  We present a general derivation of the spectrum of excitations for gapless
states of zero entropy density in Bethe ansatz solvable models. Our formalism
is valid for an arbitrary choice of bare energy function which is relevant to
situations where the Hamiltonian for time evolution differs from the
Hamiltonian in a (generalized) Gibbs ensemble, i.e. out of equilibrium. The
energy of particle and hole excitations, as measured with the time-evolution
Hamiltonian, is shown to include additional contributions stemming from the
shifts of the Fermi points that may now have finite energy. The finite-size
effects are also derived and the connection with conformal field theory
discussed. The critical exponents can still be obtained from the finite-size
spectrum, however the velocity occurring here differs from the one in the
constant Casimir term. The derivation highlights the importance of the phase
shifts at the Fermi points for the critical exponents of asymptotes of
correlations. We generalize certain results known for the ground state and
discuss the relation to the dressed charge (matrix). Finally, we discuss the
finite-size corrections in the presence of an additional particle or hole which
are important for dynamical correlation functions.
