Wick Rotation and Abelian Bosonization

We investigate the connection between Abelian bosonization in the Minkowski and Euclidean formalisms. The relation is best seen in the complex time formalism of S. A. Fulling and S. N. M. Ruijsenaars \cite{fulling}.Comment: 8 pages, Latex 2e, 3 figure

Jaggedness of Path Integral Trajectories

We define and investigate the properties of the jaggedness of path integral trajectories. The new quantity is shown to be scale invariant and to satisfy a self-averaging property. Jaggedness allows for a classification of path integral trajectories according to their relevance. We show that in the continuum limit the only paths that are not of measure zero are those with jaggedness 1/2, i.e. belonging to the same equivalence class as random walks. The set of relevant trajectories is thus narrowed down to a specific subset of non-differentiable paths. For numerical calculations, we show that jaggedness represents an important practical criterion for assessing the quality of trajectory generating algorithms. We illustrate the obtained results with Monte Carlo simulations of several different models.Comment: 11 pages, 7 figures, uses elsart.cl

Scaling exponents and phase separation in a nonlinear network model inspired by the gravitational accretion

We study dynamics and scaling exponents in a nonlinear network model inspired by the formation of planetary systems. Dynamics of this model leads to phase separation to two types of condensate, light and heavy, distinguished by how they scale with mass. Light condensate distributions obey power laws given in terms of several identified scaling exponents that do not depend on initial conditions. The analyzed properties of heavy condensates have been found to be scale-free. Calculated mass distributions agree well with more complex models, and fit observations of both our own Solar System, and the best observed extra-solar planetary systems.Comment: 20 pages, 7 figures, 3 tables, uses elsarticle.cl

Generalization of Euler's Summation Formula to Path Integrals

A recently developed analytical method for systematic improvement of the convergence of path integrals is used to derive a generalization of Euler's summation formula for path integrals. The first $p$ terms in this formula improve convergence of path integrals to the continuum limit from 1/N to $1/N^p$, where $N$ is the coarseness of the discretization. Monte Carlo simulations performed on several different models show that the analytically derived speedup holds.Comment: 12 pages, 1 figure, uses elsart.cls, ref. [15] resolve

Asymptotic Properties of Path Integral Ideals

We introduce and analyze a new quantity, the path integral ideal, governing the flow of generic discrete theories to the continuum limit and greatly increasing their convergence. The said flow is classified according to the degree of divergence of the potential at spatial infinity. Studying the asymptotic behavior of path integral ideals we isolate the dominant terms in the effective potential that determine the behavior of a generic theory for large discrete time steps.Comment: 4 pages, 1 figure, revte

Properties of Quantum Systems via Diagonalization of Transition Amplitudes I: Discretization Effects

We analyze the method for calculation of properties of non-relativistic quantum systems based on exact diagonalization of space-discretized short-time evolution operators. In this paper we present a detailed analysis of the errors associated with space discretization. Approaches using direct diagonalization of real-space discretized Hamiltonians lead to polynomial errors in discretization spacing $\Delta$. Here we show that the method based on the diagonalization of the short-time evolution operators leads to substantially smaller discretization errors, vanishing exponentially with $1/\Delta^2$. As a result, the presented calculation scheme is particularly well suited for numerical studies of few-body quantum systems. The analytically derived discretization errors estimates are numerically shown to hold for several models. In the followup paper [1] we present and analyze substantial improvements that result from the merger of this approach with the recently introduced effective-action scheme for high-precision calculation of short-time propagation.Comment: 8 pages, 7 figures, uses revtex

Systematic Speedup of Path Integrals of a Generic NN-fold Discretized Theory

We present and discuss a detailed derivation of a new analytical method that systematically improves the convergence of path integrals of a generic $N$-fold discretized theory. We develop an explicit procedure for calculating a set of effective actions $S^{(p)}$, for $p=1,2,3,...$ which have the property that they lead to the same continuum amplitudes as the starting action, but that converge to that continuum limit ever faster. Discretized amplitudes calculated using the $p$ level effective action differ from the continuum limit by a term of order $1/N^p$. We obtain explicit expressions for the effective actions for levels $p\le 9$. We end by analyzing the speedup of Monte Carlo simulations of two different models: an anharmonic oscillator with quartic coupling and a particle in a modified P\"oschl-Teller potential.Comment: 10 pages, 5 figures, biblio info correcte

Energy Estimators and Calculation of Energy Expectation Values in the Path Integral Formalism

A recently developed method, introduced in Phys. Rev. Lett. 94 (2005) 180403, Phys. Rev. B 72 (2005) 064302, Phys. Lett. A 344 (2005) 84, systematically improved the convergence of generic path integrals for transition amplitudes. This was achieved by analytically constructing a hierarchy of $N$-fold discretized effective actions $S^{(p)}_N$ labeled by a whole number $p$ and starting at $p=1$ from the naively discretized action in the mid-point prescription. The derivation guaranteed that the level $p$ effective actions lead to discretized transition amplitudes differing from the continuum limit by a term of order $1/N^p$. Here we extend the applicability of the above method to the calculation of energy expectation values. This is done by constructing analytical expressions for energy estimators of a general theory for each level $p$. As a result of this energy expectation values converge to the continuum as $1/N^p$. Finally, we perform a series of Monte Carlo simulations of several models, show explicitly the derived increase in convergence, and the ensuing speedup in numerical calculation of energy expectation values of many orders of magnitude.Comment: 12 pages, 3 figures, 1 appendix, uses elsart.cl

Abelian Bosonization, the Wess-Zumino Functional and Conformal Symmetry

We look at the equivalence of the massive Thirring and sine-Gordon models. Previously, this equivalence was derived perturbatively in mass (though to all orders). Our calculation goes beyond that and uncovers an underlying conformal symmetry.Comment: 7 pages, Latex 2e, no figure

The Role of Conformal Symmetry in Abelian Bosonization of the Massive Thirring Model

We show equivalence between the massive Thirring model and the sine-Gordon theory by gauge fixing a wider gauge invariant theory in two different ways. The exact derivation of the equivalence hinges on the existence of an underlying conformal symmetry. Previous derivations were all perturbative in mass (althought to all orders).Comment: 5 pages, Latex 2e, Lectures given at 11th Yugoslav Symposium on Nuclear and Particle Physics, Studenica, September 199