Kinematics of Acceleration-Induced Excitations in Confined Quantum Fields

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.