A Note on Boltzmann Brains

Understanding the observed arrow of time is equivalent, under general assumptions, to explaining why Boltzmann brains do not overwhelm ordinary observers. It is usually thought that this provides a condition on the decay rate of every cosmologically accessible de Sitter vacuum, and that this condition is determined by the production rate of Boltzmann brains calculated using semiclassical theory built on each such vacuum. We argue, based on a recently developed picture of microscopic quantum gravitational degrees of freedom, that this thinking needs to be modified. In particular, depending on the structure of the fundamental theory, the decay rate of a de Sitter vacuum may not have to satisfy any condition except for the one imposed by the Poincare recurrence. The framework discussed here also addresses the question of whether a Minkowski vacuum may produce Boltzmann brains.Comment: 10 pages, 1 figure; discussion in Section 4 modified and expande

Two-magnon excitations in resonant inelastic x-ray scattering studied by spin-density-wave formalism

We study two-magnon excitations in resonant inelastic x-ray scattering (RIXS) at the transition-metal $K$-edge. Instead of working with effective Heisenberg spin models, we work with a Hubbard-type model ($d$-$p$ model) for a typical insulating cuprate La$_2$CuO$_4$. For the antiferromagnetic ground state within the spin-density-wave (SDW) mean-field formalism, we calculate the dynamical correlation function within the random-phase approximation (RPA), and then obtain two-magnon excitation spectra by calculating the convolution of it. Coupling between the $K$-shell hole and the magnons in the intermediate state is calculated by means of diagrammatic perturbation expansion in the Coulomb interaction. Calculated momentum dependence of RIXS spectra agrees well with that of experiments. A notable difference from previous calculations based on the Heisenberg spin models is that RIXS spectra have a large two-magnon weight near the zone center, which may be confirmed by further careful high-resolution experiments.Comment: 16 pages, 7 figures. Accepted to Phys. Rev.

Spacetime and universal soft modes: Black holes and beyond

Recently, a coherent picture of the quantum mechanics of an evaporating black hole has been presented which reconciles unitarity with the predictions of the equivalence principle. The thermal nature of a black hole as viewed in a distant reference frame arises from entanglement between the hard and soft modes generated by the chaotic dynamics at the string scale. In this paper, we elaborate on this picture, particularly emphasizing the importance of the chaotic nature of the string (UV) dynamics across all low-energy species in generating large (IR) spacetime behind the horizon. Implications of this UV/IR relation include O(1) breaking of global symmetries at the string scale and a self-repair mechanism of black holes restoring the smoothness of their horizons. We also generalize the framework to other systems, including Rindler, de Sitter, and asymptotically flat spacetimes, and find a consistent picture in each case. Finally, we discuss the origin of the particular construction adopted in describing the black hole interior as well as the outside of a de Sitter horizon. We argue that the construction is selected by the quantum-to-classical transition, in particular, the applicability of the Born rule in a quantum mechanical world