Quantum weak measurements with states both pre- and postselected offer a window into a hitherto neglected sector of quantum mechanics. A class of such systems involves time dependent evolution with transitions possible. In this paper we explore two v
ery simple systems in this class. The first is a toy model representing the decay of an excited atom. The second is the tunneling of a particle through a barrier. The postselection criteria are chosen as follows: at the final time, the atom remains in its initial excited state for the first example and the particle remains behind the barrier for the second. We then ask what weak values are predicted in the physical environment of the atom (to which no net energy has been transferred) and in the region beyond the barrier (to which the particle has not tunneled). Previous work suggests that very large weak values might arise in these regions for long durations between pre- and postselection times. Our calculations reveal some distinct differences between the two model systems.
Field theories in black hole spacetimes undergo dimensional reduction near horizon (in the Rindler limit) to two dimensional conformal field theories. We investigate this enhancement of symmetries in the context of gauge/gravity duality by considerin
g Rindler space as boundary of Anti-de Sitter space in three spacetime dimensions. We show that the loxodromy conjugacy class of the SO(2,2) isometry group is responsible for generating the special conformal transformations on the boundary under RG flow. We use this approach to present an alternative derivation of the two-point function in Rindler space using AdS/CFT correspondence.
We obtain all the stationary vacua of de Sitter space by classifying the inequivalent timelike isometries of the de Sitter group. Besides the static vacuum, de Sitter space also admits a family of rotating vacua, which we use to obtain Kerr-de Sitter
solutions in various dimensions. By writing the metric in a coordinate system adapted to the rotating Hamiltonian, we show that empty de Sitter space admits not only an observer-dependent horizon but also an observer-dependent ergosphere.
