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The recursive Neville algorithm allows one to calculate interpolating functions recursively. Upon a judicious choice of the abscissas used for the interpolation (and extrapolation), this algorithm leads to a method for convergence acceleration. For example, one can use the Neville algorithm in order to successively eliminate inverse powers of the upper limit of the summation from the partial sums of a given, slowly convergent input series. Here, we show that, for a particular choice of the abscissas used for the extrapolation, one can replace the recursive Neville scheme by a simple one-step transformation, while also obtaining access to subleading terms for the transformed series after convergence acceleration. The matrix-based, unified formulas allow one to estimate the rate of convergence of the partial sums of the input series to their limit. In particular, Bethe logarithms for hydrogen are calculated to 100 decimal digits., Comment: 13 pages; RevTeX

We analyze and model the stochastic behavior of paleoclimate time series and assess the implications for the coupling of climate variables during the Pleistocene glacial cycles. We examine 800 kiloyears of carbon dioxide, methane, nitrous oxide, and temperature proxy data from the European Project for Ice Coring in Antarctica (EPICA) Dome-C ice core, which are characterized by 100 ky glacial cycles overlain by fluctuations across a wide range of timescales. We quantify this behavior through multifractal time-weighted detrended fluctuation analysis, which distinguishes near-red-noise and white-noise behavior below and above the 100 ky glacial cycle, respectively, in all records. This allows us to model each time series as a one-dimensional periodic nonautonomous stochastic dynamical system, and assess the stability of physical processes and the fidelity of model-simulated time series. We extend this approach to a four-variable model with intervariable coupling terms, which we interpret in terms of possible interrelationships among the four time series. Within the framework of our coupling coefficients, we find that carbon dioxide and temperature act to stabilize each other and methane and nitrous oxide, whereas the latter two destabilize each other and carbon dioxide and temperature. We also compute the response function for each pair of variables to assess the model performance by comparison to the data and confirm the model predictions regarding stability amongst variables. Taken together, our results are consistent with glacial pacing dominated by carbon dioxide and temperature that is modulated by terrestrial biosphere feedbacks associated with methane and nitrous oxide emissions., QC 20240209

The Landauer principle sets a fundamental thermodynamic constraint on the minimum amount of heat that must be dissipated to erase one logical bit of information through a quasistatically slow protocol. For finite time information erasure, the thermodynamic costs depend on the specific physical realization of the logical memory and how the information is erased. Here we treat the problem within the paradigm of a Brownian particle in a symmetric double-well potential. The two minima represent the two values of a logical bit, 0 and 1, and the particle's position is the current state of the memory. The erasure protocol is realized by applying an external time-dependent tilting force. We derive analytical tools to evaluate the work required to erase a classical bit of information in finite time via an arbitrary continuous erasure protocol, which is a relevant setting for practical applications. Importantly, our method is not restricted to the average work, but instead gives access to the full work distribution arising from many independent realizations of the erasure process. Using the common example of an erasure protocol that changes linearly with time acting on a double-parabolic potential, we explicitly calculate all relevant quantities and verify them numerically., QC 20230831

We generalize stochastic resonance to the nonadiabatic limit by treating the double-well potential using two quadratic potentials. We use a singular perturbation method to determine an approximate analytical solution for the probability density function that asymptotically connects local solutions in boundary layers near the two minima with those in the region of the maximum that separates them. The validity of the analytical solution is confirmed numerically. Free from the constraints of the adiabatic limit, the approach allows us to predict the escape rate from one stable basin to another for systems experiencing a more complex periodic forcing., QC 20211122

For a long time, the predictive limits of perturbative quantum field theory have been limited by our inability to carry out loop calculations to arbitrarily high order, which become increasingly complex as the order of perturbation theory is increased. This problem is exacerbated by the fact that perturbation series derived from loop diagram (Feynman diagram) calculations represent asymptotic (divergent) series which limits the predictive power of perturbative quantum field theory. Here, we discuss an ansatz which could overcome these limits, based on the observations that (i) for many phenomenologically relevant field theories, one can derive dispersion relations which relate the large-order growth (the asymptotic limit of "infinite loop order") with the imaginary part of arbitrary correlation functions, for negative coupling ("unstable vacuum"), and (ii) one can analyze the imaginary part for negative coupling in terms of classical field configurations (instantons). Unfortunately, the perturbation theory around instantons, which could lead to much more accurate predictions for the large-order behavior of Feynman diagrams, poses a number of technical as well as computational difficulties. Here, we study, to further the above mentioned ansatz, correlation functions in a one-dimensional (1D) field theory with a quartic self-interaction and an O(N) internal symmetry group, otherwise known as the 1D N-vector model. Our focus is on corrections to the large-order growth of perturbative coefficients, i.e., the limit of a large number of loops in the Feynman diagram expansion. We evaluate, in momentum space, the two-loop corrections for the two-point correlation function, and its derivative with respect to the momentum, as well as the two-point correlation function with a wigglet insertion. Also, we study the four-point function., Comment: 27 pages; RevTeX

In stochastic resonance, a periodically forced Brownian particle in a double-well potential jumps between minima at rare increments, the prediction of which poses a major theoretical challenge. Here, we use a path-integral method to find a precursor to these transitions by determining the most probable (or "optimal") space-time path of a particle. We characterize the optimal path using a direct comparison principle between the Langevin and Hamiltonian dynamical descriptions, allowing us to express the jump condition in terms of the accumulation of noise around the stable periodic path. In consequence, as a system approaches a rare event these fluctuations approach one of the deterministic minimizers, thereby providing a precursor for predicting a stochastic transition. We demonstrate the method numerically, which allows us to determine whether a state is following a stable periodic path or will experience an incipient jump with a high probability. The vast range of systems that exhibit stochastic resonance behavior insures broad relevance of our framework, which allows one to extract precursor fluctuations from data. open access editor's choice Copyright, QC 20200729

For a long time, the predictive limits of perturbative quantum field theory have been limited by our inability to carry out loop calculations to an arbitrarily high order, which become increasingly complex as the order of perturbation theory is increased. This problem is exacerbated by the fact that perturbation series derived from loop diagram (Feynman diagram) calculations represent asymptotic (divergent) series which limits the predictive power of perturbative quantum field theory. Here, we discuss an ansatz that could overcome these limits, based on the observations that (i) for many phenomenologically relevant field theories, one can derive dispersion relations which relate the large-order growth (the asymptotic limit of "infinite loop order") with the imaginary part of arbitrary correlation functions, for negative coupling ("unstable vacuum"), and (ii) one can analyze the imaginary part for negative coupling in terms of classical field configurations (instantons). Unfortunately, the perturbation theory around instantons, which could lead to much more accurate predictions for the large-order behavior of Feynman diagrams, poses a number of technical as well as computational difficulties. Here, we study, to further the above-mentioned ansatz, correlation functions in a one-dimensional (1D) field theory with a quartic self-interaction and an O(N) internal symmetry group, otherwise known as the 1D N-vector model. Our focus is on corrections to the large-order growth of perturbative coefficients, i.e., the limit of a large number of loops in the Feynman diagram expansion. We evaluate, in momentum space, the two-loop corrections for the two-point correlation function, and its derivative with respect to the momentum, as well as the two-point correlation function with a wigglet insertion. Also, we study the four-point function. These quantities, computed at zero momentum transfer, enter the renormalization-group functions (Callan-Symanzik equation) of the model. Our ca, QC 20220215Nordita SU

For a long time, the predictive limits of perturbative quantum field theory have been limited by our inability to carry out loop calculations to arbitrarily high order, which become increasingly complex as the order of perturbation theory is increased. This problem is exacerbated by the fact that perturbation series derived from loop diagram (Feynman diagram) calculations represent asymptotic (divergent) series which limits the predictive power of perturbative quantum field theory. Here, we discuss an ansatz which could overcome these limits, based on the observations that (i) for many phenomenologically relevant field theories, one can derive dispersion relations which relate the large-order growth (the asymptotic limit of "infinite loop order") with the imaginary part of arbitrary correlation functions, for negative coupling ("unstable vacuum"), and (ii) one can analyze the imaginary part for negative coupling in terms of classical field configurations (instantons). Unfortunately, the perturbation theory around instantons, which could lead to much more accurate predictions for the large-order behavior of Feynman diagrams, poses a number of technical as well as computational difficulties. Here, we study, to further the above mentioned ansatz, correlation functions in a one-dimensional (1D) field theory with a quartic self-interaction and an O(N) internal symmetry group, otherwise known as the 1D N-vector model. Our focus is on corrections to the large-order growth of perturbative coefficients, i.e., the limit of a large number of loops in the Feynman diagram expansion. We evaluate, in momentum space, the two-loop corrections for the two-point correlation function, and its derivative with respect to the momentum, as well as the two-point correlation function with a wigglet insertion. Also, we study the four-point function., Comment: 27 pages; RevTeX

We use asymptotic methods from the theory of differential equations to obtain an analytical expression for the survival probability of an Ornstein–Uhlenbeck process with a potential defined over a broad domain. We form a uniformly continuous analytical solution covering the entire domain by asymptotically matching approximate solutions in an interior region, centered around the origin, to those in boundary layers, near the lateral boundaries of the domain. The analytic solution agrees extremely well with the numerical solution and takes into account the non-negligible leakage of probability that occurs at short times when the stochastic process begins close to one of the boundaries. Given the range of applications of Ornstein–Uhlenbeck processes, the analytic solution is of broad relevance across many fields of natural and engineering science., QC 20211001