  We consider the behaviour of a critical system in the presence of a gradient
perturbation of the couplings. In the direction of the gradient an interface
region separates the ordered phase from the disordered one. We develop a
scaling theory for the density profiles induced by the gradient perturbation
which involves a characteristic length given by the width of the interface
region. The scaling predictions are tested in the framework of the mean-field
Ginzburg-Landau theory. Then we consider the Ising quantum chain in a linearly
varying transverse field which corresponds to the extreme anisotropic limit of
a classical two-dimensional Ising model. The quantum Hamiltonian can be
diagonalized exactly in the scaling limit where the eigenvalue problem is the
same as for the quantum harmonic oscillator. The energy density, the
magnetization profile and the two-point correlation function are studied either
analytically or by exact numerical calculations. Their scaling behaviour are in
agreement with the predictions of the scaling theory.
