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

Abel Rojo-Francàs, Artur Polls and Bruno Juliá-Díaz
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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

Mathematics, 2020, vol. 8, issue 7, 1-38

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.

Keywords: few-body systems; one-dimensional trap; trapped atoms; direct diagonalization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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