Related papers: Convergence Behavior of Variational Perturbation E…
Perturbation theory is a powerful tool in manipulating dynamical system. However, it is legal only for infinitesimal perturbations. We propose to dispose this problem by means of perturbation group, and find that the coupling constant…
The tight-coupling approximation (TCA) used to describe the early dynamics of the baryons-photons system is systematically built to higher orders in the inverse of the interaction rate. This expansion can be either used to grasp the…
We analyze the resurgence properties of finite-dimensional exponential integrals which are prototypes for partition functions in quantum field theories. In these simple examples, we demonstrate that perturbation theory, even at arbitrarily…
We study the dynamics of long-wavelength fluctuations in one-dimensional (1D) many-particle systems as described by self-consistent mode-coupling theory. The corresponding nonlinear integro-differential equations for the relevant…
The effects of three-dimensional perturbations in two-dimensional turbulence are investigated, through a conformal field theory approach. We compute scaling exponents for the energy spectra of enstrophy and energy cascades, in a strong…
We evaluate perturbatively the density matrix in the low-temperature limit and thus the ground-state wave function of the anharmonic oscillator up to second order in the coupling constant. We then employ Kleinert's variational perturbation…
We investigate the weak-strong coupling transition of two linearly coupled systems under the influence of a phase fluctuating coupling. In the weak coupling regime the exponential decay of quantum properties is well known. A different…
We consider a chain of weakly harmonic coupled oscillators perturbed by a conservative noise. We show that by tuning accordingly the coupling constant energy can diffuse like a Brownian motion or superdiffuse like a maximally 3/2-stable…
This work provides some general theorems about unconditional and conditional weak convergence of empirical processes in the case of Poisson sampling designs. The theorems presented in this work are stronger than previously published…
We consider a population of two-dimensional oscillators with random couplings, and explore the collective states. The coupling strength between oscillators is randomly quenched with two values one of which is positive while the other is…
We develop a general framework for identifying phase reduced equations for finite populations of coupled oscillators that is valid far beyond the weak coupling approximation. This strategy represents a general extension of the theory from…
Amorphous solids tend to present an abundance of soft elastic modes, which diminish their transport properties, generate heterogeneities in their elastic response, and affect non-linear processes like thermal activation of plasticity. This…
Interacting fixed points in four-dimensional gauge theories coupled to matter are investigated using perturbation theory up to three loop order. It is shown how fixed points, scaling exponents, and anomalous dimensions are obtained as a…
We improve and generalize in several accounts the recent rigorous proof of convergence of delta expansion - order dependent mappings (variational perturbation expansion) for the energy eigenvalues of anharmonic oscillator. For the…
A common statistical task lies in showing asymptotic normality of certain statistics. In many of these situations, classical textbook results on weak convergence theory suffice for the problem at hand. However, there are quite some…
Coupled oscillator networks often display transitions between qualitatively different phase-locked solutions -- such as synchrony and rotating wave solutions -- following perturbation or parameter variation. In the limit of weak coupling,…
We present a direct comparison studying equilibration through kinetic theory at weak coupling and through holography at strong coupling in the same set-up. The set-up starts with a homogeneous thermal state, which then smoothly transitions…
Perturbation expansions appear to be divergent series in many physically interesting situations, including in quantum field theories like quantum electrodynamics (QED) and quantum chromodynamics (QCD), where the perturbative coefficients…
We show some interesting properties of tridiagonal and pentadiagonal matrices in the weak coupling limits. In the former case of this limit the ground state wave function amplitudes are identical to the Taylor expansion coefficients of the…
Weak-coupling expansions (conserving approximations) are carried out for the attractive Holstein and Hubbard models (on an infinite-dimensional hypercubic lattice) that include all bandstructure and vertex correction effects. Quantum…