TY - JOUR
AB - We consider a 2D quantum system of N bosons in a trapping potential |x|s, interacting via a pair potential of the form N2β−1 w(Nβ x). We show that for all 0 < β < (s + 1)/(s + 2), the leading order behavior of ground states of the many-body system is described in the large N limit by the corresponding cubic nonlinear Schrödinger energy functional. Our result covers the focusing case (w < 0) where even the stability of the many-body system is not obvious. This answers an open question mentioned by X. Chen and J. Holmer for harmonic traps (s = 2). Together with the BBGKY hierarchy approach used by these authors, our result implies the convergence of the many-body quantum dynamics to the focusing NLS equation with harmonic trap for all 0 < β < 3/4.
AU - Lewin, Mathieu
AU - Nam, Phan
AU - Rougerie, Nicolas
ID - 632
IS - 6
JF - Proceedings of the American Mathematical Society
TI - A note on 2D focusing many boson systems
VL - 145
ER -
TY - JOUR
AB - We study the ionization problem in the Thomas-Fermi-Dirac-von Weizsäcker theory for atoms and molecules. We prove the nonexistence of minimizers for the energy functional when the number of electrons is large and the total nuclear charge is small. This nonexistence result also applies to external potentials decaying faster than the Coulomb potential. In the case of arbitrary nuclear charges, we obtain the nonexistence of stable minimizers and radial minimizers.
AU - Nam, Phan
AU - Van Den Bosch, Hanne
ID - 1079
IS - 2
JF - Mathematical Physics, Analysis and Geometry
SN - 13850172
TI - Nonexistence in Thomas Fermi-Dirac-von Weizsäcker theory with small nuclear charges
VL - 20
ER -
TY - JOUR
AB - The existence of a self-localization transition in the polaron problem has been under an active debate ever since Landau suggested it 83 years ago. Here we reveal the self-localization transition for the rotational analogue of the polaron -- the angulon quasiparticle. We show that, unlike for the polarons, self-localization of angulons occurs at finite impurity-bath coupling already at the mean-field level. The transition is accompanied by the spherical-symmetry breaking of the angulon ground state and a discontinuity in the first derivative of the ground-state energy. Moreover, the type of the symmetry breaking is dictated by the symmetry of the microscopic impurity-bath interaction, which leads to a number of distinct self-localized states. The predicted effects can potentially be addressed in experiments on cold molecules trapped in superfluid helium droplets and ultracold quantum gases, as well as on electronic excitations in solids and Bose-Einstein condensates.
AU - Li, Xiang
AU - Seiringer, Robert
AU - Lemeshko, Mikhail
ID - 1120
IS - 3
JF - Physical Review A
SN - 24699926
TI - Angular self-localization of impurities rotating in a bosonic bath
VL - 95
ER -
TY - JOUR
AB - 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.
AU - Moser, Thomas
AU - Seiringer, Robert
ID - 1198
IS - 3
JF - Letters in Mathematical Physics
SN - 03779017
TI - Triviality of a model of particles with point interactions in the thermodynamic limit
VL - 107
ER -
TY - JOUR
AB - We consider a many-body system of fermionic atoms interacting via a local pair potential and subject to an external potential within the framework of Bardeen-Cooper-Schrieffer (BCS) theory. We measure the free energy of the whole sample with respect to the free energy of a reference state which allows us to define a BCS functional with boundary conditions at infinity. Our main result is a lower bound for this energy functional in terms of expressions that typically appear in Ginzburg-Landau functionals.
AU - Deuchert, Andreas
ID - 912
IS - 8
JF - Journal of Mathematical Physics
SN - 00222488
TI - A lower bound for the BCS functional with boundary conditions at infinity
VL - 58
ER -