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Anderson's orthogonality catastrophe | | Martin Gebert
; Heinrich Küttler
; Peter Müller
; | | Date: |
25 Feb 2013 | | Abstract: | We give an upper bound on the modulus of the ground-state overlap of two
non-interacting fermionic quantum systems with N particles in a large but
finite volume L^d of d-dimensional Euclidean space. The underlying one-particle
Hamiltonians of the two systems are standard Schr"odinger operators that
differ by a non-negative compactly supported scalar potential. In the
thermodynamic limit, the bound exhibits an asymptotic power-law decay in the
system size L, showing that the ground-state overlap vanishes for macroscopic
systems. The decay exponent can be interpreted in terms of the total scattering
cross section averaged over all incident directions. The result confirms and
generalises P. W. Anderson’s informal computation [Phys. Rev. Lett. 18,
1049--1051 (1967)]. | | Source: | arXiv, 1302.6124 | | Services: | Forum | Review | PDF | Favorites | |
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