@article{18656, abstract = {We consider the time evolution of the out-of-time-ordered correlator (OTOC) of two general observables and in a mean field chaotic quantum system described by a random Wigner matrix as its Hamiltonian. We rigorously identify three time regimes separated by the physically relevant scrambling and relaxation times. The main feature of our analysis is that we express the error terms in the optimal Schatten (tracial) norms of the observables, allowing us to track the exact dependence of the errors on their rank. In particular, for significantly overlapping observables with low rank the OTOC is shown to exhibit a significant local maximum at the scrambling time, a feature that may not have been noticed in the physics literature before. Our main tool is a novel multi-resolvent local law with Schatten norms that unifies and improves previous local laws involving either the much cruder operator norm (cf. [10]) or the Hilbert-Schmidt norm (cf. [11]).}, author = {Cipolloni, Giorgio and Erdös, László and Henheik, Sven Joscha}, issn = {1095-0753}, journal = {Advances in Theoretical and Mathematical Physics}, number = {6}, pages = {2025--2083}, publisher = {International Press of Boston}, title = {{Out-of-time-ordered correlators for Wigner matrices}}, doi = {10.4310/ATMP.241031013250}, volume = {28}, year = {2024}, } @article{484, abstract = {We consider the dynamics of a large quantum system of N identical bosons in 3D interacting via a two-body potential of the form N3β-1w(Nβ(x - y)). For fixed 0 = β < 1/3 and large N, we obtain a norm approximation to the many-body evolution in the Nparticle Hilbert space. The leading order behaviour of the dynamics is determined by Hartree theory while the second order is given by Bogoliubov theory.}, author = {Nam, Phan and Napiórkowski, Marcin M}, issn = {1095-0761}, journal = {Advances in Theoretical and Mathematical Physics}, number = {3}, pages = {683 -- 738}, publisher = {International Press of Boston}, title = {{Bogoliubov correction to the mean-field dynamics of interacting bosons}}, doi = {10.4310/ATMP.2017.v21.n3.a4}, volume = {21}, year = {2017}, } @article{483, abstract = {We prove the universality for the eigenvalue gap statistics in the bulk of the spectrum for band matrices, in the regime where the band width is comparable with the dimension of the matrix, W ~ N. All previous results concerning universality of non-Gaussian random matrices are for mean-field models. By relying on a new mean-field reduction technique, we deduce universality from quantum unique ergodicity for band matrices.}, author = {Bourgade, Paul and Erdös, László and Yau, Horng and Yin, Jun}, issn = {1095-0761}, journal = {Advances in Theoretical and Mathematical Physics}, number = {3}, pages = {739 -- 800}, publisher = {International Press of Boston}, title = {{Universality for a class of random band matrices}}, doi = {10.4310/ATMP.2017.v21.n3.a5}, volume = {21}, year = {2017}, } @article{2350, abstract = {Using the Pauli-Fierz model of non-relativistic quantum electrodynamics, we calculate the binding energy of an electron in the field of a nucleus of charge Z and in presence of the quantized radiation field. We consider the case of small coupling constant α, but fixed Zα and ultraviolet cut-off Λ. We prove that after renormalizing the mass the binding energy has, to leading order in α, a finite limit as Λ goes to infinity; i.e., the cut-off can be removed. The expression for the ground state energy shift thus obtained agrees with Bethe's formula for small values of Zα, but shows a different behavior for bigger values.}, author = {Hainzl, Christian and Seiringer, Robert}, issn = {1095-0761}, journal = {Advances in Theoretical and Mathematical Physics}, number = {5}, pages = {847 -- 871}, publisher = {International Press}, title = {{Mass renormalization and energy level shift in non-relativistic QED}}, doi = {10.4310/ATMP.2002.v6.n5.a3}, volume = {6}, year = {2002}, } @article{2736, abstract = {We consider the time evolution of N bosonic particles interacting via a mean field Coulomb potential. Suppose the initial state is a product wavefunction. We show that at any finite time the correlation functions factorize in the limit N → ∞. Furthermore, the limiting one particle density matrix satisfies the nonlinear Hartree equation. The key ingredients are the uniqueness of the BBGKY hierarchy for the correlation functions and a new apriori estimate for the many-body Schrödinger equations.}, author = {Erdös, László and Yau, Horng}, issn = {1095-0761}, journal = {Advances in Theoretical and Mathematical Physics}, number = {6}, pages = {1169 -- 1205}, publisher = {International Press}, title = {{Derivation of the nonlinear Schrödinger equation from a many body Coulomb system}}, doi = {10.48550/arXiv.math-ph/0111042}, volume = {5}, year = {2001}, } @article{1450, abstract = {In this paper we consider the topological side of a problem which is the analogue of Sen's S-duality testing conjecture for Hitchin's moduli space M of rank 2 stable Higgs bundles of fixed determinant of odd degree over a Riemann surface ∑. We prove that all intersection numbers in the compactly supported cohomology of M vanish, i.e. "there are no topological L2 harmonic forms on M". This result generalizes the well known vanishing of the Euler characteristic of the moduli space of rank 2 stable bundles N of fixed determinant of odd degree over ∑. Our proof shows that the vanishing of all intersection numbers of H* cpt(M) is given by relations analogous to the Mumford relations in the cohomology ring of N.}, author = {Hausel, Tamas}, issn = {1095-0761}, journal = {Advances in Theoretical and Mathematical Physics}, number = {5}, pages = {1011 -- 1040}, publisher = {International Press}, title = {{Vanishing of intersection numbers on the moduli space of Higgs bundles}}, doi = {10.4310/ATMP.1998.v2.n5.a3}, volume = {2}, year = {1998}, }