@article{7685,
abstract = {We consider a gas of interacting bosons trapped in a box of side length one in the Gross–Pitaevskii limit. We review the proof of the validity of Bogoliubov’s prediction for the ground state energy and the low-energy excitation spectrum. This note is based on joint work with C. Brennecke, S. Cenatiempo and B. Schlein.},
author = {Boccato, Chiara},
issn = {0129-055X},
journal = {Reviews in Mathematical Physics},
number = {1},
publisher = {World Scientific},
title = {{The excitation spectrum of the Bose gas in the Gross-Pitaevskii regime}},
doi = {10.1142/S0129055X20600065},
volume = {33},
year = {2021},
}
@article{7900,
abstract = {Hartree–Fock theory has been justified as a mean-field approximation for fermionic systems. However, it suffers from some defects in predicting physical properties, making necessary a theory of quantum correlations. Recently, bosonization of many-body correlations has been rigorously justified as an upper bound on the correlation energy at high density with weak interactions. We review the bosonic approximation, deriving an effective Hamiltonian. We then show that for systems with Coulomb interaction this effective theory predicts collective excitations (plasmons) in accordance with the random phase approximation of Bohm and Pines, and with experimental observation.},
author = {Benedikter, Niels P},
issn = {0129-055X},
journal = {Reviews in Mathematical Physics},
number = {1},
publisher = {World Scientific},
title = {{Bosonic collective excitations in Fermi gases}},
doi = {10.1142/s0129055x20600090},
volume = {33},
year = {2021},
}
@article{9005,
abstract = {Studies on the experimental realization of two-dimensional anyons in terms of quasiparticles have been restricted, so far, to only anyons on the plane. It is known, however, that the geometry and topology of space can have significant effects on quantum statistics for particles moving on it. Here, we have undertaken the first step toward realizing the emerging fractional statistics for particles restricted to move on the sphere instead of on the plane. We show that such a model arises naturally in the context of quantum impurity problems. In particular, we demonstrate a setup in which the lowest-energy spectrum of two linear bosonic or fermionic molecules immersed in a quantum many-particle environment can coincide with the anyonic spectrum on the sphere. This paves the way toward the experimental realization of anyons on the sphere using molecular impurities. Furthermore, since a change in the alignment of the molecules corresponds to the exchange of the particles on the sphere, such a realization reveals a novel type of exclusion principle for molecular impurities, which could also be of use as a powerful technique to measure the statistics parameter. Finally, our approach opens up a simple numerical route to investigate the spectra of many anyons on the sphere. Accordingly, we present the spectrum of two anyons on the sphere in the presence of a Dirac monopole field.},
author = {Brooks, Morris and Lemeshko, Mikhail and Lundholm, D. and Yakaboylu, Enderalp},
issn = {10797114},
journal = {Physical Review Letters},
number = {1},
publisher = {American Physical Society},
title = {{Molecular impurities as a realization of anyons on the two-sphere}},
doi = {10.1103/PhysRevLett.126.015301},
volume = {126},
year = {2021},
}
@article{8603,
abstract = {We consider the Fröhlich polaron model in the strong coupling limit. It is well‐known that to leading order the ground state energy is given by the (classical) Pekar energy. In this work, we establish the subleading correction, describing quantum fluctuation about the classical limit. Our proof applies to a model of a confined polaron, where both the electron and the polarization field are restricted to a set of finite volume, with linear size determined by the natural length scale of the Pekar problem.},
author = {Frank, Rupert and Seiringer, Robert},
issn = {10970312},
journal = {Communications on Pure and Applied Mathematics},
number = {3},
pages = {544--588},
publisher = {Wiley},
title = {{Quantum corrections to the Pekar asymptotics of a strongly coupled polaron}},
doi = {10.1002/cpa.21944},
volume = {74},
year = {2021},
}
@article{9246,
abstract = {We consider the Fröhlich Hamiltonian in a mean-field limit where many bosonic particles weakly couple to the quantized phonon field. For large particle numbers and a suitably small coupling, we show that the dynamics of the system is approximately described by the Landau–Pekar equations. These describe a Bose–Einstein condensate interacting with a classical polarization field, whose dynamics is effected by the condensate, i.e., the back-reaction of the phonons that are created by the particles during the time evolution is of leading order.},
author = {Leopold, Nikolai K and Mitrouskas, David Johannes and Seiringer, Robert},
issn = {14320673},
journal = {Archive for Rational Mechanics and Analysis},
pages = {383--417},
publisher = {Springer Nature},
title = {{Derivation of the Landau–Pekar equations in a many-body mean-field limit}},
doi = {10.1007/s00205-021-01616-9},
volume = {240},
year = {2021},
}