  We determine the excitation spectrum of a bosonic dipolar quantum gas in a
one-dimensional geometry, from the dynamical density-density correlation
functions simulated by means of Reptation Quantum Monte Carlo techniques. The
excitation energy is always vanishing at the first vector of the reciprocal
lattice in the whole crossover from the liquid-like at low density to the
quasi-ordered state at high density, demonstrating the absence of a roton
minimum. Gaps at higher reciprocal lattice vectors are seen to progressively
close with increasing density, while the quantum state evolves into a
quasi-periodic structure. The simulational data together with the
uncertainty-principle inequality also provide a rigorous proof of the absence
of long-range order in such a super-strongly correlated system. Our conclusions
confirm that the dipolar gas is in a Luttinger-liquid state, significantly
affected by the dynamical correlations. The connection with ongoing experiments
is also discussed.
