Dimensions. Found Phys 53, 25 (2023). https://doi.org/10.1007/s10701-022-00665-8
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DOI: https://doi.org/10.1007/s10701-022-00665-8