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Static and Dynamic Properties of a Few Spin 1/2 Interacting Fermions Trapped in a Harmonic Potential Rojo Francàs, Abel Polls Martí, Artur Juliá-Díaz, Bruno Fermions Energia Física de partícules Fermions Energy Particle physics 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. 2021-10-22T13:04:10Z 2021-10-22T13:04:10Z 2020-07-21 2021-10-22T13:04:10Z info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Reproducció del document publicat a: https://doi.org/10.3390/math8071196 Mathematics, 2020, vol. 8, num. 7, p. 1196 https://doi.org/10.3390/math8071196 cc-by (c) Rojo Francàs, Abel et al., 2020 https://creativecommons.org/licenses/by/4.0/ info:eu-repo/semantics/openAccess MDPI Articles publicats en revistes (Física Quàntica i Astrofísica)