Enhancement and Suppression of Decay Rates in an Accelerated Fermionic Cavity Coupled to a Massive Field

Abstract

We study a (1+1)-dimensional model in which a massless Dirac field, initially in an excited state inside a uniformly accelerated cavity, decays to its ground state, accompanied by the excitation of an external massive Dirac field of mass $M$, through a local coupling confined to the physical extent of the cavity. The confinement mechanism is modeled via MIT bag boundary conditions and their probabilistic extensions, which depend on a boundary angle $\theta \in[0,2\pi)$ and $s\in(0,1)$. For intermediate-sized cavities ($a l \sim c^2$) with light external massive Dirac field ($Mc^2 \ll \hbar a/c$), we demonstrate that the total long-time asymptotic decay rate factorizes as $ \Gamma_{\text{acc}}/ \Gamma_{\text{in}} \sim F_g F_T $ with $\Gamma_{\text{in}}$ the inertial decay rate. Here, $F_g=\frac{al/c^2}{\ln(1 + al/c^2)}$ is a geometric factor, and $F_T= (1 + e^{-2\pi\beta})^{-1}$ is the thermal stimulation factor from the Unruh bath ($\beta = \frac{\Omega_1 c}{a} =\frac{(1+s)\pi}{\ln(1 + a l/c^2)}$). Crucially, in this regime, the thermal factor $F_T$ remains approximately unity for all admissible boundary conditions, while the geometric factor $\frac{a l/c^2}{\ln(1 + a l/c^2)}$ produces measurable enhancements up to 26\% for realistic parameters ($a=10^{20}$ m/s$^2$, $l=500~\mu$m), and represents a measurable signature accessible through quantum simulation platforms. In contrast, for heavy external fermionic fields (such as the electron field), the condition $M c^2 \gg \hbar a / c$ is satisfied at all achievable accelerations, placing the system in a regime of exponential suppression, $\Gamma_{\text{acc}}/\Gamma_{\text{in}} \sim \exp(-2 M c^2 / (\hbar a/c))$, for all cavity sizes....