Il Nuovo Cimento B (1965-1970)

, Volume 63, Issue 1, pp 265–270 | Cite as

Phase transitions and long-wavelength collective modes in one-dimensional systems

  • J. Nyberg


The particle-hole vertex part equations for one-dimensional Fermi many-body systems are investigated in the Hartree-Fock approximation. Explicit solutions of these equations are obtained in the long-wavelength limit, and the corresponding collective modes are found. The possible presence of unstable collective modes is seen to be connected with the appearance of phase transitions in the Hartree-Fock model.


Collective Mode Vertex Function Spin Susceptibility Collective Oscillation Vertex Part 
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Фаэовые переходы и длинно-волновые коллективные моды в одномерных системах


В приближении Хартри-Фока исследуются уравнения для верщинных частей « частица-дырка » для одномерных многочастичных Ферми систем. В пределе длинных волн получаются точные рещения зтих уравнений, и находятся соответствуюшие коллективные моды. Воэможное присутствие неустойчивых коллективных мод, повидимому, свяэано с появлением фаэовых переходов в модели Хартри-Фока.


Si studiano nell’approssimazione di Hartree-Fock le equazioni della parte del vertice particella-buca per sistemi di Fermi unidimensionali a molti corpi. Si ottengono le soluzioni esplicite di queste equazioni nel limite di grandi lunghezze d’onda, e si trovano i corrispondenti modi collettivi. Si vede che la possibile presenza di modi collettivi instabili è connessa con la comparsa di transizioni di fase nel modello di Hartree-Fock.


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  1. (1).
    See,e.g.,P. Nozières:Theory of Interacting Fermi Systems (New York, 1964) Chap. 6.Google Scholar
  2. (2).
    J. Nyberg:Phys. Norvegica,3, 79 (1968).Google Scholar
  3. (3).
    L. D. Landau andE. M. Lifshitz:Statistical Physics (London, 1958), p. 482. References to many papers on this subject, and also reprints of some of them, are found inE. H. Lieb andD. C. Mattis:Mathematical Physics in One Dimension (New York, 1966).Google Scholar
  4. (4).
    The possibility of superconductivity in one dimension is discussed byYu. A. Bychkov, L. P. Gorkov andI. E. Dzyaloshinski:Sov. Phys. JETP,23, 489 (1966). See also the references contained therein.ADSGoogle Scholar
  5. (5).
    L. D. Landau:Sov. Phys. JETP,8, 70 (1959).Google Scholar
  6. (6).
    I. Ia. Pomeranchuk:Sov. Phys. JETP,8, 361 (1959).Google Scholar

Copyright information

© Società Italiana di Fisica 1969

Authors and Affiliations

  • J. Nyberg
    • 1
  1. 1.Institute for Theoretical PhysicsUniversity of OsloOslo

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