Wigner function method for the Gibbons-Hawking and the Unruh effect

TL;DR

This paper introduces a Wigner function approach to analyze the Gibbons-Hawking and Unruh effects in realistic, non-ideal conditions, revealing both Planckian and non-Planckian vacuum spectra in cosmological and laboratory models.

Contribution

It develops a time-dependent spectral analysis method using the Wigner function to study quantum vacuum effects in realistic, non-ideal scenarios.

Findings

Planck spectra in certain cosmological models

Non-Planckian, negative Wigner functions in laboratory analogues

Effective characterization of vacuum fluctuations in non-uniform conditions

Abstract

An observer at rest with the expanding universe experiences some extra noise in the quantum vacuum, and so does an accelerated observer in a vacuum at rest (in Minkowski space). The literature mainly focuses on the ideal cases of exponential expansion (de-Sitter space) or uniform acceleration (Rindler trajectories) or both, but the real cosmic expansion is non-exponential and real accelerations are non-uniform. Here we use the frequency-time Wigner function of vacuum correlations to define time-dependent spectra. We found excellent Planck spectra for a class of realistic cosmological models, but also strongly non-Planckian, negative Wigner functions for a standard scenario testable with laboratory analogues.