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Numerical simulations of p-wave fermions in a one-dimensional harmonic trap

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Màster Oficial de Ciència i Tecnologia Quàntiques / Quantum Science and Technology, Facultat de Física, Universitat de Barcelona. Curs: 2024-2025. Tutors: Bruno Juliá Díaz, Abel Rojo Francàs.

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We consider a system of N spin-aligned p-wave fermions confined within a one-dimensional harmonic trap. We study the energy spectrum and ground state properties across different regimes of interaction strength by performing numerical calculations. We compute the particle density and the eigenvalues of the one-body density matrix. Additionally, we study two-particle properties by calculating the pair correlation matrix. In the infinitely interacting limit, our results coincide with those of a fermionic Tonks-Girardeau gas. We analyze the discontinuity behavior near the non-interacting limit and provide an explanation. We propose a novel square well representation of the p-wave interaction in discrete space. We demonstrate the efficiency of this representation by comparing the results obtained with it to those obtained from analytical solutions and other numerical methods. We simulate the dynamics of the system after altering a parameter of the system, such as the trap depth or the interaction
strength. We compute spectral properties of the system by analyzing the Fourier transform of the time-dependent spatial spread of the wave function.

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Màster Oficial - Ciència i Tecnologia Quàntiques / Quantum Science and Technology

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Numerical simulations of p-wave fermions in a one-dimensional harmonic trap