arXiv subjects

Antun Balaz

Publications and source records attributed to Antun Balaz.

49 records · Page 3Linked to original sources

arXiv2008

Recursive Schr\" odinger Equation Approach to Faster Converging Path Integrals

By recursively solving the underlying Schr\" odinger equation, we set up an efficient systematic approach for deriving analytic expressions for discretized effective actions. With this we obtain discrete short-time propagators for both one and many particles in arbitrary dimension to orders which have not been accessible before. They can be used to substantially speed up numerical Monte Carlo calculations of path integrals, as well as for setting up a new analytical approximation scheme for energy spectra, density of states, and other statistical properties of quantum systems.

cond-mat.stat-mech↗

arXiv2008

Consequences of increased longevity for wealth, fertility, and population growth

We present, solve and numerically simulate a simple model that describes the consequences of increased longevity on fertility rates, population growth and the distribution of wealth in developed societies. We look at the consequences of the repeated use of life extension techniques and show that they represent a novel commodity whose introduction will profoundly influence key aspects of economy and society in general. In particular, we uncover two phases within our simplified model, labeled as 'mortal' and 'immortal'. Within the life extension scenario it is possible to have sustainable economic growth in a population of stable size, as a result of dynamical equilibrium between the two phases.

q-fin.GN↗

arXiv2008

Fast Convergence of Path Integrals for Many-body Systems

We generalize a recently developed method for accelerated Monte Carlo calculation of path integrals to the physically relevant case of generic many-body systems. This is done by developing an analytic procedure for constructing a hierarchy of effective actions leading to improvements in convergence of $N$-fold discretized many-body path integral expressions from 1/N to $1/N^p$ for generic $p$. In this paper we present explicit solutions within this hierarchy up to level $p=5$. Using this we calculate the low lying energy levels of a two particle model with quartic interactions for several values of coupling and demonstrate agreement with analytical results governing the increase in efficiency of the new method. The applicability of the developed scheme is further extended to the calculation of energy expectation values through the construction of associated energy estimators exhibiting the same speedup in convergence.

cond-mat.stat-mech↗

arXiv2006

Efficient Calculation of Energy Spectra Using Path Integrals

A newly developed method for systematically improving the convergence of path integrals for transition amplitudes, introduced in Phys. Rev. Lett. 94 (2005) 180403, Phys. Rev. B 72 (2005) 064302, Phys. Lett. A 344 (2005) 84, and expectation values, introduced in Phys. Lett. A 360 (2006) 217, is here applied to the efficient calculation of energy spectra. We show how the derived hierarchies of effective actions lead to substantial speedup of the standard path integral Monte Carlo evaluation of energy levels. The general results and the ensuing increase in efficiency of several orders of magnitude are shown using explicit Monte Carlo simulations of several distinct models.

cond-mat.stat-mech↗

arXiv2006

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.

cond-mat.stat-mech↗

arXiv2005

Systematic Speedup of Path Integrals of a Generic $N$-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 Pöschl-Teller potential.

cond-mat.stat-mech↗

arXiv2005

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.

cond-mat.stat-mech↗

arXiv2005

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.

cond-mat.stat-mech↗

arXiv2005

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.

cond-mat.stat-mech↗

arXiv2005

Dyons in Nonabelian Born-Infeld Theory

We analyze a nonabelian extension of Born--Infeld action for the SU(2) group. In the class of spherically symmetric solutions we find that, besides the Gal'tsov--Kerner glueballs, only the analytic dyons have finite energy. The presented analytic and numerical investigation excludes the existence of pure magnetic monopoles of 't Hooft--Polyakov type.

hep-th↗

arXiv2005

Systematically Accelerated Convergence of Path Integrals

We present a new analytical method that systematically improves the convergence of path integrals of a generic $N$-fold discretized theory. Using it we calculate the effective actions $S^{(p)}$ for $p\le 9$ which lead to the same continuum amplitudes as the starting action, but that converge to that continuum limit as $1/N^p$. We checked this derived speedup in convergence by performing Monte Carlo simulations on several different models.

cond-mat.stat-mech↗

arXiv1998

Improved Gaussian Approximation

In a recently developed approximation technique for quantum field theory the standard one-loop result is used as a seed for a recursive formula that gives a sequence of improved Gaussian approximations for the generating functional. In this paper we work with the generic $ϕ^3+ϕ^4$ model in $d=0$ dimensions. We compare the first, and simplest, approximation in the above sequence with the one-loop and two-loop approximations, as well as the exact results (calculated numericaly).

hep-th↗

arXiv1998

An Improved Gaussian Approximation for Quantum Field Theory

We present a new approximation technique for quantum field theory. The standard one-loop result is used as a seed for a recursive formula that gives a sequence of improved Gaussian approximations for the generating functional. In a different setting, the basic idea of this recursive scheme is used in the second part of the paper to substantialy speed up the standard Monte Carlo algorithm.

hep-th↗