  We study the sensitivity of large-scale xenon detectors to low-energy solar
neutrinos, to coherent neutrino-nucleus scattering and to neutrinoless double
beta decay. As a concrete example, we consider the xenon part of the proposed
DARWIN (Dark Matter WIMP Search with Noble Liquids) experiment. We perform
detailed Monte Carlo simulations of the expected backgrounds, considering
realistic energy resolutions and thresholds in the detector. In a low-energy
window of 2-30 keV, where the sensitivity to solar pp and $^7$Be-neutrinos is
highest, an integrated pp-neutrino rate of 5900 events can be reached in a
fiducial mass of 14 tons of natural xenon, after 5 years of data. The
pp-neutrino flux could thus be measured with a statistical uncertainty around
1%, reaching the precision of solar model predictions. These low-energy solar
neutrinos will be the limiting background to the dark matter search channel for
WIMP-nucleon cross sections below $\sim$2$\times$10$^{-48}$ cm$^2$ and WIMP
masses around 50 GeV$\cdot$c$^{-2}$, for an assumed 99.5% rejection of
electronic recoils due to elastic neutrino-electron scatters. Nuclear recoils
from coherent scattering of solar neutrinos will limit the sensitivity to WIMP
masses below $\sim$6 GeV$\cdot$c$^{-2}$ to cross sections above
$\sim$4$\times$10$^{-45}$cm$^2$. DARWIN could reach a competitive half-life
sensitivity of 5.6$\times$10$^{26}$ y to the neutrinoless double beta decay of
$^{136}$Xe after 5 years of data, using 6 tons of natural xenon in the central
detector region.
