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 ($al\sim c^2$) with light external massive Dirac field ($M{c}^2\ll \hslash a/c$), 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 ($\beta =\frac{{\Omega }_{1}c}{a}=\frac{(1+s)\pi }{\ln (1+al/c^2)}$). Crucially, in this regime, the thermal factor $F_T$ remains approximately unity for all admissible boundary conditions, while the geometric factor $\frac{al/c^2}{\ln (1+al/c^2)}$ 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 $M{c}^2\gg \hslash a/c$ is satisfied at all achievable accelerations, placing the system in a regime of exponential suppression, ${\Gamma }_{\text{acc}}/{\Gamma }_{\text{in}}\sim \exp (-2M{c}^2/(\hslash a/c))$, for all cavity sizes....

39 pages, published version, Abstract is shortened due to arXiv character limit

References in corpus (5)

• The Unruh effect and its applications
• Entanglement of Dirac fields in non-inertial frames
• Relativistic Quantum Teleportation with Superconducting Circuits
• Unruh-DeWitt detector's response to fermions in flat spacetimes
• Minkowski vacuum in Rindler spacetime and Unruh thermal state for Dirac fields