A semiquantal approach to finite systems of interacting particles

Details A semiquantal approach to finite systems of interacting particles A semiquantal approach to finite systems of interacting particles

2001-06-25

arxiv.org/abs/nlin/0106036v1

Phys.Rev.Lett. 88 (2002) 054101

Nonlinear Sciences

Chaotic Dynamics

4 pages, 2 figures

Scientific paper

10.1103/PhysRevLett.88.054101

A novel approach is suggested for the statistical description of quantum systems of interacting particles. The key point of this approach is that a typical eigenstate in the energy representation (shape of eigenstates, SE) has a well defined classical analog which can be easily obtained from the classical equations of motion. Therefore, the occupation numbers for single-particle states can be represented as a convolution of the classical SE with the quantum occupation number operator for non-interacting particles. The latter takes into account the wavefunctions symmetry and depends on the unperturbed energy spectrum only. As a result, the distribution of occupation numbers $n_s$ can be numerically found for a very large number of interacting particles. Using the model of interacting spins we demonstrate that this approach gives a correct description of $n_s$ even in a deep quantum region with few single-particle orbitals.

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