We analyse the performance of two quantum-state-transfer Hamiltonians in the presence of diagonal and off-diagonal disorder, and in terms of different measures. The first Hamiltonian pertains to a fully-engineered chain and the second to a chain with modified boundary couplings. The task is to find which Hamiltonian is the most robust to given levels of disorder and irrespective of the input state. In this respect, it is shown that the performance of the two protocols are approximately equivalent.

In this note, we discuss the low and high temperature contribution of Thermodynamic Bethe Ansatz (TBA) dressed excitations in the thermodynamics and energy-magnetization relaxation within the Generalized Hydrodynamics approach in the linear response regime. In particular, we show how the temperature dependent dispersions of the excitations reproduce well known behavior of the specific heat, magnetic susceptibility, spin and energy Drude weights. In this context, we derive a further formulation of the Drude weights from the finite wavevector relaxation. Furthermore, we contrast the TBA description of thermodynamics and dynamics in terms of a multitude of string excitations to that in terms of a single quasi-particle in low energy effective theories. 2

We investigate the propagation of magnetic skyrmions on elastically deformable geometries by employing imaginary time quantum field theory methods. We demonstrate that the Euclidean action of the problem carries information of the elements of the surface space metric, and develop a description of the skyrmion dynamics in terms of a set of collective coordinates. We reveal that curvature-driven effects emerge in geometries with nonconstant curvature, which explicitly break the translational invariance of flat space. In particular, for a skyrmion stabilized by a curvilinear defect, an inertia term and a pinning potential are generated by the varying curvature, while both of these terms vanish in the flat-space limit.