On the Symmetry Foundation of Double Soft Theorems

Double-soft theorems, like its single-soft counterparts, arises from the underlying symmetry principles that constrain the interactions of massless particles. While single soft theorems can be derived in a non-perturbative fashion by employing current algebras, recent attempts of extending such an approach to known double soft theorems has been met with difficulties. In this work, we have traced the difficulty to two inequivalent expansion schemes, depending on whether the soft limit is taken asymmetrically or symmetrically, which we denote as type A and B respectively. We show that soft-behaviour for type A scheme can simply be derived from single soft theorems, and are thus non-preturbatively protected. For type B, the information of the four-point vertex is required to determine the corresponding soft theorems, and thus are in general not protected. This argument can be readily extended to general multi-soft theorems. We also ask whether unitarity can be emergent from locality together with the two kinds of soft theorems, which has not been fully investigated before.Comment: 45 pages, 7 figure

Modeling incompressible thermal flows using a central-moment-based lattice Boltzmann method

In this paper, a central-moment-based lattice Boltzmann (CLB) method for incompressible thermal flows is proposed. In the method, the incompressible Navier-Stokes equations and the convection-diffusion equation for the temperature field are sloved separately by two different CLB equations. Through the Chapman-Enskog analysis, the macroscopic governing equations for incompressible thermal flows can be reproduced. For the flow field, the tedious implementation for CLB method is simplified by using the shift matrix with a simplified central-moment set, and the consistent forcing scheme is adopted to incorporate forcing effects. Compared with several D2Q5 multiple-relaxation-time (MRT) lattice Boltzmann methods for the temperature equation, the proposed method is shown to be better Galilean invariant through measuring the thermal diffusivities on a moving reference frame. Thus a higher Mach number can be used for convection flows, which decreases the computational load significantly. Numerical simulations for several typical problems confirm the accuracy, efficiency, and stability of the present method. The grid convergence tests indicate that the proposed CLB method for incompressible thermal flows is of second-order accuracy in space

Electron-electron scatttering in Sn-doped indium oxide thick films

We have measured the low-field magnetoresistances (MRs) of a series of Sn-doped indium oxide thick films in the temperature $T$ range 4--35 K. The electron dephasing rate $1/\tau_{\varphi}$ as a function of $T$ for each film was extracted by comparing the MR data with the three-dimensional (3D) weak-localization theoretical predictions. We found that the extracted $1/\tau_{\varphi}$ varies linearly with $T^{3/2}$. Furthermore, at a given $T$, $1/\tau_{\varphi}$ varies linearly with $k_F^{-5/2}l^{-3/2}$, where $k_{F}$ is the Fermi wavenumber, and $l$ is the electron elastic mean free path. These features are well explained in terms of the small-energy-transfer electron-electron scattering time in 3D disordered conductors. This electron dephasing mechanism dominates over the electron-phonon ($e$-ph) scattering process because the carrier concentrations in our films are $\sim$ 3 orders of magnitude lower than those in typical metals, which resulted in a greatly suppressed $e$-ph relaxation rate.Comment: 5 pages, 3 figure