Evolution of confined quantum scalar fields in curved spacetime. Part I

Abstract

We develop a method for computing the Bogoliubov transformation experienced by a confined quantum scalar field in a globally hyperbolic spacetime, due to the changes in the geometry and/or the confining boundaries. The method constructs a basis of modes of the field associated to each Cauchy hypersurface, by means of an eigenvalue problem posed in the hypersurface. The Bogoliubov transformation between bases associated to different times can be computed through a differential equation, which coefficients have simple expressions in terms of the solutions to the eigenvalue problem. This transformation can be interpreted physically when it connects two regions of the spacetime where the metric is static. Conceptually, the method is a generalisation of Parker’s early work on cosmological particle creation. It proves especially useful in the regime of small perturbations, where it allows one to easily make quantitative predictions on the amplitude of the resonances of the field, providing an important tool in the growing research area of confined quantum fields in table-top experiments. We give examples within the perturbative regime (gravitational waves) and the non-perturbative regime (cosmological particle creation). This is the first of two articles introducing the method, dedicated to spacetimes without boundaries or which boundaries remain static in some synchronous gauge.

Introduction to gravitational redshift of quantum photons propagating in curved spacetime

“…If the notion of time is not easily obtainable, in the sense that there is no preferred timelike Killing vector to choose, one can still try to look for consistent ways to propagate solutions from one foliation of the spacetime to the next, but this becomes extremely difficult from an algebraic perspective. Some work in this direction has been performed with a reasonable degree of success [68,69].…”

Evolution of confined quantum scalar fields in curved spacetime. Part II

“…In the preceding article [ 13 ], which we shall call “Part I”, we constructed a method for computing the evolution of a confined quantum scalar field in a globally hyperbolic spacetime, by means of a time-dependent Bogoliubov transformation. The method proved especially useful for addressing the kind of problems just mentioned, related to confined quantum fields undergoing small perturbations, although it is of general applicability (under some minor assumptions).…”