@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 = {15730530},
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 = {15730530},
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{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 = {15730530},
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{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 = {03779017},
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},
}