Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Thouless numbers for few-particle systems with disorder and interactions   Considering N spinless Fermions in a random potential, we study how a short
range pairwise interaction delocalizes the N-body states in the basis of the
one-particle Slater determinants, and the spectral rigidity of the N-body
spectrum. The maximum number g_N of consecutive levels exhibiting the universal
Wigner-Dyson rigidity (the Thouless number) is given as a function of the
strength U of the interaction for the bulk of the spectrum. In the dilute
limit, one finds two thresholds: When U<U_{c1}, there is a perturbative mixing
between a few Slater determinants (Rabi oscillations) and g_N \propto |U|^P <1,
where P=N/2 (even N) or (N+1)/2 (odd N). When U=U_{c1}, the level spacing
distribution exhibits a crossover from Poisson to Wigner, related to the
crossover between weak perturbative mixing and effective golden-rule decay, and
g_N \approx 1. Moreover, we show that the same U_{c1} signifies also the
breakdown of the perturbation theory in U. For U_{c1}<U<U_{c2}, the states are
extended over the energetically nearby Slater determinants with a non-ergodic
hierarchical structure related to the sparse form of the Hamiltonian. Above a
second threshold U_{c2}, the sparsity becomes irrelevant, and the states are
extended more or less ergodically over g_N consecutive Slater determinants. A
self-consistent argument gives g_N ~ U^{N/(N-1)}. We compare our predictions to
a numerical study of three spinless Fermions in a disordered cubic lattice.
Implications for the interaction-induced N-particle delocalization in real
space are discussed. The applicability of Fermi's golden rule for decay in this
dilute gas of "real" particles is compared with the one characterizing a
finite-density Fermi gas. The latter is related to the recently suggested
Anderson transition in Fock space.

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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
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The categories of this paper are: math
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat