Gas in external fields: the weird case of the logarithmic trap

References

• D.E. Pritchard, Cooling neutral atoms in a magnetic trap for precision spectroscopy, Phys. Rev. Lett.51(15) (1983), pp. 1336–1339. DOI: 10.1103/PhysRevLett.51.1336Bibcode:1983PhRvL..51.1336P.
   Web of Science ®Google Scholar
• J.J. Tollett, C.C. Bradley, C.A. Sackett, and R.G. Hulet, Permanent magnet trap for cold atoms, Phys. Rev. A. 51 (1995), pp. R22–R25.
   PubMed Web of Science ®Google Scholar
• V. Vuletic, T. Hnsch, and C. Zimmermann, Steep magnetic trap for ultra cold atoms, Europhys. Lett.36 (1996), pp. 349–354.
   Google Scholar
• J. Fortgh and C. Zimmermann, Magnetic microtraps for ultra cold atoms, Rev. Mod. Phys. 79 (2007), pp. 235–289.
   Web of Science ®Google Scholar
• J. Pérez-Ríos and A.S. Sanz, How does a magnetic trap work? Am. J. Phys. 81 (2013), pp. 836–843.
   Web of Science ®Google Scholar
• V. Romero and S. Bagnato, Thermodynamics of an ideal gas of bosons harmonically trapped: Equation of state and susceptibilities, Braz. J. Phys. 35 (2005), pp. 607–613. See, for instance.
   Web of Science ®Google Scholar
• W.D. Phillips, Laser cooling and trapping of neutral atoms, Rev. Mod. Phys. 70 (1988), pp. 721–741.
   Google Scholar
• K.B. Davis, M-O. Mewes, M.R. Andrews, N.J. van Druten, D.S. Dufree, D.M. Kurm, and W. Ketterle, Bose–Einstein condensation in a gas of sodium atoms, Phys. Rev. Lett. 75 (1995), pp. 3969–3973.
   PubMed Web of Science ®Google Scholar
• C.C. Bradley, C.A. Sackett, J.J. Tollett, and R.G. Hulet, Evidence of Bose–Einstein condensation in an atomic gas with attractive interactions, Phys. Rev. Lett 75 (1995), pp. 1687–1690.
   PubMed Web of Science ®Google Scholar
• K. Frye, S. Abend, and W. Barttosch, The Bose–Einstein condensate and cold atom laboratory, Eur. Phys. J. Quantum Technol. 8 (2021). DOI: 10.1140/epjqt/s40507-020-00090-8
   Google Scholar
• H. Mütinga et al., Interferometry with Bose–Einstein condensates in microgravity, Phys. Rev. Lett. 110 (2013), pp. 093602–093607.
   PubMed Web of Science ®Google Scholar
• O. Carraz, C. Siemes, L. Massotti, R. Hiagmans, and P. Silvestrin, A spaceborn gravity gradiometer concept based on cold atom interferometers for measuring Eath's gravity field. arXiv preprint arXiv: 1406.0765v2 [phys-atom-ph] (2014).
   Google Scholar
• M. Meister, A. Roura, E.M. Rasel, and W.P. Schich, The space atom laser: An isotropic souce for ultra-cold atoms in microgravity, New J. Phys. 21 (2019), pp. 013039–013063.
   Web of Science ®Google Scholar
• T. Bravo, D. Rätzel, and I. Fuentes, Phononic gravity gradiometry with Bose–Einstein condensates. arXiv preprint arXiv:2001.10104v2 [quant-phis] (2020).
   Google Scholar
• V. Bagnato, D.F. Pritchard, and D. Kleppner, Bose–Einstein condensation in an external potential, Phys. Rev. A. 35 (1987), pp. 4354–4358.
   PubMed Web of Science ®Google Scholar
• R.M. Cavalcanti, P. Giacconi, G. Pupillo, and R. Soldati, Bose–Einstein condensation in the presence of a uniform field and a pointloke impurity, Phy. Rev. A. 65 (2002), pp. 0536056–0536063.
   Web of Science ®Google Scholar
• R.H. Hooverman, Charged particles orbits in a logarithmic potential, J. Appl. Phys. 34 (1963), pp. 3505–3508.
   Web of Science ®Google Scholar
• Y. Muraki, A new mass formula of elementary particles, Progr. Theor. Phys. 41 (1969), pp. 473–478.
   Google Scholar
• Y. Muraki, K. Mori, and N. Nakagawa, Logarithmic mass formula for elementary particles and a new quantum number, N. Cim. 23 (1978), pp. 27–31.
   Google Scholar
• K. Paasch, The logarithmic potential and an exponential mass function for elementary particles, Prog. Phys. 1 (2009), pp. 36–39.
   Google Scholar
• A. Dechant, E. Lutz, E. Barkai, and D.A. Kessler, Solution of the Fokker–Planck equation with a logarithminc potential, J. Stat. Phys. 145 (2011), pp. 1524–1545.
   Web of Science ®Google Scholar
• F. Guarnieri, W. Moon, and J.S. Wettlaufer, Solution of the Fokker–Planck equation with a logarithminc potential and mixed eigenvalue spectrum, J. Math. Phys. 58 (2017), pp. 093301.
   Web of Science ®Google Scholar
• J.P. Bouchaud, Weak ergodicity breaking and aging in disordered systems, J. Phys. France 2 (1992), pp. 1705–1713.
   Google Scholar
• E. Aghion, D.A. Kessler, and E. Barkai, From non-normalizable Boltzmann statistics to infinite-ergodic theory, Phiys. Rev. Lett. 122 (2019), pp. 01601.
   Web of Science ®Google Scholar
• E. Aghion, D.A. Kessler, and E. Barkai, Infinite-ergodic theory meets Boltzmann statistics, Chaos, Solitons Fractals 138 (2020), pp. 109890.
   Web of Science ®Google Scholar
• N.I. Shakura and G.V. Lipunova, Logarithmic potential for the gravitational field of schwarzschild black holes, Mon. Not. R. Astron. Soc. 480 (2018), pp. 4273–4277.
   Web of Science ®Google Scholar
• S. Da-ming, Ionizing characteristics of an orbitron-type pump, J. Phys. E: Sci. Instrum. 22 (1989), pp. 438–440.
   Google Scholar
• B. Petit and M-L. Feidt, A theoretical statistical model applied to an orbitron device, and its validity in comparison with the experimental orbitron pump's behaviour, Vacuum 34 (1984), pp. 759–763.
   Web of Science ®Google Scholar
• G.S. Manning, Limiting laws and continuous counterions condensation in polyelectrolyte solutions I. Colligative properties, J. Chem. Phys. 51 (1969), pp. 924–933.
   Web of Science ®Google Scholar
• R.K. Pathria, An ideal quantum gas in a finite-sized container, Am. J. of Phys. 66 (1998), pp. 1080–1085.
   Web of Science ®Google Scholar
• S. Mogliacci, I. Kolb, and W.A. Horowitz, Geometrically confined thermal field theory: Finite size corrections and phase transitions, Phys. Rev. D. 102 (2020), pp. 116017–116052.
   Web of Science ®Google Scholar
• Supplemental Materials: Section A.
   Google Scholar
• Supplemental Materials: Section B.
   Google Scholar
• I.F. Silveira, Bose–Einstein condensation, Am. J. Phys. 65 (1999), pp. 570–574. DOI: 10.119/1.18591
   Web of Science ®Google Scholar
• L. Ferrari, Approaching Bose–Einstein condensation, Eur. J. Phys. 32 (2011), pp. 1547–1557.
   Web of Science ®Google Scholar
• Use, for example Wolfram Mathematica 7.01.0 or higher versions.
   Google Scholar
• Supplemental Materials: Section C.
   Google Scholar
• Supplemental Materials: Section D.
   Google Scholar
• H. Ciftci, E. Ateser, and H. Koru, The power-law and the logarithmic potentials. arXiv preprint arXiv: math-ph/0212072v1. 2002, pp. 1–16.
   Google Scholar
• A.K. Roy, Calculation of the bound states of power-law and logarithmic potentials through a generalized pseudopotential method. arXiv preprint arXiv: 1307.1525v1 [quant-ph]. 2013, pp. 1–14.
   Google Scholar
• A.A. Abdel-Hardy, Calculation of the power-law and logarithmic potential using the J-matrix method, Int. J. App. Sc. IJBAS-IJENS 11 (2011), pp. 53–59.
   Google Scholar
• B. de Marco and D. Jin, Onset of Fermi degeneracy in a trapped atomic gas, Sciences 285 (1999), pp. 1703–1706. DOI: 10.1126/science.285.543.1703
   PubMed Web of Science ®Google Scholar