Diffusion-annihilation dynamics in one spatial dimension

We discuss a reaction-diffusion model in one dimension subjected to an external driving force. Each lattice site may be occupied by at most one particle. The particles hop with asymmetric rates (the sum of which is one) to the right or left nearest neighbour site if it is vacant, and annihilate with rate one if it is occupied. We compute the long time behaviour of the space dependent average density in states where the initial density profiles are step functions. We also compute the exact time dependence of the particle density for uncorrelated random initial conditions. The representation of the uncorrelated random initial state and also of the step function profile in terms of free fermions allows the calculation of time-dependent higher order correlation functions. We outline the procedure using a field theoretic approach.Comment: 26 pages, 1 Postscript figure, uses epsf.st

Three-dimensional quasi-Tonks gas in a harmonic trap

We analyze the macroscopic dynamics of a Bose gas in a harmonic trap with a superimposed two-dimensional optical lattice, assuming a weak coupling between different lattice sites. We consider the situation in which the local chemical potential at each lattice site can be considered as that provided by the Lieb-Liniger solution. Due to the weak coupling between sites and the form of the chemical potential, the three-dimensional ground-state density profile and the excitation spectrum acquire remarkable properties different from both 1D and 3D gases. We call this system a quasi-Tonks gas. We discuss the range of applicability of this regime, as well as realistic experimental situations where it can be observed.Comment: 4 pages, 3 figures, misprints correcte

Three dimensional Lifshitz black hole and the Korteweg-de Vries equation

We consider a solution of three dimensional New Massive Gravity with a negative cosmological constant and use the AdS/CTF correspondence to inquire about the equivalent two dimensional model at the boundary. We conclude that there should be a close relation with the Korteweg-de Vries equation.Comment: 4 page