Kinematics of Acceleration-Induced Excitations in Confined Quantum Fields

TL;DR

We address acceleration-induced excitations of a massless scalar field confined in a rigid 1+1D cavity with fixed proper length. The main approach uses exact Bogoliubov transformations between inertial and accelerated mode bases to quantify particle creation during a sudden inertial-to-accelerated transition and to reveal a universal, acceleration-dominated spectrum. A key finding is that the frequency-domain spectrum scales as $P(\Omega_O) \propto a_O^2/\Omega_O^3$ and is independent of the cavity size or observer position, signaling a kinematic universality related to horizon physics. The work further extends to time-dependent accelerations, where the Bogoliubov coefficients acquire a convolution structure and can exhibit resonant enhancement of specific modes, with implications for cavity QED and related quantum technologies.

Abstract

We investigate quantum field excitations in a rigid cavity that undergoes a transition from inertial motion to uniform acceleration while maintaining constant proper length. By constructing exact Bogoliubov transformations between inertial and accelerated mode bases, we analyze the induced excitations and identify a universal power-law decay in the excitation power spectrum and an alternating pattern in particle production. The spectrum's dependence solely on the acceleration, and not on the size of the box or the observer's position, highlights a kinematic universality akin to that seen in horizon thermodynamics. Generalization to time-dependent accelerations reveals a convolution structure for the Bogoliubov coefficients, with resonant oscillations selectively enhancing mode excitations. These results provide new analytical insights into the interplay between acceleration, confinement, and quantum excitations.

Figures (7)

• Figure 1: Worldlines of the left and right edges of the box confining the field, plotted in Minkowski coordinates $(T,X)$. The box transitions from inertial motion to uniform acceleration at $T = 0$.
• Figure 2: The spectra of particles created as the box starts accelerating, plotted for different values of $aL$.
• Figure 3: A plot showing the excitation spectrum in the low $aL$ limit.
• Figure 4: A generic plot of the function $p(y)$.
• Figure 5: Exact spectra of excitations, as calculated before, shown on a log-log plot, with the large-$n$ fit shown in dashed lines.