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Static and Dynamic Properties of a Few Spin 1/2 Interacting Fermions Trapped in a Harmonic Potential

Author

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  • Abel Rojo-Francàs

    (Departament de Física Quàntica i Astrofísica, Facultat de Física, and Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona, E–08028 Barcelona, Spain)

  • Artur Polls

    (Departament de Física Quàntica i Astrofísica, Facultat de Física, and Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona, E–08028 Barcelona, Spain)

  • Bruno Juliá-Díaz

    (Departament de Física Quàntica i Astrofísica, Facultat de Física, and Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona, E–08028 Barcelona, Spain)

Abstract

We provide a detailed study of the properties of a few interacting spin 1 / 2 fermions trapped in a one-dimensional harmonic oscillator potential. The interaction is assumed to be well represented by a contact delta potential. Numerical results obtained by means of direct diagonalization techniques are combined with analytical expressions for both the non-interacting and strongly interacting regime. The N = 2 case is used to benchmark our numerical techniques with the known exact solution of the problem. After a detailed description of the numerical methods, in a tutorial-like manner, we present the static properties of the system for N = 2 , 3 , 4 and 5 particles, e.g., low-energy spectrum, one-body density matrix, ground-state densities. Then, we consider dynamical properties of the system exploring first the excitation of the breathing mode, using the dynamical structure function and corresponding sum-rules, and then a sudden quench of the interaction strength.

Suggested Citation

  • Abel Rojo-Francàs & Artur Polls & Bruno Juliá-Díaz, 2020. "Static and Dynamic Properties of a Few Spin 1/2 Interacting Fermions Trapped in a Harmonic Potential," Mathematics, MDPI, vol. 8(7), pages 1-38, July.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:7:p:1196-:d:387510
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    References listed on IDEAS

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    1. A. G. Volosniev & D. V. Fedorov & A. S. Jensen & M. Valiente & N. T. Zinner, 2014. "Strongly interacting confined quantum systems in one dimension," Nature Communications, Nature, vol. 5(1), pages 1-7, December.
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