The Widom-Sobolev formula for discontinuous matrix-valued symbols
arXiv:2311.06036 · doi:10.1016/j.jfa.2024.110651
Abstract
We prove the Widom-Sobolev formula for the asymptotic behaviour of truncated Wiener-Hopf operators with discontinuous matrix-valued symbols for three different classes of test functions. The symbols may depend on both position and momentum except when closing the asymptotics for twice differentiable test functions with Hölder singularities. The cut-off domains are allowed to have piecewise differentiable boundaries. In contrast to the case where the symbol is smooth in one variable, the resulting coefficient in the enhanced area law we obtain here remains as explicit for matrix-valued symbols as it is for scalar-valued symbols.
41 pages; v3: as published; changes in v2: Introduction changed. New Remark 3.4 adds information on the scaling properties of the constants in Lemma 3.3. Proof of Theorem 3.9 corrected and expanded. Proof of Theorem 4.22 reorganised with parts of it now contained in the new Lemma 4.19
References in corpus (13)
- Entanglement entropy of fermions in any dimension and the Widom conjecture
- Scaling of Rényi entanglement entropies of the free Fermi-gas ground state: a rigorous proof
- On the Area Law for Disordered Free Fermions
- A Special Case Of A Conjecture By Widom With Implications To Fermionic Entanglement Entropy
- Wiener-Hopf operators in higher dimensions: the Widom conjecture for piece-wise smooth domains
- Functions of self-adjoint operators in ideals of compact operators
- Large Block Properties of the Entanglement Entropy of Disordered Fermions
- How much delocalisation is needed for an enhanced area law of the entanglement entropy?
- Stability of the enhanced area law of the entanglement entropy
- Asymptotic growth of the local ground-state entropy of the ideal Fermi gas in a constant magnetic field
- Full Szegő-type trace asymptotics for ergodic operators on large boxes
- Stability of a Szegő-type asymptotics
- The Fermionic Entanglement Entropy of the Vacuum State of a Schwarzschild Black Hole Horizon