A semiquantal approach to finite systems of interacting particles

Abstract

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.

4 pages, 2 figures

References in corpus (1)

• Delocalization border and onset of chaos in a model of quantum computation

Cited by in corpus (5)

• Quantum Chaos and Thermalization in Isolated Systems of Interacting Particles
• Broken Ergodicity in classically chaotic spin systems
• The Non--Ergodicity Threshold: Time Scale for Magnetic Reversal
• Emergence of correlations in the process of thermalization of interacting bosons
• Canonical density matrices from eigenstates of mixed systems