  We study the total particle current fluctuations in a one-dimensional
stochastic system of classical particles consisting of branching and death
processes which is a variant of asymmetric zero-temperature Glauber dynamics.
The full spectrum of a modified Hamiltonian, whose minimum eigenvalue generates
the large deviation function for the total particle current fluctuations
through a Legendre-Fenchel transformation, is obtained analytically. Three
examples are presented and numerically exact results are compared to our
analytical calculations.
