Equilibration and Approximate Conservation Laws: Dipole Oscillations and Perfect Drag of Ultracold Atoms in a Harmonic Trap

The presence of (approximate) conservation laws can prohibit the fast relaxation of interacting many-particle quantum systems. We investigate this physics by studying the center-of-mass oscillations of two species of fermionic ultracold atoms in a harmonic trap. If their trap frequencies are equal, a dynamical symmetry (spectrum generating algebra), closely related to Kohn's theorem, prohibits the relaxation of center-of-mass oscillations. A small detuning $\delta\omega$ of the trap frequencies for the two species breaks the dynamical symmetry and ultimately leads to a damping of dipole oscillations driven by inter-species interactions. Using memory-matrix methods, we calculate the relaxation as a function of frequency difference, particle number, temperature, and strength of inter-species interactions. When interactions dominate, there is almost perfect drag between the two species and the dynamical symmetry is approximately restored. The drag can either arise from Hartree potentials or from friction. In the latter case (hydrodynamic limit), the center-of-mass oscillations decay with a tiny rate, $1/\tau \propto (\delta\omega)^2/\Gamma$, where $\Gamma$ is a single particle scattering rate.Comment: 9 pages + 5 pages of appendix, 9 figures; changes in v2: updated citation

Phase-Space Berry Phases in Chiral Magnets: Dzyaloshinskii-Moriya Interaction and the Charge of Skyrmions

The semiclassical motion of electrons in phase space, x=(R, k), is influenced by Berry phases described by a 6-component vector potential, A=(A^R, A^k). In chiral magnets Dzyaloshinskii-Moriya (DM) interactions induce slowly varying magnetic textures (helices and skyrmion lattices) for which all components of A are important inducing effectively a curvature in mixed position and momentum space. We show that for smooth textures and weak spin-orbit coupling phase space Berry curvatures determine the DM interactions and give important contributions to the charge. Using ab initio methods we calculate the strength of DM interactions in MnSi in good agreement with experiment and estimate the charge of skyrmions.Comment: 5 pages, 1 figure; 5 pages of supplemental material with 1 figure; substantial changes: Berry phase theory of DM interactions + extra Fermi surface contribution

Phase-Space Berry Phases in Chiral Magnets: Skyrmion Charge, Hall Effect, and Dynamics of Magnetic Skyrmions

The dynamics of electrons in solids is influenced by Berry phases in phase space (combined position and momentum space). Phase-space Berry phases lead to an effective force on the electrons, an anomalous contribution to the group velocity, and a correction to the density of states in phase space. In addition, Berry phases in position and in momentum space are related to topological winding numbers and can be used to characterize topologically distinct phases of matter. We study theoretically the effects of phase-space Berry phases in magnetic materials with weak spin-orbit coupling and a smoothly varying magnetization texture. Such magnetic textures appear generically in non-centrosymmetric magnetic materials with weak spin-orbit coupling due to a competition between the ferromagnetic exchange interaction and the weaker Dzyaloshinskii-Moriya interaction. In particular, the discovery of topologically stable whirls, so-called skyrmions, in the magnetization texture of these materials has attracted considerable attention due to prospects of applications in future magnetic storage devices. In part I of this thesis, we investigate the influence of phase-space Berry phases on the equilibrium properties of electrons in chiral magnets with weak spin-orbit coupling. We show that the strength of the Dzyaloshinskii-Moriya interaction in the long-wavelength limit can be calculated from Berry phases in mixed position/momentum space and that the same Berry phases lead to an electric charge of skyrmions in metallic chiral magnets. In insulators, the skyrmion charge of magnetic skyrmions turns out to be proportional to the topologically quantized second Chern number in phase space. This establishes a link between skyrmions in chiral magnets and the charged excitations in integer quantum Hall systems with small Zeeman splitting. In part II, we consider the Hall effect in the skyrmion lattice phase of chiral magnets in presence of spin-orbit coupling. It has been previously known that Berry phases in momentum space lead to the intrinsic part of the anomalous Hall effect, and that Berry phases in position space lead to an effective Lorentz force, resulting in the so-called topological Hall effect. By expanding the Kubo-Středa Formula for the Hall conductivity in gradients in position and momentum space, we show that the interplay between smooth magnetic textures and spin-orbit coupling leads to a previously disregarded contribution to the Hall effect, and we find a correction to the semiclassical formulation of the topological Hall effect. In part III, we study the influence of phase-space Berry phases on the dynamics of skyrmions in chiral magnets. Berry phases in mixed position/momentum space lead to a dissipationless momentum transfer from conduction electrons to skyrmions that is proportional to an applied electric field and independent of the (spin or electric) current. We further show that the electric charge of skyrmions, discussed in part I, influences the skyrmion motion only via hydrodynamic drag and ohmic friction in metals. In insulators, the quantized skyrmion charge couples directly to an applied electric field