@article{20925, abstract = {We prove normal typicality and dynamical typicality for a (centered) random block-band matrix model with block-dependent variances. A key feature of our model is that we achieve intermediate equilibration times, an aspect that has not been proven rigorously in any model before. Our proof builds on recently established concentration estimates for products of resolvents of Wigner type random matrices (Erdős and Riabov in Commun Math Phys 405(12): 282, 2024) and an intricate analysis of the deterministic approximation.}, author = {Erdös, László and Henheik, Sven Joscha and Vogel, Cornelia}, issn = {1573-0530}, journal = {Letters in Mathematical Physics}, publisher = {Springer Nature}, title = {{Normal typicality and dynamical typicality for a random block-band matrix model}}, doi = {10.1007/s11005-025-02037-5}, volume = {116}, year = {2026}, } @article{22404, abstract = {We consider a class of two-dimensional tight binding models displaying conical intersections of the Bloch bands at the Fermi level. The setting includes the case of generic transitions between quantum Hall phases. We consider the longitudinal conductivity, as given by Kubo formula, describing the variation of the current after introducing a space-homogeneous electric field, in an adiabatic way. We obtain an explicit expression for the longitudinal conductivity, completely determined by the number of conical intersections and by the shape of the cones. In particular, the formula reproduces the known quantized values found for graphene and for the critical Haldane model. Furthermore, we discuss the validity of Kubo formula in presence of conical intersections in the spectrum, starting from the time-dependent Schrödinger equation. For electric fields which are weak and slowly varying in space and in time, we prove the validity of linear response from quantum dynamics.}, author = {Marcelli, Giovanna and Pigozzi, Lorenzo and Porta, Marcello}, issn = {1573-0530}, journal = {Letters in Mathematical Physics}, number = {4}, publisher = {Springer Nature}, title = {{Longitudinal conductivity at integer quantum Hall transitions}}, doi = {10.1007/s11005-026-02087-3}, volume = {116}, year = {2026}, } @article{13226, abstract = {We consider the ground state and the low-energy excited states of a system of N identical bosons with interactions in the mean-field scaling regime. For the ground state, we derive a weak Edgeworth expansion for the fluctuations of bounded one-body operators, which yields corrections to a central limit theorem to any order in 1/N−−√. For suitable excited states, we show that the limiting distribution is a polynomial times a normal distribution, and that higher-order corrections are given by an Edgeworth-type expansion.}, author = {Bossmann, Lea and Petrat, Sören P}, issn = {1573-0530}, journal = {Letters in Mathematical Physics}, number = {4}, publisher = {Springer Nature}, title = {{Weak Edgeworth expansion for the mean-field Bose gas}}, doi = {10.1007/s11005-023-01698-4}, volume = {113}, year = {2023}, } @article{12246, abstract = {The Lieb–Oxford inequality provides a lower bound on the Coulomb energy of a classical system of N identical charges only in terms of their one-particle density. We prove here a new estimate on the best constant in this inequality. Numerical evaluation provides the value 1.58, which is a significant improvement to the previously known value 1.64. The best constant has recently been shown to be larger than 1.44. In a second part, we prove that the constant can be reduced to 1.25 when the inequality is restricted to Hartree–Fock states. This is the first proof that the exchange term is always much lower than the full indirect Coulomb energy.}, author = {Lewin, Mathieu and Lieb, Elliott H. and Seiringer, Robert}, issn = {1573-0530}, journal = {Letters in Mathematical Physics}, keywords = {Mathematical Physics, Statistical and Nonlinear Physics}, number = {5}, publisher = {Springer Nature}, title = {{Improved Lieb–Oxford bound on the indirect and exchange energies}}, doi = {10.1007/s11005-022-01584-5}, volume = {112}, year = {2022}, } @article{10642, abstract = {Based on a result by Yarotsky (J Stat Phys 118, 2005), we prove that localized but otherwise arbitrary perturbations of weakly interacting quantum spin systems with uniformly gapped on-site terms change the ground state of such a system only locally, even if they close the spectral gap. We call this a strong version of the local perturbations perturb locally (LPPL) principle which is known to hold for much more general gapped systems, but only for perturbations that do not close the spectral gap of the Hamiltonian. We also extend this strong LPPL-principle to Hamiltonians that have the appropriate structure of gapped on-site terms and weak interactions only locally in some region of space. While our results are technically corollaries to a theorem of Yarotsky, we expect that the paradigm of systems with a locally gapped ground state that is completely insensitive to the form of the Hamiltonian elsewhere extends to other situations and has important physical consequences.}, author = {Henheik, Sven Joscha and Teufel, Stefan and Wessel, Tom}, issn = {1573-0530}, journal = {Letters in Mathematical Physics}, keywords = {mathematical physics, statistical and nonlinear physics}, number = {1}, publisher = {Springer Nature}, title = {{Local stability of ground states in locally gapped and weakly interacting quantum spin systems}}, doi = {10.1007/s11005-021-01494-y}, volume = {112}, year = {2022}, } @article{9121, abstract = {We show that the energy gap for the BCS gap equation is Ξ=μ(8e−2+o(1))exp(π2μ−−√a) in the low density limit μ→0. Together with the similar result for the critical temperature by Hainzl and Seiringer (Lett Math Phys 84: 99–107, 2008), this shows that, in the low density limit, the ratio of the energy gap and critical temperature is a universal constant independent of the interaction potential V. The results hold for a class of potentials with negative scattering length a and no bound states.}, author = {Lauritsen, Asbjørn Bækgaard}, issn = {1573-0530}, journal = {Letters in Mathematical Physics}, keywords = {Mathematical Physics, Statistical and Nonlinear Physics}, publisher = {Springer Nature}, title = {{The BCS energy gap at low density}}, doi = {10.1007/s11005-021-01358-5}, volume = {111}, year = {2021}, } @article{9225, abstract = {The Landau–Pekar equations describe the dynamics of a strongly coupled polaron. Here, we provide a class of initial data for which the associated effective Hamiltonian has a uniform spectral gap for all times. For such initial data, this allows us to extend the results on the adiabatic theorem for the Landau–Pekar equations and their derivation from the Fröhlich model obtained in previous works to larger times.}, author = {Feliciangeli, Dario and Rademacher, Simone Anna Elvira and Seiringer, Robert}, issn = {1573-0530}, journal = {Letters in Mathematical Physics}, publisher = {Springer Nature}, title = {{Persistence of the spectral gap for the Landau–Pekar equations}}, doi = {10.1007/s11005-020-01350-5}, volume = {111}, year = {2021}, } @article{9256, abstract = {We consider the ferromagnetic quantum Heisenberg model in one dimension, for any spin S≥1/2. We give upper and lower bounds on the free energy, proving that at low temperature it is asymptotically equal to the one of an ideal Bose gas of magnons, as predicted by the spin-wave approximation. The trial state used in the upper bound yields an analogous estimate also in the case of two spatial dimensions, which is believed to be sharp at low temperature.}, author = {Napiórkowski, Marcin M and Seiringer, Robert}, issn = {1573-0530}, journal = {Letters in Mathematical Physics}, number = {2}, publisher = {Springer Nature}, title = {{Free energy asymptotics of the quantum Heisenberg spin chain}}, doi = {10.1007/s11005-021-01375-4}, volume = {111}, year = {2021}, } @article{9333, abstract = {We revise a previous result about the Fröhlich dynamics in the strong coupling limit obtained in Griesemer (Rev Math Phys 29(10):1750030, 2017). In the latter it was shown that the Fröhlich time evolution applied to the initial state φ0⊗ξα, where φ0 is the electron ground state of the Pekar energy functional and ξα the associated coherent state of the phonons, can be approximated by a global phase for times small compared to α2. In the present note we prove that a similar approximation holds for t=O(α2) if one includes a nontrivial effective dynamics for the phonons that is generated by an operator proportional to α−2 and quadratic in creation and annihilation operators. Our result implies that the electron ground state remains close to its initial state for times of order α2, while the phonon fluctuations around the coherent state ξα can be described by a time-dependent Bogoliubov transformation.}, author = {Mitrouskas, David Johannes}, issn = {1573-0530}, journal = {Letters in Mathematical Physics}, publisher = {Springer Nature}, title = {{A note on the Fröhlich dynamics in the strong coupling limit}}, doi = {10.1007/s11005-021-01380-7}, volume = {111}, year = {2021}, } @article{7611, abstract = {We consider a system of N bosons in the limit N→∞, interacting through singular potentials. For initial data exhibiting Bose–Einstein condensation, the many-body time evolution is well approximated through a quadratic fluctuation dynamics around a cubic nonlinear Schrödinger equation of the condensate wave function. We show that these fluctuations satisfy a (multi-variate) central limit theorem.}, author = {Rademacher, Simone Anna Elvira}, issn = {1573-0530}, journal = {Letters in Mathematical Physics}, pages = {2143--2174}, publisher = {Springer Nature}, title = {{Central limit theorem for Bose gases interacting through singular potentials}}, doi = {10.1007/s11005-020-01286-w}, volume = {110}, year = {2020}, } @article{7618, abstract = {This short note aims to study quantum Hellinger distances investigated recently by Bhatia et al. (Lett Math Phys 109:1777–1804, 2019) with a particular emphasis on barycenters. We introduce the family of generalized quantum Hellinger divergences that are of the form ϕ(A,B)=Tr((1−c)A+cB−AσB), where σ is an arbitrary Kubo–Ando mean, and c∈(0,1) is the weight of σ. We note that these divergences belong to the family of maximal quantum f-divergences, and hence are jointly convex, and satisfy the data processing inequality. We derive a characterization of the barycenter of finitely many positive definite operators for these generalized quantum Hellinger divergences. We note that the characterization of the barycenter as the weighted multivariate 1/2-power mean, that was claimed in Bhatia et al. (2019), is true in the case of commuting operators, but it is not correct in the general case. }, author = {Pitrik, Jozsef and Virosztek, Daniel}, issn = {1573-0530}, journal = {Letters in Mathematical Physics}, number = {8}, pages = {2039--2052}, publisher = {Springer Nature}, title = {{Quantum Hellinger distances revisited}}, doi = {10.1007/s11005-020-01282-0}, volume = {110}, year = {2020}, } @article{1198, abstract = {We consider a model of fermions interacting via point interactions, defined via a certain weighted Dirichlet form. While for two particles the interaction corresponds to infinite scattering length, the presence of further particles effectively decreases the interaction strength. We show that the model becomes trivial in the thermodynamic limit, in the sense that the free energy density at any given particle density and temperature agrees with the corresponding expression for non-interacting particles.}, author = {Moser, Thomas and Seiringer, Robert}, issn = {0377-9017}, journal = {Letters in Mathematical Physics}, number = {3}, pages = { 533 -- 552}, publisher = {Springer}, title = {{Triviality of a model of particles with point interactions in the thermodynamic limit}}, doi = {10.1007/s11005-016-0915-x}, volume = {107}, year = {2017}, } @article{2346, abstract = {By means of a generalization of the Fefferman - de la Llave decomposition we derive a general lower bound on the interaction energy of one-dimensional quantum systems. We apply this result to a specific class of lowest Landau band wave functions.}, author = {Hainzl, Christian and Seiringer, Robert}, issn = {0377-9017}, journal = {Letters in Mathematical Physics}, number = {2}, pages = {133 -- 142}, publisher = {Springer}, title = {{Bounds on one-dimensional exchange energies with application to lowest Landau band quantum mechanics}}, doi = {10.1023/A:1010951905548}, volume = {55}, year = {2001}, } @article{2723, abstract = {The ground-state density of the Pauli operator in the case of a nonconstant magnetic field with constant direction is studied. It is shown that in the large field limit, the naturally rescaled ground-state density function is bounded from above by the megnetic field, and under some additional conditions, the limit density function is equal to the magnetic field. A restatement of this result yields an estimate on the density of complex orthogonal polynomials with respect to a fairly general weight function. We also prove a special case of the paramagnetic inequality. }, author = {Erdös, László}, issn = {0377-9017}, journal = {Letters in Mathematical Physics}, number = {3}, pages = {219 -- 240}, publisher = {Springer}, title = {{Ground-state density of the Pauli operator in the large field limit}}, doi = {10.1007/BF00761110}, volume = {29}, year = {1993}, }