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Localization results for a class of random Schrödinger operators within the Hartree–Fock approximation are proved in two regimes: Large disorder and weak disorder/extreme energies. A large disorder threshold λHF analogous to the threshold λAnd obtained in Schenker [Lett. Math. Phys. 105(1), 1–9 (2015)] is provided. We also show certain stability results for this large disorder threshold by giving examples of distributions for which λHF converges to λAnd, or to a number arbitrarily close to it, as the interaction strength tends to zero.
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Global-in-time semiclassical regularity for the Hartree–Fock equation
For arbitrarily large times T > 0, we prove the uniform-in-ℏ propagation of semiclassical regularity for the solutions to the Hartree–Fock equation with singular interactions of the form V(x)=±x−a with a∈(0,12). As a by-product of this result, we extend to arbitrarily long times the derivation of the Hartree–Fock and the Vlasov equations from the many-body dynamics provided in the work of Chong et al. [arXiv:2103.10946 (2021)].
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- Award ID(s):
- 1840314
- PAR ID:
- 10588205
- Publisher / Repository:
- American Institute of Physics
- Date Published:
- Journal Name:
- Journal of Mathematical Physics
- Volume:
- 63
- Issue:
- 8
- ISSN:
- 0022-2488
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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