Related papers: A formula for hidden regular variation behavior fo…
In this article we investigate the energy spectrum statistics of fractals at the quantum level. We show that the energy-level distribution of a fractal follows a power-law behaviour, if its energy spectrum is a limit set of piece-wise…
A mechanism is proposed for the appearance of power law distributions in various complex systems. It is shown that in a conservative mechanical system composed of subsystems with different numbers of degrees of freedom a robust power-law…
We determine the late-time dynamics of a generic spin ensemble with inhomogeneous broadening - equivalently, qubits with arbitrary Zeeman splittings - coupled to a dissipative environment with strength decreasing as $1/t$. The approach to…
Variational perturbation theory is used to determine the decay rates of metastable states across a cubic barrier of arbitrary height. For high barriers, a variational resummation procedure is applied to the complex energy eigenvalues…
The use of statistical methods for the description of complex quantum systems was primarily motivated by the failure of a line-by-line interpretation of atomic spectra. Such methods reveal regularities and trends in the distributions of…
Stable laws can be tempered by modifying the L\'evy measure to cool the probability of large jumps. Tempered stable laws retain their signature power law behavior at infinity, and infinite divisibility. This paper develops random walk…
This paper aims to investigate the diffusion behavior of particles moving in stochastic flows under a structure-preserving scheme. We compute the effective diffusivity for normal diffusive random flows and establish the power law between…
We propose formulas of the nuclear beta-decay rate that are useful in a practical calculation. The decay rate is determined by the product of the lepton and hadron current densities. A widely used formula relies upon the fact that the…
Decay laws of moving unstable quantum systems with oscillating decay rates are analyzed over intermediate times. The transformations of the decay laws at rest and of the intermediate times at rest, which are induced by the change of…
We present the outcomes of a very recent investigation of the decay constants of nonstrange and strange heavy-light beauty vector mesons, with special emphasis on the ratio of any such decay constant to the decay constant of the…
We investigate the spectral properties of non-Hermitian real random matrices whose entries exhibit long-range correlations decaying as~$|r-r'|^{-\alpha}$. We find a progressive breakdown of the circular law, controlled by the decrease…
In dynamical systems theory, there is a lack of a straightforward rule to distinguish exact center solutions from decaying center-like solutions, as both require the damping force function to be zero [1, 2]. By adopting a multi-scale…
We study the dynamics of a simple model for quantum decay, where a single state is coupled to a set of discrete states, the pseudo continuum, each coupled to a real continuum of states. We find that for constant matrix elements between the…
A theory of lepton decay constants based on the path-integral formalism is given for chiral and vector mesons. Decay constants of the pseudoscalar and vector mesons are calculated and compared to other existing results.
A statistical model of discrete finite length random processes with negative power law spectral densities is presented. The definition of terms is followed by a description of the spectral density trend. An algorithmic construction of…
Background: Decay constants of unstable nuclei and particles are quantum constants. Recent controversy on the existence (versus non-existence) of variability in the observation of decay rate can be settled by considering mixing in decay…
The modelling of linear and nonlinear reaction-subdiffusion processes is more subtle than normal diffusion and causes different phenomena. The resulting equations feature a spatial Laplacian with a temporal memory term through a time…
We discuss several models in order to shed light on the origin of power-law distributions and power-law correlations in financial time series. From an empirical point of view, the exponents describing the tails of the price increments…
Ensembles of quantum chaotic systems are expected to exhibit energy eigenvalues with random-matrix-like level repulsion between pairs of energies separated by less than the inverse Thouless time. Recent research has shown that exact and…
From the analysis of the relaxation process of isolated lattice many-body quantum systems quenched far from equilibrium, we deduce a criterion for predicting when they are certain to thermalize. It is based on the algebraic behavior…