Alberto Hernando, Jiri Vanicek
An imaginary-time nonuniform mesh method for finding eigenvalues and eigenstates of an arbitrary multidimensional Hamiltonian is presented. The main ingredients are (i) a sampling procedure optimizing the distribution of grid points and (ii) a diagonalization of a real-valued sparse matrix whose eigenvectors are the eigenfunctions evaluated at the selected grid points. The method is applied to find the eigenstates of up to five interacting spinless quantum Lennard-Jones particles trapped in a 1D harmonic potential. Eigenstates of both bosonic and fermionic counterparts are obtained, the former exhibiting the phenomenon of fermionization. Finally, the computed excited states are used to describe the melting of the Lennard-Jones clusters at finite temperature.
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http://arxiv.org/abs/1304.8015
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