Improved variational description of the Wick-Cutkosky model with the most general quadratic trial action

We generalize the worldline variational approach to field theory by introducing a trial action which allows for anisotropic terms to be induced by external 4-momenta of Green's functions. By solving the ensuing variational equations numerically we demonstrate that within the (quenched) scalar Wick-Cutkosky model considerable improvement can be achieved over results obtained previously with isotropic actions. In particular, the critical coupling associated with the instability of the model is lowered, in accordance with expectations from Baym's proof of the instability in the unquenched theory. The physical picture associated with a different quantum mechanical motion of the dressed particle along and perpendicular to its classical momentum is discussed. Indeed, we find that for large couplings the dressed particle is strongly distorted in the direction of its four-momentum. In addition, we obtain an exact relation between the renormalized coupling of the theory and the propagator. Along the way we introduce new and efficient methods to evaluate the averages needed in the variational approach and apply them to the calculation of the 2-point function.Comment: 32 pages, 4 figures, Latex. Some typos corrected and expanded discussion of the instability of the model provided. Accepted in Eur. Phys. J.

Integrable impurities for an open fermion chain

Employing the graded versions of the Yang-Baxter equation and the reflection equations, we construct two kinds of integrable impurities for a small-polaron model with general open boundary conditions: (a) we shift the spectral parameter of the local Lax operator at arbitrary sites in the bulk, and (b) we embed the impurity fermion vertex at each boundary of the chain. The Hamiltonians with different types of impurity terms are given explicitly. The Bethe ansatz equations, as well as the eigenvalues of the Hamiltonians, are constructed by means of the quantum inverse scattering method. In addition, we discuss the ground-state properties in the thermodynamic limit.Comment: 20 pages, 4 figure

Partitioning Schemes and Non-Integer Box Sizes for the Box-Counting Algorithm in Multifractal Analysis

We compare different partitioning schemes for the box-counting algorithm in the multifractal analysis by computing the singularity spectrum and the distribution of the box probabilities. As model system we use the Anderson model of localization in two and three dimensions. We show that a partitioning scheme which includes unrestricted values of the box size and an average over all box origins leads to smaller error bounds than the standard method using only integer ratios of the linear system size and the box size which was found by Rodriguez et al. (Eur. Phys. J. B 67, 77-82 (2009)) to yield the most reliable results.Comment: 10 pages, 13 figure

Variational calculation of relativistic meson-nucleon scattering in zeroth order

We extend the polaron variational treatment previously developed for the propagator to the case where one nucleon and n external mesons are present. Using the particle representation of the scalar Wick-Cutkosky model this is done in lowest order of an expansion of the exact action around a retarded quadratic trial action. In particular, we evaluate the form factor for scattering of mesons from the scalar nucleon and determine the radius of the dressed particle. After analytic continuation to Minkowski space we study elastic meson-nucleon scattering both analytically and numerically near threshold and show that it is essential to incorporate the correct behaviour of the retardation function at large proper times. Only if this is done the optical theorem is approximately fulfilled over a range of energies and coupling constants