  We study the pointwise behavior of the linearized Boltzmann equation on torus
for non-smooth initial perturbation. The result reveals both the fluid and
kinetic aspects of this model. The fluid-like waves are constructed as part of
the long-wave expansion in the spectrum of the Fourier mode for the space
variable, the time decay rate of the fluid-like waves depends on the size of
the domain. We design a Picard-type iteration for constructing the increasingly
regular kinetic-like waves, which are carried by the transport equations and
have exponential time decay rate. Moreover, the mixture lemma plays an
important role in constructing the kinetic-like waves, we supply a new proof of
this lemma to avoid constructing explicit solution of the damped transport
equations
