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Spectrum of the Pauli projector of a quantum many-body system is studied. It is proven that the kern of the complete many-body projector is identical to the kern of the sum of two-body projectors. Since the kern of the many-body Pauli projector defines an allowed subspace of the complete Hilbert space, it is argued that a truncation of the many-body model space following the two-body Pauli projectors is a natural way when solving the Schr{o}dinger equation for the many-body system. These relations clarify a role of the many-body Pauli forces in a multicluster system.
The Complete Manifold of Ground State Eigenfunctions for the Purely Magnetic 2D Pauli Operator is considered as a by-product of the new reduction found by the present authors few years ago for the Algebrogeometric Inverse Spectral Data (i.e. Riemann
We propose an index for pairs of a unitary map and a clustering state on many-body quantum systems. We require the map to conserve an integer-valued charge and to leave the state, e.g. a gapped ground state, invariant. This index is integer-valued an
We study the many body quantum evolution of bosonic systems in the mean field limit. The dynamics is known to be well approximated by the Hartree equation. So far, the available results have the form of a law of large numbers. In this paper we go one
We consider the many-body quantum evolution of a factorized initial data, in the mean-field regime. We show that fluctuations around the limiting Hartree dynamics satisfy large deviation estimates, that are consistent with central limit theorems that have been established in the last years.
We present a new proof of the convergence of the N-particle Schroedinger dynamics for bosons towards the dynamics generated by the Hartree equation in the mean-field limit. For a restricted class of two-body interactions, we obtain convergence estima