@article{14715, abstract = {We consider N trapped bosons in the mean-field limit with coupling constant λN = 1/(N − 1). The ground state of such systems exhibits Bose–Einstein condensation. We prove that the probability of finding ℓ particles outside the condensate wave function decays exponentially in ℓ.}, author = {Mitrouskas, David Johannes and Pickl, Peter}, issn = {1089-7658}, journal = {Journal of Mathematical Physics}, number = {12}, publisher = {AIP Publishing}, title = {{Exponential decay of the number of excitations in the weakly interacting Bose gas}}, doi = {10.1063/5.0172199}, volume = {64}, year = {2023}, } @article{11783, abstract = {We consider a gas of N bosons with interactions in the mean-field scaling regime. We review the proof of an asymptotic expansion of its low-energy spectrum, eigenstates, and dynamics, which provides corrections to Bogoliubov theory to all orders in 1/ N. This is based on joint works with Petrat, Pickl, Seiringer, and Soffer. In addition, we derive a full asymptotic expansion of the ground state one-body reduced density matrix.}, author = {Bossmann, Lea}, issn = {1089-7658}, journal = {Journal of Mathematical Physics}, keywords = {Mathematical Physics, Statistical and Nonlinear Physics}, number = {6}, publisher = {AIP Publishing}, title = {{Low-energy spectrum and dynamics of the weakly interacting Bose gas}}, doi = {10.1063/5.0089983}, volume = {63}, year = {2022}, } @article{10600, abstract = {We show that recent results on adiabatic theory for interacting gapped many-body systems on finite lattices remain valid in the thermodynamic limit. More precisely, we prove a generalized super-adiabatic theorem for the automorphism group describing the infinite volume dynamics on the quasi-local algebra of observables. The key assumption is the existence of a sequence of gapped finite volume Hamiltonians, which generates the same infinite volume dynamics in the thermodynamic limit. Our adiabatic theorem also holds for certain perturbations of gapped ground states that close the spectral gap (so it is also an adiabatic theorem for resonances and, in this sense, “generalized”), and it provides an adiabatic approximation to all orders in the adiabatic parameter (a property often called “super-adiabatic”). In addition to the existing results for finite lattices, we also perform a resummation of the adiabatic expansion and allow for observables that are not strictly local. Finally, as an application, we prove the validity of linear and higher order response theory for our class of perturbations for infinite systems. While we consider the result and its proof as new and interesting in itself, we also lay the foundation for the proof of an adiabatic theorem for systems with a gap only in the bulk, which will be presented in a follow-up article.}, author = {Henheik, Sven Joscha and Teufel, Stefan}, issn = {1089-7658}, journal = {Journal of Mathematical Physics}, keywords = {mathematical physics, statistical and nonlinear physics}, number = {1}, publisher = {AIP Publishing}, title = {{Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap}}, doi = {10.1063/5.0051632}, volume = {63}, year = {2022}, } @article{12083, abstract = {We consider the many-body time evolution of weakly interacting bosons in the mean field regime for initial coherent states. We show that bounded k-particle operators, corresponding to dependent random variables, satisfy both a law of large numbers and a central limit theorem.}, author = {Rademacher, Simone Anna Elvira}, issn = {0022-2488}, journal = {Journal of Mathematical Physics}, number = {8}, publisher = {AIP Publishing}, title = {{Dependent random variables in quantum dynamics}}, doi = {10.1063/5.0086712}, volume = {63}, year = {2022}, } @article{12110, abstract = {A recently proposed approach for avoiding the ultraviolet divergence of Hamiltonians with particle creation is based on interior-boundary conditions (IBCs). The approach works well in the non-relativistic case, i.e., for the Laplacian operator. Here, we study how the approach can be applied to Dirac operators. While this has successfully been done already in one space dimension, and more generally for codimension-1 boundaries, the situation of point sources in three dimensions corresponds to a codimension-3 boundary. One would expect that, for such a boundary, Dirac operators do not allow for boundary conditions because they are known not to allow for point interactions in 3D, which also correspond to a boundary condition. Indeed, we confirm this expectation here by proving that there is no self-adjoint operator on a (truncated) Fock space that would correspond to a Dirac operator with an IBC at configurations with a particle at the origin. However, we also present a positive result showing that there are self-adjoint operators with an IBC (on the boundary consisting of configurations with a particle at the origin) that are away from those configurations, given by a Dirac operator plus a sufficiently strong Coulomb potential.}, author = {Henheik, Sven Joscha and Tumulka, Roderich}, issn = {0022-2488}, journal = {Journal of Mathematical Physics}, number = {12}, publisher = {AIP Publishing}, title = {{Interior-boundary conditions for the Dirac equation at point sources in three dimensions}}, doi = {10.1063/5.0104675}, volume = {63}, year = {2022}, } @article{12184, abstract = {We review recent results on adiabatic theory for ground states of extended gapped fermionic lattice systems under several different assumptions. More precisely, we present generalized super-adiabatic theorems for extended but finite and infinite systems, assuming either a uniform gap or a gap in the bulk above the unperturbed ground state. The goal of this Review is to provide an overview of these adiabatic theorems and briefly outline the main ideas and techniques required in their proofs.}, author = {Henheik, Sven Joscha and Wessel, Tom}, issn = {0022-2488}, journal = {Journal of Mathematical Physics}, number = {12}, publisher = {AIP Publishing}, title = {{On adiabatic theory for extended fermionic lattice systems}}, doi = {10.1063/5.0123441}, volume = {63}, year = {2022}, } @article{12243, abstract = {We consider the eigenvalues of a large dimensional real or complex Ginibre matrix in the region of the complex plane where their real parts reach their maximum value. This maximum follows the Gumbel distribution and that these extreme eigenvalues form a Poisson point process as the dimension asymptotically tends to infinity. In the complex case, these facts have already been established by Bender [Probab. Theory Relat. Fields 147, 241 (2010)] and in the real case by Akemann and Phillips [J. Stat. Phys. 155, 421 (2014)] even for the more general elliptic ensemble with a sophisticated saddle point analysis. The purpose of this article is to give a very short direct proof in the Ginibre case with an effective error term. Moreover, our estimates on the correlation kernel in this regime serve as a key input for accurately locating [Formula: see text] for any large matrix X with i.i.d. entries in the companion paper [G. Cipolloni et al., arXiv:2206.04448 (2022)]. }, author = {Cipolloni, Giorgio and Erdös, László and Schröder, Dominik J and Xu, Yuanyuan}, issn = {1089-7658}, journal = {Journal of Mathematical Physics}, keywords = {Mathematical Physics, Statistical and Nonlinear Physics}, number = {10}, publisher = {AIP Publishing}, title = {{Directional extremal statistics for Ginibre eigenvalues}}, doi = {10.1063/5.0104290}, volume = {63}, year = {2022}, } @article{9891, abstract = {Extending on ideas of Lewin, Lieb, and Seiringer [Phys. Rev. B 100, 035127 (2019)], we present a modified “floating crystal” trial state for jellium (also known as the classical homogeneous electron gas) with density equal to a characteristic function. This allows us to show that three definitions of the jellium energy coincide in dimensions d ≥ 2, thus extending the result of Cotar and Petrache [“Equality of the Jellium and uniform electron gas next-order asymptotic terms for Coulomb and Riesz potentials,” arXiv: 1707.07664 (2019)] and Lewin, Lieb, and Seiringer [Phys. Rev. B 100, 035127 (2019)] that the three definitions coincide in dimension d ≥ 3. We show that the jellium energy is also equivalent to a “renormalized energy” studied in a series of papers by Serfaty and others, and thus, by the work of Bétermin and Sandier [Constr. Approximation 47, 39–74 (2018)], we relate the jellium energy to the order n term in the logarithmic energy of n points on the unit 2-sphere. We improve upon known lower bounds for this renormalized energy. Additionally, we derive formulas for the jellium energy of periodic configurations.}, author = {Lauritsen, Asbjørn Bækgaard}, issn = {1089-7658}, journal = {Journal of Mathematical Physics}, keywords = {Mathematical Physics, Statistical and Nonlinear Physics}, number = {8}, publisher = {AIP Publishing}, title = {{Floating Wigner crystal and periodic jellium configurations}}, doi = {10.1063/5.0053494}, volume = {62}, year = {2021}, } @article{2727, abstract = {Diamagnetism of the magnetic Schrödinger operator and paramagnetism of the Pauli operator are rigorously proven for nonhomogeneous magnetic fields in the large field, in the large temperature and in the semiclassical asymptotic regimes. New counterexamples are presented which show that neither dia-nor paramagnetism is true in a robust sense (without asymptotics). In particular, we demonstrate that the recent diamagnetic comparison result by Loss and Thaller [M. Loss and B. Thaller, Commun. Math. Phys. (submitted)] is essentially the best one can hope for.}, author = {Erdös, László}, issn = {0022-2488}, journal = {Journal of Mathematical Physics}, number = {3}, pages = {1289 -- 1317}, publisher = {American Institute of Physics}, title = {{Dia- and paramagnetism for nonhomogeneous magnetic fields}}, doi = {10.1063/1.531909}, volume = {38}, year = {1997}, }