Related papers: Systematics of strength function sum rules
A major barrier in semiclassical calculations is the sheer number of terms that contribute as time increases; for classically chaotic dynamics, the proliferation is exponential. We have been able to overcome this ``exponential wall'' for…
Detailed empirical studies of publicly traded business firms have established that the standard deviation of annual sales growth rates decreases with increasing firm sales as a power law, and that the sales growth distribution is…
We prove a functional central limit theorem for partial sums of symmetric stationary long range dependent heavy tailed infinitely divisible processes with a certain type of negative dependence. Previously only positive dependence could be…
A wide range of natural and social phenomena result in observables whose distributions can be well approximated by a power-law decay. The well-known Hill estimator of the tail exponent provides results which are in many respects superior to…
We present a novel formulation for biochemical reaction networks in the context of signal transduction. The model consists of input-output transfer functions, which are derived from differential equations, using stable equilibria. We select…
The spin market model [S. Bornholdt, Int.J.Mod.Phys. C 12 (2001) 667] is extended into co-evolutionary version, where strategies of interacting and competitive traders are represented by local and global couplings between the nodes of…
We investigate the influence of technical parameters in dynamic electrical conductivity calculations by the Kubo-Greenwood formula on the value of the so-called sum rule. We propose a possible explanation of the slight overestimation of the…
Using unitarity, analyticity and crossing symmetry, we derive universal sum rules for scattering amplitudes in theories invariant under an arbitrary symmetry group. The sum rules relate the coefficients of the energy expansion of the…
In \cite{CGPWW2021}, it was conjectured that a particular shifted sum of even divisor sums vanishes, and in \cite{SDK}, a formal argument was given for this vanishing. Shifted convolution sums of this form appear when computing the Fourier…
A large variety of materials, widely encountered both in engineering applications and in the biological realm, are characterised by a non-vanishing internal stress distribution, even in the absence of external deformations or applied…
For special kinematic configurations involving a single momentum scale, certain standard relations, originating from the Slavnov-Taylor identities of the theory, may be interpreted as ordinary differential equations for the ``kinetic term''…
Inspired by experiments on dynamic extensile gels of biofilaments and motors, we propose a model of a network of linear springs with a kinetics consisting of growth at a prescribed rate, death after a lifetime drawn from a distribution, and…
We address this work to investigate some statistical properties of symbolic sequences generated by a numerical procedure in which the symbols are repeated following a power law probability density. In this analysis, we consider that the sum…
This paper presents some asymptotic results for statistics of Brownian semi-stationary (BSS) processes. More precisely, we consider power variations of BSS processes, which are based on high frequency (possibly higher order) differences of…
Energy functionals of the Green's function can simultaneously provide spectral and thermodynamic properties of interacting electrons' systems. Though powerful in principle, these formulations need to deal with dynamical…
Hamilton et al. have suggested an invaluable scaling formula which describes how the power spectra of density fluctuations evolve into the nonlinear regime of hierarchical clustering. This paper presents an extension of their method to…
Stable limit cycle as a stabilized mechanical oscillation is the primary result of the dynamical evolution of an optomechanical system under sufficiently powerful pump. Because this dynamical process is highly nonlinear, it was not clear…
Evidently, some relaxation dynamics, e.g. exponential decays, are much more common in nature than others. Recently there have been attempts to explain this observation on the basis of ``typicality of perturbations'' with respect to their…
We develop a formula for the power-law decay of various sets for symmetric stable random vectors in terms of how many vectors from the support of the corresponding spectral measure are needed to enter the set. One sees different decay rates…
There has been great interest in applying the results of statistical mechanics to single molecule experiements. Recent work has highlighted so-called non-equilibrium work-energy relations and Fluctuation Theorems which take on an…