214 research outputs found
On the Schatten-von Neumann properties of some pseudo-differential operators
We obtain a number of explicit estimates for quasi-norms of
pseudo-differential operators in the Schatten-von Neumann classes with
. The estimates are applied to derive semi-classical bounds for
operators with smooth or non-smooth symbols.Comment: 22 page
Large-scale behaviour of local and entanglement entropy of the free Fermi gas at any temperature
The leading asymptotic large-scale behaviour of the spatially bipartite
entanglement entropy (EE) of the free Fermi gas infinitely extended in
multidimensional Euclidean space at zero absolute temperature, T=0, is by now
well understood. Here, we present and discuss the first rigorous results for
the corresponding EE of thermal equilibrium states at T>0. The leading
large-scale term of this thermal EE turns out to be twice the first-order
finite-size correction to the infinite-volume thermal entropy (density). Not
surprisingly, this correction is just the thermal entropy on the interface of
the bipartition. However, it is given by a rather complicated integral derived
from a semiclassical trace formula for a certain operator on the underlying
one-particle Hilbert space. But in the zero-temperature limit the leading
large-scale term of the thermal EE considerably simplifies and displays a
ln(1/T)-singularity which one may identify with the known logarithmic
enhancement at T=0 of the so-called area-law scaling.Comment: The paper has been slightly rewritten to improve its readability. In
particular, we now restrict ourselves to von Neumann entropies. The title and
the abstract have been changed. The references have been updated. 10 page
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