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Si us plau utilitzeu sempre aquest identificador per citar o enllaçar aquest document: https://hdl.handle.net/2445/180778
Static and Dynamic Properties of a Few Spin 1/2 Interacting Fermions Trapped in a Harmonic Potential
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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.
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ROJO FRANCÀS, Abel, POLLS MARTÍ, Artur and JULIÁ-DÍAZ, Bruno. Static and Dynamic Properties of a Few Spin 1/2 Interacting Fermions Trapped in a Harmonic Potential. Mathematics. 2020. Vol. 8, num. 7, pags. 1196. ISSN 2227-7390. [consulted: 19 of August of 2026]. Available at: https://hdl.handle.net/2445/180778