Low-temperature ordered states of matter with spontaneously broken symmetry host collective excitations - Goldstone modes - that are coupled to the order parameter field. The collective excitations act on the order parameter as a thermal bath and give rise to its non-trivial dynamics that include effects like "quantum friction," a stochastic Langevin force and effective Brownian motion. In this talk, I will discuss new theoretical and experimental results and ideas on such quantum friction effects in superfluids and magnetic systems. In the first part of my talk, I will focus on quantum dynamics of topological textures, in particular solitons/domain walls, propagating in low-dimensional superfluids/magnets. An effective quasi-classical equations of motion will be derived. It will be shown that interestingly the familiar Ohmic friction is absent in the integrable setup, but the equations contain non-Markovian dissipative forces . I will explain a way to restore and control the Ohmic friction force and related Brownian motion of topological textures, as was demonstrated in a recent experiment . In the second part of the talk, I will explain our general geometric theory of fluctuations and dissipation in non-equilibrium superfluids . The theory relies on the observation that collective excitations in a moving superfluid satisfy the wave equation in a curved space time, with the metric determined by the underlying superflow. This leads to a compact and elegant geometric formulation of two-fluid hydrodynamics that suggests interesting observable effects from synthetic Hawking radiation to synthetic lensing of phonons/magnons. Possible experimental platforms (in superfluids, superconductors, and magnets) to observe these exotic phenomena will be discussed.
 D. Efimkin, J. Hofmann, and V. Galitski, "Non-Markovian quantum friction of bright solitons in superfluids," Phys. Rev. Lett. 116, 225301 (2016)
 L. Ayckock et al., "Brownian motion of solitons," Proc. Nat. Acad. Sciences 114, 2503 (2017)
 A. Keser and V. Galitski, "Analogue Stochastic Gravity in Strongly-Interacting BECs," arXiv:1612.08980
Quantum friction effects in superfluids