Dimensional Crossovers in a Gas of Noninteracting Spinless Fermions

  • Guillaume LangEmail author
Part of the Springer Theses book series (Springer Theses)


In order to describe ultracold atom experiments with high accuracy, in addition to selecting a model that accounts for the interactions, several other aspects have to be taken into account, such as finite temperature, system size and number of particles, or inhomogeneities of the atomic cloud. Such refinements have already been illustrated on the example of the Lieb-Liniger model in the previous chapters. Tackling several effects simultaneously is technically challenging, but it is not easy either to rank them by relative importance and decide which of them could be neglected or should be incorporated in priority.


  1. 1.
    G. Lang, F. Hekking, A. Minguzzi, Dimensional crossover in a Fermi gas and a cross-dimensional Tomonaga-Luttinger model. Phys. Rev. A 93, 013603 (2016)Google Scholar
  2. 2.
    J.P. Van Es, P. Wicke, A.H. Van Amerongen, C. Rétif, S. Whitlock et al., Box traps on an atom chip for one-dimensional quantum gases. J. Phys. B 43(15), 155002 (2010)Google Scholar
  3. 3.
    A.L. Gaunt, T.F. Schmidutz, I. Gotlibovych, R.P. Smith, Z. Hadzibabic, Bose-Einstein condensation of atoms in a uniform potential. Phys. Rev. Lett. 110, 200406 (2013)Google Scholar
  4. 4.
    B. Mukherjee, Z. Yan, P.B. Patel, Z. Hadzibabic, T. Yefsah, J. Struck, M.W. Zwierlein, Homogeneous atomic Fermi gases. Phys. Rev. Lett. 118, 123401 (2017)Google Scholar
  5. 5.
    K. Hueck, N. Luick, L. Sobirey, J. Siegl, T. Lompe, H. Moritz, Two-dimensional homogeneous Fermi gases. Phys. Rev. Lett. 120, 060402 (2018)Google Scholar
  6. 6.
    P. Nozières, D. Pines, The Theory of Quantum Liquids: Superfluid Bose Liquids (Addison-Wesley, Redwood, 1990)Google Scholar
  7. 7.
    A.L. Fetter, J.D. Waleczka, Quantum Theory of Many-Particle Systems (McGraw-Hill, New York, 2003)Google Scholar
  8. 8.
    V.N. Golovach, A. Minguzzi, L.I. Glazman, Dynamic response of one-dimensional bosons in a trap. Phys. Rev. A 80, 043611 (2009)Google Scholar
  9. 9.
    P. Vignolo, A. Minguzzi, One-dimensional non-interacting fermions in harmonic confinement: equilibrium and dynamical properties. J. Phys. B Atomic Mol. Opt. Phys. 34, 4653–4662 (2001)ADSCrossRefGoogle Scholar
  10. 10.
    S.M. Bahauddin, M.M. Faruk, Virial coefficients from unified statistical thermodynamics of quantum gases trapped under generic power law potential in d dimension and equivalence of quantum gases. Commun. Theor. Phys. 66, 291–296 (2016)ADSMathSciNetCrossRefGoogle Scholar
  11. 11.
    M.A. Cazalilla, A.F. Ho, Instabilities in binary mixtures of one-dimensional quantum degenerate gases. Phys. Rev. Lett. 91, 150403 (2003)Google Scholar
  12. 12.
    K.A. Matveev, L.I. Glazman, Conductance and coulomb blockade in a multi-mode quantum wire. Physica B 189, 266–274 (1993)ADSCrossRefGoogle Scholar
  13. 13.
    A. Iucci, G.A. Fiete, T. Giamarchi, Fourier transform of the \(2k_F\) Luttinger liquid density correlation function with different spin and charge velocities. Phys. Rev. B 75, 205116 (2007)Google Scholar
  14. 14.
    E. Orignac, M. Tsuchiizu, Y. Suzumuru, Spectral functions of two-band spinless fermion and single-band spin-\(1/2\) fermion models. Phys. Rev. B 84, 165128 (2011)Google Scholar
  15. 15.
    E. Orignac, R. Citro, Response functions in multicomponent Luttinger liquids. J. Stat. Mech. 2012, P12020 (2012)MathSciNetCrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Laboratoire de Physique et de Modélisation des Milieux Condensés (LPMMC)GrenobleFrance

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