@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},
}
@article{6788,
abstract = {We consider the Nelson model with ultraviolet cutoff, which describes the interaction between non-relativistic particles and a positive or zero mass quantized scalar field. We take the non-relativistic particles to obey Fermi statistics and discuss the time evolution in a mean-field limit of many fermions. In this case, the limit is known to be also a semiclassical limit. We prove convergence in terms of reduced density matrices of the many-body state to a tensor product of a Slater determinant with semiclassical structure and a coherent state, which evolve according to a fermionic version of the Schrödinger–Klein–Gordon equations.},
author = {Leopold, Nikolai K and Petrat, Sören P},
issn = {1424-0661},
journal = {Annales Henri Poincare},
number = {10},
pages = {3471–3508},
publisher = {Springer Nature},
title = {{Mean-field dynamics for the Nelson model with fermions}},
doi = {10.1007/s00023-019-00828-w},
volume = {20},
year = {2019},
}
@article{7100,
abstract = {We present microscopic derivations of the defocusing two-dimensional cubic nonlinear Schrödinger equation and the Gross–Pitaevskii equation starting froman interacting N-particle system of bosons. We consider the interaction potential to be given either by Wβ(x)=N−1+2βW(Nβx), for any β>0, or to be given by VN(x)=e2NV(eNx), for some spherical symmetric, nonnegative and compactly supported W,V∈L∞(R2,R). In both cases we prove the convergence of the reduced density corresponding to the exact time evolution to the projector onto the solution of the corresponding nonlinear Schrödinger equation in trace norm. For the latter potential VN we show that it is crucial to take the microscopic structure of the condensate into account in order to obtain the correct dynamics.},
author = {Jeblick, Maximilian and Leopold, Nikolai K and Pickl, Peter},
issn = {1432-0916},
journal = {Communications in Mathematical Physics},
number = {1},
pages = {1--69},
publisher = {Springer Nature},
title = {{Derivation of the time dependent Gross–Pitaevskii equation in two dimensions}},
doi = {10.1007/s00220-019-03599-x},
volume = {372},
year = {2019},
}
@article{5983,
abstract = {We study a quantum impurity possessing both translational and internal rotational degrees of freedom interacting with a bosonic bath. Such a system corresponds to a “rotating polaron,” which can be used to model, e.g., a rotating molecule immersed in an ultracold Bose gas or superfluid helium. We derive the Hamiltonian of the rotating polaron and study its spectrum in the weak- and strong-coupling regimes using a combination of variational, diagrammatic, and mean-field approaches. We reveal how the coupling between linear and angular momenta affects stable quasiparticle states, and demonstrate that internal rotation leads to an enhanced self-localization in the translational degrees of freedom.},
author = {Yakaboylu, Enderalp and Midya, Bikashkali and Deuchert, Andreas and Leopold, Nikolai K and Lemeshko, Mikhail},
issn = {2469-9950},
journal = {Physical Review B},
number = {22},
publisher = {American Physical Society},
title = {{Theory of the rotating polaron: Spectrum and self-localization}},
doi = {10.1103/physrevb.98.224506},
volume = {98},
year = {2018},
}
@inproceedings{11,
abstract = {We report on a novel strategy to derive mean-field limits of quantum mechanical systems in which a large number of particles weakly couple to a second-quantized radiation field. The technique combines the method of counting and the coherent state approach to study the growth of the correlations among the particles and in the radiation field. As an instructional example, we derive the Schrödinger–Klein–Gordon system of equations from the Nelson model with ultraviolet cutoff and possibly massless scalar field. In particular, we prove the convergence of the reduced density matrices (of the nonrelativistic particles and the field bosons) associated with the exact time evolution to the projectors onto the solutions of the Schrödinger–Klein–Gordon equations in trace norm. Furthermore, we derive explicit bounds on the rate of convergence of the one-particle reduced density matrix of the nonrelativistic particles in Sobolev norm.},
author = {Leopold, Nikolai K and Pickl, Peter},
location = {Munich, Germany},
pages = {185 -- 214},
publisher = {Springer},
title = {{Mean-field limits of particles in interaction with quantised radiation fields}},
doi = {10.1007/978-3-030-01602-9_9},
volume = {270},
year = {2018},
}