Derivative Expansion Research Articles

The open effective field theory of inflation

In our quest to understand the generation of cosmological perturbations, we face two serious obstacles: we do not have direct information about the environment experienced by primordial perturbations during inflation, and our observables are practically limited to correlators of massless fields, heavier fields and derivatives decaying exponentially in the number of e-foldings. The flexible and general framework of open systems has been developed precisely to face similar challenges. Building on previous work, we develop a Schwinger-Keldysh path integral description for an open effective field theory of inflation, describing the possibly dissipative and non-unitary evolution of the Goldstone boson of time translations interacting with an unspecified environment, under the key assumption of locality in space and time. Working in the decoupling limit, we study the linear and interacting theory in de Sitter and derive predictions for the power spectrum and bispectrum that depend on a finite number of effective couplings organised in a derivative expansion. The smoking gun of interactions with the environment is an enhanced but finite bispectrum close to the folded kinematical limit. We demonstrate the generality of our approach by matching our open effective theory to an explicit model. Our construction provides a standard model to simultaneously study phenomenological predictions as well as quantum information aspects of the inflationary dynamics.

Numerical accuracy of the derivative-expansion-based functional renormalization group

Abstract We investigate the precision of the numerical implementation of the functional renormalization group based on extracting the eigenvalues from the linearized renormalization group transformation. For this purpose, we implement the local potential approximation and O ( ∂ 2 ) orders of the derivative expansion for the three-dimensional O(N) models with N ∈ { 1 , 2 , 3 } . We identify several categories of numerical error and devise simple tests to track their magnitude as functions of numerical parameters. Our numerical schemes converge properly and are characterized by errors of several orders of magnitude smaller than the error bars of the derivative expansion for these models. We highlight situations in which our methods cease to converge, most often due to rounding errors. In particular, we observe an impaired convergence of the discretization scheme when the ρ ~ grid is cut off at the value ρ ~ Max smaller than 3.5 times the local potential minimum. The program performing the numerical calculations for this study is shared as an open-source library accessible for review and reuse.

Ultrasonic and volumetric investigation of aqueous disodium EDTA with PEG 400 and PEG 4000 at different temperatures

Polyethylene glycol (PEG) 400 and 4000 thermodynamic characteristics in water-based disodium ethylenediaminetetraacetic acid solutions provide important clues about the nature of the intermolecular interactions taking place in this liquid environment. In order to make these determinations, the present study reports data for density and sound velocity at a variety of temperatures and then analyses the volumetric-acoustic features of the solutions. The experimental data for PEG 400 and PEG 4000, which are polyethylene glycols, were recorded at a constant atmospheric pressure of 0.1 MPa and at temperatures ranging from 288.15 to 318.15 K. The values were 0.007, 0.008, and 0.009 mol·kg−1. From the experimental density and speed of sound values, the following are computed: apparent molar properties, partial molar properties, partial molar transfer properties, and the partial molar expansibility, along with its first derivative and thermal expansion coefficient. According to the co-sphere overlap model, the results are described using these generated parameters, these are thought of as the type of interactions taking place within the combination. This study also uses partial molar characteristics to assess the pair interaction coefficients and triplet interaction coefficients.

A Study on Profitable of Futures with the Reference to SBI Bank

New instruments and reengineering of the financial system were introduced in India in 1992 as apart of economic market reforms. One among them was that the growth and innovation were slow infamiliarizing Securities. The formation and expansion of derivatives in Indian markets are moderately alatest spectacle. Subsequently its commencement in June 2000, the products need devises displayedepidemicaugmentation in magnitude and the number of bartered conventional agreements. Significanttermend product guides an expansive class of financial tools that specifically possess options andfutures. These mechanisms emanate their significance from the underlying asset's price and otherrelated variables. They accomplish not having a value of their own and originate their importance fromthe prerogative they give to their proprietors to own some additional financial support or safety. Thepresent study is deliberate in examining the financial results obeying SBI Bank Ltd.

Analyzing the Kuralay-II equation: bifurcation, chaos, and sensitivity insights through conformable derivative and Jacobi elliptic function expansion

This study explores the intricate dynamics of the Kuralay-II equation by employing the conformable derivative. Using the Galilean transformation, we can establish a dynamical system related to the equation. We investigate bifurcation methods in this derived system using planar dynamical systems theory. By introducing a perturbed term, we thoroughly investigate the possibility of chaotic behaviors in the Kuralay-II equation using comprehensive two-phase portraiture. Through careful analysis, we have determined that even small changes in the initial conditions have little impact on the stability of the solution, which has been confirmed by employing the Runge–Kutta method. In addition, we obtain exact solutions for the Kuralay-II equation by the Jacobi elliptic function expansion method. Graphical results of some solutions are showcased, offering a comprehensive evaluation using MATLAB across various dimensions. This study has yielded significant findings, such as the discovery of bifurcation points, the determination of conditions for chaos, and the analysis of stability under perturbations. These results have enhanced our understanding of the behavior of the Kuralay-II equation.

Derivative Sampling Expansions in Shift-Invariant Spaces With Error Estimates Covering Discontinuous Signals

Derivative Sampling Expansions in Shift-Invariant Spaces With Error Estimates Covering Discontinuous Signals

A view of optical soliton solution of the coupled Schrödinger equation with a different approach

The goal of this study is to investigate to optical soliton solution of the nonlinear coupled space-time Schrödinger equation using the Beta derivative and Sine-Gordon Expansion Method. All calculations in this study are made using some software program and the solutions obtained are substituted in the equations. New soliton solutions have been found using the suggested method for solving these problems. The solutions obtained have important areas of use in the fields of mathematical physics, in the field of quantum physics, optic and engineering.

Functional renormalization group for “p = 2” like glassy matrices in the planar approximation II. Ward identities method in the deep IR

This paper, as a continuation of our previous investigation [Nucl. Phys. B 1005 (2024) 116582] aims to study the glassy random matrices with quenched Wigner disorder. In this previous work, we have constructed a renormalization group based on the effective deterministic kinetic spectrum emerging from large N limit, and we extended approximate solutions using standard vertex expansion, at the leading order of the derivative expansion. Now in the following work, by introducing the non-trivial Ward identities which come from the (U(N))×2 symmetry broken of the effective kinetic action, we provide in the deep IR the explicit solution of the functional renormalization group for a model with quartic coupling by solving the Hierarchy to all orders in the local sector, which in particular imply the vanishing of the anomalous dimension. The numerical investigations confirm the first-order phase transition discovered in the vertex expansion framework, both in the active and passive schemes. Finally, we extend the discussion to hermitian matrices.

The one-loop bispectrum of galaxies in redshift space from the Effective Field Theory of Large-Scale Structure

We derive the Effective Field Theory of Large-Scale Structure kernels and counterterms for the one-loop bispectrum of dark matter and of biased tracers in real and redshift space. This requires the expansion of biased tracers up to fourth order in fluctuations. In the process, we encounter several subtleties related to renormalization. One is the fact that, in renormalizing the momentum, a local counterterm contributes non-locally. A second subtlety is related to the renormalization of local products of the velocity fields, which need to be expressed in terms of the renormalized velocity in order to preserve Galilean symmetry. We check that the counterterms we identify are necessary and sufficient to renormalize the one-loop bispectrum at leading and subleading order in the derivative expansion. The kernels that we originally present here have already been used for the first analyses of the one-loop bispectrum in BOSS data [1,2].

Conformal invariance and composite operators: A strategy for improving the derivative expansion of the nonperturbative renormalization group.

It is expected that conformal symmetry is an emergent property of many systems at their critical point. This imposes strong constraints on the critical behavior of a given system. Taking them into account in theoretical approaches can lead to a better understanding of the critical physics or improve approximation schemes. However, within the framework of the nonperturbative or functional renormalization group and, in particular, of one of its most used approximation schemes, the derivative expansion (DE), nontrivial constraints apply only from third order [usually denoted O(∂^{4})], at least in the usual formulation of the DE that includes correlation functions involving only the order parameter. In this work we implement conformal constraints on a generalized DE including composite operators and show that new constraints already appear at second order of the DE [or O(∂^{2})]. We show how these constraints can be used to fix nonphysical regulator parameters.

Debt load as a fundamental factor of changes in the conditions of global economic development

The relevance of the problems investigated in the article is determined by the fact that the world economy fragmentation worsens its dynamics, but its actual fragility became relevant after the global crisis of 2008–2009. In this regard, developing countries are increasingly characterized by extreme risks associated with the global markets’ instability – not only commodity markets, but also financial ones, where the innovative derivatives expansion has increased the speculators’ role, thereby making commodity markets more volatile. The overall situation is aggravated by debt problems in many countries. The purpose of the study is to investigate the nature and extent of the debt burden that has developed in the global economy in recent years and to assess the key challenges facing the monetary policies of countries around the world in order to counter the rising debt burden. The main results of the study include the assessment of the scale and nature of the debt burden in terms of its negative impact on global economic development, identification of the relationship between the business cycle passage and the debt accumulation in foreign countries, as well as the main directions of prospective monetary policy that will contribute to the debt burden reduction in the foreseeable future.

Experimental Study on Pore Structure Evolution of Unloaded Rock Mass during Excavation of Reservoir Slope under Dry–Wet Cycle

There is a long sequence of periodic characteristics of reservoir water storage and discharge in large hydropower stations. The unloaded rock mass formed by blasting and excavation in the reservoir slope of the reservoir fluctuation zone is not only subjected to the penetration erosion caused by the change of the water level of the reservoir slope, but also the dry–wet cycle caused by the reservoir water storage and discharge. There is an obvious process of crack derivation and pore structure expansion, and the subsequent strength degradation breeds reservoir slope risks, which is one of the important factors restricting the operation safety of power stations. To study the pore structure evolution law of unloaded rock mass in reservoir slope excavation of reservoir fluctuation zones, the dry–wet cycle test simulating the periodic storage and discharge environment was carried out with samples of equal unloading amount obtained by indoor triaxial unloading test. The variation law of mesoscopic parameters such as wave velocity, mass, and nuclear magnetic resonance spectrum under dry–wet cycle was compared and analyzed, and the physical and mechanical mechanism of the pore structure evolution of the unloaded specimen under dry–wet cycles was explored. The results show that: (1) With the increase of dry–wet cycles, the evolution of wave velocity and dry mass of unloaded samples has obvious stage characteristics, which generally presents a rapid change in the early stage, moderate in the middle stage, and gradually stable in the late stage; (2) nuclear magnetic resonance (NMR) shows that the number of macropore structures in unloaded samples increases gradually with the dry–wet cycles; (3) the smaller the initial confining pressure, the larger the first peak area and the peak value of unloaded samples, and the spectral area corresponding to each peak under low confining pressure is significantly larger than that under medium and high confining pressure; (4) the unloading amount affects the overall proportion of macropores in the sample, which determines the deterioration process and evolution law of the mesostructure of the sample under dry–wet cycles.

Critical dynamics within the real-time FRG approach

The Schwinger-Keldysh functional renormalization group developed by Y.-y. Tan [Real-time dynamics of the O(4) scalar theory within the fRG approach, ] is employed to investigate critical dynamics related to a second-order phase transition. The effective action of model A is expanded to the order of O(∂2) in the derivative expansion for the O(N) symmetry. By solving the fixed-point equations of effective potential and wave function, we obtain static and dynamic critical exponents for different values of the spatial dimension d and the field component number N. It is found that one has z≥2 in the whole range of 2≤d≤4 for the case of N=1, while in the case of N=4, the dynamic critical exponent turns to z<2 when the dimension approach towards d=2. Published by the American Physical Society 2024

Vanishing of nonlinear tidal Love numbers of Schwarzschild black holes

It is well known that asymptotically flat Schwarzschild black holes in general relativity in four spacetime dimensions have vanishing induced linear tidal response. We extend this result beyond linear order for the polar sector, by solving the static nonlinear Einstein equations for the perturbations of the Schwarzschild metric and computing the quadratic corrections to the electric-type tidal Love numbers. After explicitly performing the matching with the point-particle effective theory at leading order in the derivative expansion, we show that the Love number couplings remain zero at higher order in perturbation theory.

Smooth vs instant inflationary transitions: steepest growth re-examined and primordial black holes

Primordial black holes (PBHs) can be produced by a range of mechanisms in the early universe. A particular formation channel that connects PBHs with inflationary phenomenology invokes enhanced primordial curvature perturbations at small scales. In this paper, we examine how rapidly the background can transition between different values of the parameters of the Hubble hierarchy in the context of single-clock inflation, which must ultimately derive from a consistent derivative expansion for the background inflaton field. We discuss artefacts associated with instant or very rapid transitions, and consider the impact on the steepest power spectrum growth and the formation of PBHs. In particular, we highlight the robustness of the k 4 steepest growth previously found for single-field inflation with conservatively smoothed transitions and limits on how much the amplitude of the power spectrum can grow, and demonstrate that the PBH mass distribution is sensitive to the artefacts, which go away when the transitions are smoothed. We also show that the mass distribution is relatively insensitive to the steepness of the growth and subsequent decay of the power spectrum, depending primarily on the peak amplitude and the presence of any plateaus that last more than an e-fold. The shape of the power spectrum can of course be constrained by other tracers, and so understanding the physical limitations on its shape remains a pertinent question.

Asymptotic expansions for the alternating Hurwitz zeta function and its derivatives

LetζE(s,q)=∑n=0∞(−1)n(n+q)s be the alternating Hurwitz (or Hurwitz-type Euler) zeta function.In this paper, we obtain the following asymptotic expansion of ζE(s,q)ζE(s,q)∼12q−s+14sq−s−1−12q−s∑k=1∞E2k+1(0)(2k+1)!(s)2k+1q2k+1, as |q|→∞, where E2k+1(0) are the special values of odd-order Euler polynomials at 0, and we also consider representations and bounds for the remainder of the above asymptotic expansion. In addition, we derive the asymptotic expansions for the higher order derivatives of ζE(s,q) with respect to its first argumentζE(m)(s,q)≡∂m∂smζE(s,q), as |q|→∞. Finally, we also prove a new exact series representation of ζE(s,q).

Casimir Physics beyond the Proximity Force Approximation: The Derivative Expansion

We review the derivative expansion (DE) method in Casimir physics, an approach which extends the proximity force approximation (PFA). After introducing and motivating the DE in contexts other than the Casimir effect, we present different examples which correspond to that realm. We focus on different particular geometries, boundary conditions, types of fields, and quantum and thermal fluctuations. Besides providing various examples where the method can be applied, we discuss a concrete example for which the DE cannot be applied; namely, the case of perfect Neumann conditions in 2+1 dimensions. By the same example, we show how a more realistic type of boundary condition circumvents the problem. We also comment on the application of the DE to the Casimir–Polder interaction which provides a broader perspective on particle–surface interactions.

Responses of isolated balsam-fir stem segments to exogenous ACC, IAA, and IBA.

In this investigation, the effects of exogenous indole-3-acetic acid (IAA), indole-3-butyric acid (IBA), and 1-aminocyclopropane-1-carboxylic acid (ACC) on anatomical development within cultured segments of Abies balsamea (L.) Mill. were compared, using debudded and defoliated leaders produced in the preceding year as bioassay material. In stem apical regions, IAA promoted radial enlargement of pre-existing cortical resin ducts and attending parenchyma enlargement, whereas IBA promoted cell division and expansion of parenchyma on the outer edge of phloem without altering cortical duct shape. Cortical woody ducts, each partially surrounded by cambium, were observed as a novel but infrequent feature. A single cortical woody duct was spatially associated with each mature leaf as its vascular trace, and they were not encountered elsewhere in the cortex, nor were they induced to form in response to any hormone application. An unknown leaf factor induces the development of cortical woody ducts. Both IAA and IBA promoted cell division in the vascular cambium. The common cellular response at the interface between the latewood boundary and cambial zone was the radial expansion of primary-walled fusiform cambial cell derivatives with little if any ensuing tracheary element (TE) differentiation. Enhanced TE production at basal stem positions occurred when ACC was provided with IAA and/or IBA, and an IAA + IBA + ACC combination produced a basal stem response similar to that in untreated segments having intact leaves. The data support the conclusion that IAA, IBA, and ACC have distinct but complementary roles in the overall regulation of the types of cellular differentiation that contribute to cortex histogenesis and diameter growth of balsam-fir leaders.

Об интегральном подходе при использовании метода коллокации

The article describes a matrix method of polynomial Chebyshev approximation using an integral approach to construct a solution to a nonhomogeneous fourth-order differential equation with mixed boundary conditions of the first kind. The proposed method is based on the expansion of the fourth-order derivative of the desired function into a series in terms of Chebyshev polynomials of the first kind and the representation of the partial sum of this series as a product of matrices whose elements are, respectively, the Chebyshev polynomials and the coefficients in this expansion. In this paper, using analytical formulas for calculating integrals of Chebyshev polynomials, we obtain a representation of the desired function in terms of the product of the matrices defined above. The use of points of extrema and zeros of Chebyshev polynomials of the first kind as nodes, as well as the properties of the sums of products of Chebyshev polynomials at these points, made it possible to reduce the boundary value problem by the collocation method to a system of inhomogeneous linear algebraic equations with a sparse matrix of this system. It is shown that the solution constructed in this way satisfies the differential equation at all nodes, including the boundary ones, in contrast to the approximate solution obtained by approximating the exact solution in the form of a finite sum of the Chebyshev series. The effectiveness of the proposed method is demonstrated by considering a boundary value problem with a known analytical solution. The convergence analysis of the constructed solution is carried out.

Enhancing Angular Stability in Magnitude and Phase of Frequency Selective Slabs Using Partial Derivatives Expansion Based on Equivalent Medium Theory

Enhancing Angular Stability in Magnitude and Phase of Frequency Selective Slabs Using Partial Derivatives Expansion Based on Equivalent Medium Theory