This article reviews the role of reparametrization invariance (the invariance of the properties of a system with respect to the choice of the co-ordinate system used to describe it) in deriving stochastic equations that describe the growth of surfaces. By imposing reparametrization invariance on a system, the authors identify the physical origin of many of the terms in its growth equations. Both continuum-growth equations for interfaces and equations for the coarse-grained evolution of discrete-lattice models are derived with this method. A detailed analysis of the discrete-lattice case and its small-gradient expansion provides a physical basis for terms found in commonly studied growth equations. The reparametrization-invariant formulation of growth processes also has the advantage of allowing one to model shadowing effects that are lost in the no-overhang approximation and to conserve underlying symmetries of the system that are lost in a small-gradient expansion. Finally, a knowledge of the full equation of motion, beyond the lowest-order gradient expansion, may be relevant in problems where the usual perturbative renormalization methods fail

Recently M. Manzoni and N. Manini, who reanalyzed [1] the determination of parameters ξ and λ of the extended Thomas-Fermi density functional on the basis of Monte Carlo data [2], pointed out a possible error in our previous deter-mination of these parameters. By repeating the calculations we indeed find that the best-fit values are slightly different: ξ = 0.468 and λ = 0.086. This modification does not change any of the physical conclusions of our paper.[1] M. Manzoni, B.Sc. Thesis,

We consider a bosonic Josephson junction made of N ultracold and dilute atoms confined by a quasi-onedimensional double-well potential within the two-site Bose-Hubbard model framework. The behavior of the system is investigated at zero temperature by varying the interatomic interaction from the strongly attractive regime to the repulsive one. We show that the ground state exhibits a crossover from a macroscopic Schrödinger-cat state to a separable Fock state through an atomic coherent regime. By diagonalizing the Bose-Hubbard Hamiltonian we characterize the emergence of the macroscopic cat states by calculating the Fisher information F , the coherence by means of the visibility α of the interference fringes in the momentum distribution, and the quantum correlations by using the entanglement entropy S. Both Fisher information and visibility are shown to be related to the ground-state energy by employing the Hellmann-Feynman theorem. This result, together with a perturbative calculation of the ground-state energy, allows simple analytical formulas for F and α to be obtained over a range of interactions, in excellent agreement with the exact diagonalization of the Bose-Hubbard Hamiltonian. In the attractive regime the entanglement entropy attains values very close to its upper limit for a specific interaction strength lying in the region where coherence is lost and self-trapping sets in.

AIkali atoms have been shown previously to have only unstable binding states inside liquid He-4. We calculate the equilibrium configurations and binding energies of single alkali atoms near the liquid-vapor interface of He-4 and He-3. A simple interface model is used to predict the surface deformation due to the presence of the atoms. A more realistic density functional model yields somewhat higher energies in the case of He-4. For all alkali atoms, we find the surface binding energies to be around 10 to 20 K. A similar analysis with atom-H-2 interactions finds that alkali atoms tend to submerge into liquid H-2, with the exception of Li