TY - JOUR AB - It is a remarkable property of BCS theory that the ratio of the energy gap at zero temperature Ξ and the critical temperature Tc is (approximately) given by a universal constant, independent of the microscopic details of the fermionic interaction. This universality has rigorously been proven quite recently in three spatial dimensions and three different limiting regimes: weak coupling, low density and high density. The goal of this short note is to extend the universal behavior to lower dimensions d=1,2 and give an exemplary proof in the weak coupling limit. AU - Henheik, Sven Joscha AU - Lauritsen, Asbjørn Bækgaard AU - Roos, Barbara ID - 14542 JF - Reviews in Mathematical Physics SN - 0129-055X TI - Universality in low-dimensional BCS theory ER - TY - JOUR AB - We consider a class of polaron models, including the Fröhlich model, at zero total momentum, and show that at sufficiently weak coupling there are no excited eigenvalues below the essential spectrum. AU - Seiringer, Robert ID - 14662 IS - 3 JF - Journal of Spectral Theory SN - 1664-039X TI - Absence of excited eigenvalues for Fröhlich type polaron models at weak coupling VL - 13 ER - TY - JOUR AB - Recently the leading order of the correlation energy of a Fermi gas in a coupled mean-field and semiclassical scaling regime has been derived, under the assumption of an interaction potential with a small norm and with compact support in Fourier space. We generalize this result to large interaction potentials, requiring only |⋅|V^∈ℓ1(Z3). Our proof is based on approximate, collective bosonization in three dimensions. Significant improvements compared to recent work include stronger bounds on non-bosonizable terms and more efficient control on the bosonization of the kinetic energy. AU - Benedikter, Niels P AU - Porta, Marcello AU - Schlein, Benjamin AU - Seiringer, Robert ID - 13225 IS - 4 JF - Archive for Rational Mechanics and Analysis SN - 0003-9527 TI - Correlation energy of a weakly interacting Fermi gas with large interaction potential VL - 247 ER - TY - JOUR AB - 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. AU - Bossmann, Lea AU - Petrat, Sören P ID - 13226 IS - 4 JF - Letters in Mathematical Physics SN - 0377-9017 TI - Weak Edgeworth expansion for the mean-field Bose gas VL - 113 ER - TY - JOUR AB - For the Fröhlich model of the large polaron, we prove that the ground state energy as a function of the total momentum has a unique global minimum at momentum zero. This implies the non-existence of a ground state of the translation invariant Fröhlich Hamiltonian and thus excludes the possibility of a localization transition at finite coupling. AU - Lampart, Jonas AU - Mitrouskas, David Johannes AU - Mysliwy, Krzysztof ID - 14192 IS - 3 JF - Mathematical Physics, Analysis and Geometry KW - Geometry and Topology KW - Mathematical Physics SN - 1385-0172 TI - On the global minimum of the energy–momentum relation for the polaron VL - 26 ER - TY - JOUR AB - 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. AU - Mitrouskas, David Johannes AU - Pickl, Peter ID - 14715 IS - 12 JF - Journal of Mathematical Physics SN - 0022-2488 TI - Exponential decay of the number of excitations in the weakly interacting Bose gas VL - 64 ER - TY - JOUR AB - Abstract We study the spectrum of the Fröhlich Hamiltonian for the polaron at fixed total momentum. We prove the existence of excited eigenvalues between the ground state energy and the essential spectrum at strong coupling. In fact, our main result shows that the number of excited energy bands diverges in the strong coupling limit. To prove this we derive upper bounds for the min-max values of the corresponding fiber Hamiltonians and compare them with the bottom of the essential spectrum, a lower bound on which was recently obtained by Brooks and Seiringer (Comm. Math. Phys. 404:1 (2023), 287–337). The upper bounds are given in terms of the ground state energy band shifted by momentum-independent excitation energies determined by an effective Hamiltonian of Bogoliubov type. AU - Mitrouskas, David Johannes AU - Seiringer, Robert ID - 14854 IS - 4 JF - Pure and Applied Analysis KW - General Medicine SN - 2578-5885 TI - Ubiquity of bound states for the strongly coupled polaron VL - 5 ER - TY - JOUR AB - 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. AU - Seiringer, Robert AU - Solovej, Jan Philip ID - 14254 IS - 10 JF - Journal of Functional Analysis SN - 0022-1236 TI - A simple approach to Lieb-Thirring type inequalities VL - 285 ER - TY - CHAP AB - In this chapter we first review the Levy–Lieb functional, which gives the lowest kinetic and interaction energy that can be reached with all possible quantum states having a given density. We discuss two possible convex generalizations of this functional, corresponding to using mixed canonical and grand-canonical states, respectively. We present some recent works about the local density approximation, in which the functionals get replaced by purely local functionals constructed using the uniform electron gas energy per unit volume. We then review the known upper and lower bounds on the Levy–Lieb functionals. We start with the kinetic energy alone, then turn to the classical interaction alone, before we are able to put everything together. A later section is devoted to the Hohenberg–Kohn theorem and the role of many-body unique continuation in its proof. AU - Lewin, Mathieu AU - Lieb, Elliott H. AU - Seiringer, Robert ED - Cances, Eric ED - Friesecke, Gero ID - 14992 SN - 3005-0286 T2 - Density Functional Theory TI - Universal Functionals in Density Functional Theory ER - TY - JOUR AB - Ongoing development of quantum simulators allows for a progressively finer degree of control of quantum many-body systems. This motivates the development of efficient approaches to facilitate the control of such systems and enable the preparation of nontrivial quantum states. Here we formulate an approach to control quantum systems based on matrix product states (MPSs). We compare counterdiabatic and leakage minimization approaches to the so-called local steering problem that consists in finding the best value of the control parameters for generating a unitary evolution of the specific MPS in a given direction. In order to benchmark the different approaches, we apply them to the generalization of the PXP model known to exhibit coherent quantum dynamics due to quantum many-body scars. We find that the leakage-based approach generally outperforms the counterdiabatic framework and use it to construct a Floquet model with quantum scars. We perform the first steps towards global trajectory optimization and demonstrate entanglement steering capabilities in the generalized PXP model. Finally, we apply our leakage minimization approach to construct quantum scars in the periodically driven nonintegrable Ising model. AU - Ljubotina, Marko AU - Roos, Barbara AU - Abanin, Dmitry A. AU - Serbyn, Maksym ID - 12276 IS - 3 JF - PRX Quantum KW - General Medicine TI - Optimal steering of matrix product states and quantum many-body scars VL - 3 ER -