Kink excitation spectra in the (1+1)-dimensional φ8\varphi^8 model

We study excitation spectra of BPS-saturated topological solutions -- the kinks -- of the $\varphi^8$ scalar field model in $(1+1)$ dimensions, for three different choices of the model parameters. We demonstrate that some of these kinks have a vibrational mode, apart from the trivial zero (translational) excitation. One of the considered kinks is shown to have three vibrational modes. We perform a numerical calculation of the kink-kink scattering in one of the considered variants of the $\varphi^8$ model, and find the critical collision velocity v_{\scriptsize \mbox{cr}} that separates the different collision regimes: inelastic bounce of the kinks at v_{\scriptsize \mbox{in}}\ge v_{\scriptsize \mbox{cr}}, and capture at v_{\scriptsize \mbox{in}}. We also observe escape windows at some values of v_{\scriptsize \mbox{in}} where the kinks escape to infinity after bouncing off each other two or more times. We analyse the features of these windows and discuss their relation to the resonant energy exchange between the translational and the vibrational excitations of the colliding kinks.Comment: 20 pages, 14 figures; V2: minor changes to match version published in JHE

Visualizing the connection between edge states and the mobility edge in adiabatic and nonadiabatic topological charge transport

The ability to pump quantized amounts of charge is one of the hallmarks of topological materials. An archetypical example is Laughlin's gauge argument for transporting an integer number of electrons between the edges of a quantum Hall cylinder upon insertion of a magnetic flux quantum. This is mathematically equivalent to the equally famous suggestion of Thouless that an integer number of electrons is pumped between two ends of a one-dimensional quantum wire upon sliding a charge-density wave over a single wavelength. We use the correspondence between these descriptions to visualize the detailed dynamics of the electron flow during a single pumping cycle, which is difficult to do directly in the quantum Hall setup because of the gauge freedom inherent in its description. We find a close correspondence between topological edge states and the mobility edges in charge-density wave, quantum Hall, and other topological systems. We illustrate this connection by describing an alternative, nonadiabatic mode of topological transport that displaces precisely the opposite amount of charge compared to the adiabatic pump. We discuss possible experimental realizations in the context of ultracold atoms and photonic waveguide experiments