Analog Unruh effect of inhomogeneous one-dimensional Dirac fermions

We study one-dimensional Dirac fermions in the presence of a spatially varying Dirac velocity $v(x)$, that can form an approximate laboratory-based Rindler Hamiltonian describing an observer accelerating in Minkowski spacetime. A sudden switch from a spatially homogeneous velocity [$v(x)$ constant] to a spatially varying velocity [$v(x)$ inhomogeneous] leads to the phenomenon of particle creation, i.e., an analog Unruh effect. We study the dependence of the analog Unruh effect on the precise form of the velocity profile, finding that while the ideal Unruh effect occurs for $v(x)\ensuremath{\propto}|x|$, a modified Unruh effect still occurs for more realistic velocity profiles that are linear for $|x|$ smaller than a length scale $\ensuremath{\lambda}$ and constant for $|x|\ensuremath{\gg}\ensuremath{\lambda}$ [such as $v(x)\ensuremath{\propto}tanh(|x|/\ensuremath{\lambda})$]. We show that the associated particle creation is localized to $|x|\ensuremath{\ll}\ensuremath{\lambda}$.