Abstract
We study the quantum radiation of particle production by vacuum from an ultra-relativistic moving mirror (dynamical Casimir effect) solution that allows (possibly for the first time) analytically calculable time evolution of particle creation and an Airy particle spectral distribution. The reality of the beta Bogoliubov coefficients is responsible for the simplicity, and the mirror is asymptotically inertial at the speed of light, with finite energy production. We also discuss general relations regarding negative energy flux, the transformation to the 1-D Schrödinger equation, and the incompleteness of entanglement entropy.
Highlights
The dynamical Casimir effect (DCE) [1,2,3,4] is a celebrated and multidisciplinary phenomena that plays an important role in many areas of physics ranging from quantum fields, atomic physics, condensed matter, and applications in nanotechnology all the way to astrophysics, cosmology and gravitation
An interesting connection between the reality of the beta Bogoliubov coefficient, asymptotic inertia and finite energy, and mirror motion near the speed of light leads to particle radiation by quantum vacuum that is analytic in the energy flux, simple in the particle spectrum—an Airy function—and, remarkably, analytic expression of the time evolution of particle creation
The Airy mirror is asymptotically inertial, coasting at the speed of light; the total energy radiated is finite and κ/96 despite a soft particle divergence; the beta Bogoliubov coefficient is given by a real Airy-Ai function; the particle creation time evolution is analytic and exact
Summary
The dynamical Casimir effect (DCE) [1,2,3,4] is a celebrated and multidisciplinary phenomena that plays an important role in many areas of physics ranging from quantum fields, atomic physics, condensed matter, and applications in nanotechnology all the way to astrophysics, cosmology and gravitation. The simplest odd function that accelerates in the required manner is f (v) ∼ vs + v3 We will find this results in interesting dynamics, but analytic calculation of particle production spectrum and time evolution. The only difference here is that the initial asymptotic inertial state of motion saturates the speed limit and pushes the model to its extreme, but causal effects on the field are still in the past light cone of the ‘reflection’ events that disturb the quantum field and amplify zero-point fluctuations. The fact that the total energy is positive is consistent with the quantum interest conjecture [37] as derived from quantum inequalities [38]
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