@article{14931, abstract = {We prove an upper bound on the ground state energy of the dilute spin-polarized Fermi gas capturing the leading correction to the kinetic energy resulting from repulsive interactions. One of the main ingredients in the proof is a rigorous implementation of the fermionic cluster expansion of Gaudin et al. (1971) [15].}, author = {Lauritsen, Asbjørn Bækgaard and Seiringer, Robert}, issn = {1096--0783}, journal = {Journal of Functional Analysis}, number = {7}, publisher = {Elsevier}, title = {{Ground state energy of the dilute spin-polarized Fermi gas: Upper bound via cluster expansion}}, doi = {10.1016/j.jfa.2024.110320}, volume = {286}, year = {2024}, } @article{14772, abstract = {Many coupled evolution equations can be described via 2×2-block operator matrices of the form A=[ A B C D ] in a product space X=X1×X2 with possibly unbounded entries. Here, the case of diagonally dominant block operator matrices is considered, that is, the case where the full operator A can be seen as a relatively bounded perturbation of its diagonal part with D(A)=D(A)×D(D) though with possibly large relative bound. For such operators the properties of sectoriality, R-sectoriality and the boundedness of the H∞-calculus are studied, and for these properties perturbation results for possibly large but structured perturbations are derived. Thereby, the time dependent parabolic problem associated with A can be analyzed in maximal Lpt -regularity spaces, and this is applied to a wide range of problems such as different theories for liquid crystals, an artificial Stokes system, strongly damped wave and plate equations, and a Keller-Segel model.}, author = {Agresti, Antonio and Hussein, Amru}, issn = {0022-1236}, journal = {Journal of Functional Analysis}, keywords = {Analysis}, number = {11}, publisher = {Elsevier}, title = {{Maximal Lp-regularity and H∞-calculus for block operator matrices and applications}}, doi = {10.1016/j.jfa.2023.110146}, volume = {285}, year = {2023}, } @article{14254, abstract = {In [10] Nam proved a Lieb–Thirring Inequality for the kinetic energy of a fermionic quantum system, with almost optimal (semi-classical) constant and a gradient correction term. We present a stronger version of this inequality, with a much simplified proof. As a corollary we obtain a simple proof of the original Lieb–Thirring inequality.}, author = {Seiringer, Robert and Solovej, Jan Philip}, issn = {1096-0783}, journal = {Journal of Functional Analysis}, number = {10}, publisher = {Elsevier}, title = {{A simple approach to Lieb-Thirring type inequalities}}, doi = {10.1016/j.jfa.2023.110129}, volume = {285}, year = {2023}, } @article{12911, abstract = {This paper establishes new connections between many-body quantum systems, One-body Reduced Density Matrices Functional Theory (1RDMFT) and Optimal Transport (OT), by interpreting the problem of computing the ground-state energy of a finite-dimensional composite quantum system at positive temperature as a non-commutative entropy regularized Optimal Transport problem. We develop a new approach to fully characterize the dual-primal solutions in such non-commutative setting. The mathematical formalism is particularly relevant in quantum chemistry: numerical realizations of the many-electron ground-state energy can be computed via a non-commutative version of Sinkhorn algorithm. Our approach allows to prove convergence and robustness of this algorithm, which, to our best knowledge, were unknown even in the two marginal case. Our methods are based on a priori estimates in the dual problem, which we believe to be of independent interest. Finally, the above results are extended in 1RDMFT setting, where bosonic or fermionic symmetry conditions are enforced on the problem.}, author = {Feliciangeli, Dario and Gerolin, Augusto and Portinale, Lorenzo}, issn = {1096-0783}, journal = {Journal of Functional Analysis}, number = {4}, publisher = {Elsevier}, title = {{A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature}}, doi = {10.1016/j.jfa.2023.109963}, volume = {285}, year = {2023}, } @article{10732, abstract = {We compute the deterministic approximation of products of Sobolev functions of large Wigner matrices W and provide an optimal error bound on their fluctuation with very high probability. This generalizes Voiculescu's seminal theorem from polynomials to general Sobolev functions, as well as from tracial quantities to individual matrix elements. Applying the result to eitW for large t, we obtain a precise decay rate for the overlaps of several deterministic matrices with temporally well separated Heisenberg time evolutions; thus we demonstrate the thermalisation effect of the unitary group generated by Wigner matrices.}, author = {Cipolloni, Giorgio and Erdös, László and Schröder, Dominik J}, issn = {1096-0783}, journal = {Journal of Functional Analysis}, number = {8}, publisher = {Elsevier}, title = {{Thermalisation for Wigner matrices}}, doi = {10.1016/j.jfa.2022.109394}, volume = {282}, year = {2022}, } @article{10850, abstract = {We study two interacting quantum particles forming a bound state in d-dimensional free space, and constrain the particles in k directions to (0, ∞)k ×Rd−k, with Neumann boundary conditions. First, we prove that the ground state energy strictly decreases upon going from k to k+1. This shows that the particles stick to the corner where all boundary planes intersect. Second, we show that for all k the resulting Hamiltonian, after removing the free part of the kinetic energy, has only finitely many eigenvalues below the essential spectrum. This paper generalizes the work of Egger, Kerner and Pankrashkin (J. Spectr. Theory 10(4):1413–1444, 2020) to dimensions d > 1.}, author = {Roos, Barbara and Seiringer, Robert}, issn = {0022-1236}, journal = {Journal of Functional Analysis}, keywords = {Analysis}, number = {12}, publisher = {Elsevier}, title = {{Two-particle bound states at interfaces and corners}}, doi = {10.1016/j.jfa.2022.109455}, volume = {282}, year = {2022}, } @article{10887, abstract = {We introduce a new way of representing logarithmically concave functions on Rd. It allows us to extend the notion of the largest volume ellipsoid contained in a convex body to the setting of logarithmically concave functions as follows. For every s>0, we define a class of non-negative functions on Rd derived from ellipsoids in Rd+1. For any log-concave function f on Rd , and any fixed s>0, we consider functions belonging to this class, and find the one with the largest integral under the condition that it is pointwise less than or equal to f, and we call it the John s-function of f. After establishing existence and uniqueness, we give a characterization of this function similar to the one given by John in his fundamental theorem. We find that John s-functions converge to characteristic functions of ellipsoids as s tends to zero and to Gaussian densities as s tends to infinity. As an application, we prove a quantitative Helly type result: the integral of the pointwise minimum of any family of log-concave functions is at least a constant cd multiple of the integral of the pointwise minimum of a properly chosen subfamily of size 3d+2, where cd depends only on d.}, author = {Ivanov, Grigory and Naszódi, Márton}, issn = {1096-0783}, journal = {Journal of Functional Analysis}, number = {11}, publisher = {Elsevier}, title = {{Functional John ellipsoids}}, doi = {10.1016/j.jfa.2022.109441}, volume = {282}, year = {2022}, } @article{9348, abstract = {We consider the stochastic quantization of a quartic double-well energy functional in the semiclassical regime and derive optimal asymptotics for the exponentially small splitting of the ground state energy. Our result provides an infinite-dimensional version of some sharp tunneling estimates known in finite dimensions for semiclassical Witten Laplacians in degree zero. From a stochastic point of view it proves that the L2 spectral gap of the stochastic one-dimensional Allen-Cahn equation in finite volume satisfies a Kramers-type formula in the limit of vanishing noise. We work with finite-dimensional lattice approximations and establish semiclassical estimates which are uniform in the dimension. Our key estimate shows that the constant separating the two exponentially small eigenvalues from the rest of the spectrum can be taken independently of the dimension.}, author = {Brooks, Morris and Di Gesù, Giacomo}, issn = {1096-0783}, journal = {Journal of Functional Analysis}, number = {3}, publisher = {Elsevier}, title = {{Sharp tunneling estimates for a double-well model in infinite dimension}}, doi = {10.1016/j.jfa.2021.109029}, volume = {281}, year = {2021}, } @article{9462, abstract = {We consider a system of N trapped bosons with repulsive interactions in a combined semiclassical mean-field limit at positive temperature. We show that the free energy is well approximated by the minimum of the Hartree free energy functional – a natural extension of the Hartree energy functional to positive temperatures. The Hartree free energy functional converges in the same limit to a semiclassical free energy functional, and we show that the system displays Bose–Einstein condensation if and only if it occurs in the semiclassical free energy functional. This allows us to show that for weak coupling the critical temperature decreases due to the repulsive interactions.}, author = {Deuchert, Andreas and Seiringer, Robert}, issn = {1096-0783}, journal = {Journal of Functional Analysis}, number = {6}, publisher = {Elsevier}, title = {{Semiclassical approximation and critical temperature shift for weakly interacting trapped bosons}}, doi = {10.1016/j.jfa.2021.109096}, volume = {281}, year = {2021}, } @article{10070, abstract = {We extensively discuss the Rademacher and Sobolev-to-Lipschitz properties for generalized intrinsic distances on strongly local Dirichlet spaces possibly without square field operator. We present many non-smooth and infinite-dimensional examples. As an application, we prove the integral Varadhan short-time asymptotic with respect to a given distance function for a large class of strongly local Dirichlet forms.}, author = {Dello Schiavo, Lorenzo and Suzuki, Kohei}, issn = {1096-0783}, journal = {Journal of Functional Analysis}, number = {11}, publisher = {Elsevier}, title = {{Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces}}, doi = {10.1016/j.jfa.2021.109234}, volume = {281}, year = {2021}, } @article{10862, abstract = {We consider the sum of two large Hermitian matrices A and B with a Haar unitary conjugation bringing them into a general relative position. We prove that the eigenvalue density on the scale slightly above the local eigenvalue spacing is asymptotically given by the free additive convolution of the laws of A and B as the dimension of the matrix increases. This implies optimal rigidity of the eigenvalues and optimal rate of convergence in Voiculescu's theorem. Our previous works [4], [5] established these results in the bulk spectrum, the current paper completely settles the problem at the spectral edges provided they have the typical square-root behavior. The key element of our proof is to compensate the deterioration of the stability of the subordination equations by sharp error estimates that properly account for the local density near the edge. Our results also hold if the Haar unitary matrix is replaced by the Haar orthogonal matrix.}, author = {Bao, Zhigang and Erdös, László and Schnelli, Kevin}, issn = {0022-1236}, journal = {Journal of Functional Analysis}, keywords = {Analysis}, number = {7}, publisher = {Elsevier}, title = {{Spectral rigidity for addition of random matrices at the regular edge}}, doi = {10.1016/j.jfa.2020.108639}, volume = {279}, year = {2020}, } @article{8516, abstract = {The purpose of this paper is to construct examples of diffusion for E-Hamiltonian perturbations of completely integrable Hamiltonian systems in 2d-dimensional phase space, with d large. In the first part of the paper, simple and explicit examples are constructed illustrating absence of ‘long-time’ stability for size E Hamiltonian perturbations of quasi-convex integrable systems already when the dimension 2d of phase space becomes as large as log 1/E . We first produce the example in Gevrey class and then a real analytic one, with some additional work. In the second part, we consider again E-Hamiltonian perturbations of completely integrable Hamiltonian system in 2d-dimensional space with E-small but not too small, |E| > exp(−d), with d the number of degrees of freedom assumed large. It is shown that for a class of analytic time-periodic perturbations, there exist linearly diffusing trajectories. The underlying idea for both examples is similar and consists in coupling a fixed degree of freedom with a large number of them. The procedure and analytical details are however significantly different. As mentioned, the construction in Part I is totally elementary while Part II is more involved, relying in particular on the theory of normally hyperbolic invariant manifolds, methods of generating functions, Aubry–Mather theory, and Mather’s variational methods.}, author = {Bourgain, Jean and Kaloshin, Vadim}, issn = {0022-1236}, journal = {Journal of Functional Analysis}, keywords = {Analysis}, number = {1}, pages = {1--61}, publisher = {Elsevier}, title = {{On diffusion in high-dimensional Hamiltonian systems}}, doi = {10.1016/j.jfa.2004.09.006}, volume = {229}, year = {2005}, }