Series expansion
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An algebraic approach to the analytic bootstrap Open
We develop an algebraic approach to the analytic bootstrap in CFTs. By acting with the Casimir operator on the crossing equation we map the problem of doing large spin sums to any desired order to the problem of solving a set of recursion …
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Lattice QCD Equation of State at Finite Chemical Potential from an Alternative Expansion Scheme Open
In this Letter, we introduce a novel scheme for extrapolating the equation of state of QCD to finite chemical potential that features considerably improved convergence properties and allows us to extend its reach to unprecedentedly high ba…
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Conformal Dimensions via Large Charge Expansion Open
We construct an efficient Monte Carlo algorithm that overcomes the severe signal-to-noise ratio problems and helps us to accurately compute the conformal dimensions of large-Q fields at the Wilson-Fisher fixed point in the O(2) universalit…
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Radial expansion for spinning conformal blocks Open
This paper develops a method to compute any bosonic conformal block as a series expansion in the optimal radial coordinate introduced by Hogervorst and Rychkov. The method reduces to the known result when the external operators are all the…
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Ground-state energy and excitation spectrum of the Lieb-Liniger model : accurate analytical results and conjectures about the exact solution Open
We study the ground-state properties and excitation spectrum of the Lieb-Liniger model, i.e. the one-dimensional Bose gas with repulsive contact interactions. We solve the Bethe-Ansatz equations in the thermodynamic limit by using an analy…
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Gradient expansion for anisotropic hydrodynamics Open
We compute the gradient expansion for anisotropic hydrodynamics. The results\nare compared with the corresponding expansion of the underlying kinetic-theory\nmodel with the collision term treated in the relaxation time approximation. We\nf…
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Replica Resummation of the Baker-Campbell-Hausdorff Series Open
We developed a novel perturbative expansion based on the replica trick for the Floquet Hamiltonian governing the dynamics of periodically kicked systems where the kick strength is the small parameter. The expansion is formally equivalent t…
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Anisotropic Expansion of a Thermal Dipolar Bose Gas Open
We report on the anisotropic expansion of ultracold bosonic dysprosium gases at temperatures above quantum degeneracy and develop a quantitative theory to describe this behavior. The theory expresses the postexpansion aspect ratio in terms…
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Finite series expansion of a Gaussian beam for the acoustic radiation force calculation of cylindrical particles in water Open
This paper focuses on studying the interaction between an acoustical Gaussian beam and cylindrical particles. Based on the finite series method, the Gaussian beam is expanded as cylindrical functions and the beam coefficient of a Gaussian …
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Series-expansion thermal tensor network approach for quantum lattice models Open
In this work we propose a series-expansion thermal tensor network (SETTN)\napproach for efficient simulations of quantum lattice models. This\ncontinuous-time SETTN method is based on the numerically exact Taylor series\nexpansion of equil…
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Design of ultra-compact triplexer with function-expansion based topology optimization Open
In this paper, in order to optimize wavelength selective photonic devices using the function-expansion-based topology optimization method, several expansion functions are considered and the influence on the optimized structure based on eac…
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Functional renormalization group approach to the Yang-Lee edge singularity Open
Here, we determine the scaling properties of the Yang-Lee edge singularity as described by a one-component scalar field theory with imaginary cubic coupling, using the nonperturbative functional renormalization group in 3 ≤ d ≤ 6 Euclidean…
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A new method to sum divergent power series: educated match Open
We present a method to sum Borel- and Gevrey-summable asymptotic series by matching the series to be summed with a linear combination of asymptotic series of known functions that themselves are scaled versions of a single, appropriate, but…
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Phase diagrams of the extended Bose-Hubbard model in one dimension by Monte-Carlo simulation with the help of a stochastic-series expansion Open
In this paper, we study phase diagrams of the extended Bose-Hubbard model\n(EBHM) in one dimension by means of the quantum Monte-Carlo (QMC) simulation\nusing the stochastic-series expansion (SSE).In the EBHM, there exists a\nnearest-neigh…
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Expansion of Iterated Ito Stochastic Integrals of Arbitrary Multiplicity Based on Generalized Multiple Fourier Series Converging in the Mean Open
The article is devoted to the expansions of iterated Ito stochastic integrals based on generalized multiple Fourier series converging in the sense of norm in the space $L_2([t, T]^k),$ $k\in\mathbb{N}.$ The method of generalized multiple F…
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On the thermodynamic limit of form factor expansions of dynamical correlation functions in the massless regime of the XXZ spin 1/2 chain Open
This work constructs a well-defined and operational form factor expansion in a model having a massless spectrum of excitations. More precisely, the dynamic two-point functions in the massless regime of the XXZ spin-1/2 chain are expressed …
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Volterra series truncation and kernel estimation of nonlinear systems in the frequency domain Open
The Volterra series model is a direct generalisation of the linear convolution integral and is capable of displaying the intrinsic features of a nonlinear system in a simple and easy to apply way. Nonlinear system analysis using Volterra s…
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Multipole expansion of acoustical Bessel beams with arbitrary order and location Open
An exact solution of expansion coefficients for a T-matrix method interacting with acoustic scattering of arbitrary order Bessel beams from an obstacle of arbitrary location is derived analytically. Because of the failure of the addition t…
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Complete Williams asymptotic expansion of the stress field near the crack tip: Analytical solutions, interference-optic methods and numerical experiments Open
The study is aimed at theoretical, experimental and computational determination of the coefficients in crack tip asymptotic expansions for a wide class of specimens under mixed-mode loading conditions. A multiparametric presentation of the…
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Expansion of Iterated Stratonovich Stochastic Integrals of Fifth Multiplicity Based on Generalized Multiple Fourier Series Open
The article is devoted to the construction of expansion of iterated Stratonovich stochastic integrals of fifth multiplicity based on the method of generalized multiple Fourier series converging in the sense of norm in Hilbert space $L_2([t…
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Newton series expansion of bosonic operator functions Open
We show how series expansions of functions of bosonic number operators are naturally derived from finite-difference calculus. The scheme employs Newton series rather than Taylor series known from differential calculus, and also works in ca…
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Communication: Analytic continuation of the virial series through the critical point using parametric approximants Open
The mathematical structure imposed by the thermodynamic critical point motivates an approximant that synthesizes two theoretically sound equations of state: the parametric and the virial. The former is constructed to describe the critical …
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Critical properties of the Ising model in hyperbolic space Open
The Ising model exhibits qualitatively different properties in hyperbolic space in comparison to its flat space counterpart. Due to the negative curvature, a finite fraction of the total number of spins reside at the boundary of a volume i…
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Transmutation of a trans-series: the Gross-Witten-Wadia phase transition Open
We study the change in the resurgent asymptotic properties of a trans-series in two parameters, a coupling g2 and a gauge index N, as a system passes through a large N phase transition, using the universal example of the Gross-Witten-Wadia…
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A Series Solution for the Vibration of Mindlin Rectangular Plates with Elastic Point Supports around the Edges Open
A series solution for the transverse vibration of Mindlin rectangular plates with elastic point supports around the edges is studied. The series solution for the problem is obtained using improved Fourier series method, in which the vibrat…
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High-temperature thermodynamics of the honeycomb-lattice Kitaev-Heisenberg model: A high-temperature series expansion study Open
We develop high temperature series expansions for the thermodynamic properties of the honeycomb-lattice Kitaev-Heisenberg model. Numerical results for uniform susceptibility, heat capacity and entropy as a function of temperature for diffe…
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On the Summation of Divergent, Truncated, and Underspecified Power Series via Asymptotic Approximants Open
A compact and accurate solution method is provided for problems whose infinite power series solution diverges and/or whose series coefficients are only known up to a finite order. The method only requires that either the power series solut…
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Local fractional Laplace series expansion method for diffusion equation arising in fractal heat transfer Open
In this article, we first propose the local fractional Laplace series\n expansion method, which is a coupling method of series expansion method and\n Laplace transform via local fractional differential operator. An illustrative\n example f…
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Scalar and tensor spherical harmonics expansion of the velocity correlation in homogeneous anisotropic turbulence Open
The representation theory of the rotation group is applied to construct a series expansion of the correlation tensor in homogeneous anisotropic turbulence. The resolution of angular dependence is the main analytical difficulty posed by ani…
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Expansion of Iterated Stratonovich Stochastic Integrals of Multiplicity 3 Based on Generalized Multiple Fourier Series Converging in the Mean: General Case of Series Summation Open
The article is devoted to the development of the method of expansion and mean-square approximation of iterated Ito stochastic integrals based on generalized multiple Fourier series converging in the mean. We adapt this method for iterated …