@article{7226, author = {Jaksic, Vojkan and Seiringer, Robert}, issn = {00222488}, journal = {Journal of Mathematical Physics}, number = {12}, publisher = {AIP Publishing}, title = {{Introduction to the Special Collection: International Congress on Mathematical Physics (ICMP) 2018}}, doi = {10.1063/1.5138135}, volume = {60}, year = {2019}, } @article{7015, abstract = {We modify the "floating crystal" trial state for the classical homogeneous electron gas (also known as jellium), in order to suppress the boundary charge fluctuations that are known to lead to a macroscopic increase of the energy. The argument is to melt a thin layer of the crystal close to the boundary and consequently replace it by an incompressible fluid. With the aid of this trial state we show that three different definitions of the ground-state energy of jellium coincide. In the first point of view the electrons are placed in a neutralizing uniform background. In the second definition there is no background but the electrons are submitted to the constraint that their density is constant, as is appropriate in density functional theory. Finally, in the third system each electron interacts with a periodic image of itself; that is, periodic boundary conditions are imposed on the interaction potential.}, author = {Lewin, Mathieu and Lieb, Elliott H. and Seiringer, Robert}, issn = {2469-9969}, journal = {Physical Review B}, number = {3}, publisher = {American Physical Society}, title = {{Floating Wigner crystal with no boundary charge fluctuations}}, doi = {10.1103/physrevb.100.035127}, volume = {100}, year = {2019}, } @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}, } @article{554, abstract = {We analyse the canonical Bogoliubov free energy functional in three dimensions at low temperatures in the dilute limit. We prove existence of a first-order phase transition and, in the limit (Formula presented.), we determine the critical temperature to be (Formula presented.) to leading order. Here, (Formula presented.) is the critical temperature of the free Bose gas, ρ is the density of the gas and a is the scattering length of the pair-interaction potential V. We also prove asymptotic expansions for the free energy. In particular, we recover the Lee–Huang–Yang formula in the limit (Formula presented.).}, author = {Napiórkowski, Marcin M and Reuvers, Robin and Solovej, Jan}, issn = {00103616}, journal = {Communications in Mathematical Physics}, number = {1}, pages = {347--403}, publisher = {Springer}, title = {{The Bogoliubov free energy functional II: The dilute Limit}}, doi = {10.1007/s00220-017-3064-x}, volume = {360}, year = {2018}, } @article{399, abstract = {Following an earlier calculation in 3D, we calculate the 2D critical temperature of a dilute, translation-invariant Bose gas using a variational formulation of the Bogoliubov approximation introduced by Critchley and Solomon in 1976. This provides the first analytical calculation of the Kosterlitz-Thouless transition temperature that includes the constant in the logarithm.}, author = {Napiórkowski, Marcin M and Reuvers, Robin and Solovej, Jan}, journal = {EPL}, number = {1}, publisher = {IOP Publishing Ltd.}, title = {{Calculation of the critical temperature of a dilute Bose gas in the Bogoliubov approximation}}, doi = {10.1209/0295-5075/121/10007}, volume = {121}, year = {2018}, }