Related papers: On generalized scaling laws with continuously vary…
A consistent generalization of statistical mechanics is obtained by applying the maximum entropy principle to a trace-form entropy and by requiring that physically motivated mathematical properties are preserved. The emerging…
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…
The relationship between the foundations of mathematics and physics is a topic of of much interest. This paper continues this exploration by examination of the effect of space and time dependent number scaling on theoretical descriptions of…
The effect of an electric field on conduction in a disordered system is an old but largely unsolved problem. Experiments cover an wide variety of systems - amorphous/doped semiconductors, conducting polymers, organic crystals, manganites,…
We consider the R\'{e}nyi entanglement entropy of bosonic Luttinger liquids under a particle bipartition and demonstrate that the leading order finite-size scaling is logarithmic in the system size with a prefactor equal to the inverse…
Many materials quenched into their ordered phase undergo ageing and there show dynamical scaling. For any given dynamical exponent z, this can be extended to a new form of local scale-invariance which acts as a dynamical symmetry. The…
Results of perturbation theory in quantum field theory generally depend on the renormalization scheme that is in use. In particular, they depend on the scale. We try to make perturbation theory scheme invariant by re-expanding with respect…
Recent research across mathematical problem solving, proof assistant programming and multimodal jailbreaking documents a striking finding: when (multimodal) language model tackle a suite of tasks with multiple attempts per task --…
City-size distributions follow an approximate power law in various countries despite high volatility in relative city sizes over time. Our empirical evidence for the United States and Japan indicates that the scaling law stems from a…
The presence of self-organized criticality in biology is often evidenced by a power-law scaling of event size distributions, which can be measured by linear regression on logarithmic axes. We show here that such a procedure does not…
Unlike the classical exponential relaxation law, the widely prevailing universal law with its fractional power-law dependence of susceptibility on frequency cannot be explained in the framework of any intuitively simple physical concept.…
Shift and stretch invariance lead to the exponential-Boltzmann probability distribution. Rotational invariance generates the Gaussian distribution. Particular scaling relations transform the canonical exponential and Gaussian patterns into…
We explore the concept of scaling invariance in a type of dynamical systems that undergo a transition from order (regularity) to disorder (chaos). The systems are described by a two-dimensional, nonlinear mapping that preserves the area in…
The time-dependent relaxation of a dynamical system may exhibit a power-law behavior that is superimposed by log-periodic oscillations. Sornette [Phys. Rep. 297, 239 (1998)] showed that this behavior can be explained by a discrete scale…
We establish scaling limits for the random walk whose state space is the range of a simple random walk on the four-dimensional integer lattice. These concern the asymptotic behaviour of the graph distance from the origin and the spatial…
The concept of universality has shaped our understanding of many-body physics, but is mostly limited to homogenous systems. Here, we present a study of universality on a non-homogeneous graph, the long-range diluted graph (LRDG). Its…
We propose a stochastic model of a fragmentation process, developed by taking into account fragment lifetime as a function of their size based on the Gibrat process. If lifetime is determined by a power function of fragment size, numerical…
All physical process are subject to some laws which determine with math accurately its time-space evolution. These laws are described, in the last analysis for the principle of causality. The physical space can be homogeneous or…
The scaling behavior of the maximal Lyapunov exponent in chaotic systems with time-delayed feedback is investigated. For large delay times it has been shown that the delay-dependence of the exponent allows a distinction between strong and…
We consider a noninteracting disordered system designed to model particle diffusion, relaxation in glasses, and impurity bands of semiconductors. Disorder originates in the random spatial distribution of sites. We find strong numerical…