We study the many-body problem represented by $N$-coupled harmonic oscillators: $N$ same mass particles under a parabolic potential $k_0$ centered at the origin, interacting among themselves by a harmonic (parabolic) repulsion of strength $k$ kept different. This is one of the few many-body problems that possess an exact solution, due to the factorization of the many-body hamiltonian by an appropriate change of coordinates. We will study in 1st quantization these exact solutions, as a function of the hamiltonian parameters, in particular of the coupling $k$ related to correlations. We will consider also perturbation theory approximated solutions, with the perturbation chosen in two different ways, and other popular non-perturbative approximations. In the last part, we will study the electronic density as a function of the correlations and of the coupling $k$. The final purpose is to study for spontaneous symmetry breaking solutions for the ground state density as a function of correlations, giving rise to charge density waves (CDW) and so to a Wigner crystal phase.
Many-Body coupled harmonic oscillators and exact wavefunctions and density: correlations and Wigner crystal
Massimo Ladisa;
2014
Abstract
We study the many-body problem represented by $N$-coupled harmonic oscillators: $N$ same mass particles under a parabolic potential $k_0$ centered at the origin, interacting among themselves by a harmonic (parabolic) repulsion of strength $k$ kept different. This is one of the few many-body problems that possess an exact solution, due to the factorization of the many-body hamiltonian by an appropriate change of coordinates. We will study in 1st quantization these exact solutions, as a function of the hamiltonian parameters, in particular of the coupling $k$ related to correlations. We will consider also perturbation theory approximated solutions, with the perturbation chosen in two different ways, and other popular non-perturbative approximations. In the last part, we will study the electronic density as a function of the correlations and of the coupling $k$. The final purpose is to study for spontaneous symmetry breaking solutions for the ground state density as a function of correlations, giving rise to charge density waves (CDW) and so to a Wigner crystal phase.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
