Unified scaling law for earthquakes

We show that the distribution of waiting times between earthquakes occurring in California obeys a simple unified scaling law valid from tens of seconds to tens of years. The short time clustering, commonly referred to as aftershocks, is nothing but the short time limit of the general hierarchical properties of earthquakes. There is no unique operational way of distinguishing between main shocks and aftershocks. In the unified law, the Gutenberg-Richter b value, the exponent -1 of the Omori law for aftershocks, and the fractal dimension d(f) of earthquakes appear as critical indices.     

铁基超导体系基于电子关联强度的统一相图

铁基超导和铜基超导具有诸多相似性,这为建立统一的高温超导机理图像提供了可能性.然而,对铁基超导体系中无论是进行电荷掺杂、还是等价掺杂来改变化学压力,都能产生定性上类似、而细节上纷繁复杂的相图,这对建立统一的图像造成了困难.研究化学掺杂效应如何在微观上影响电子结构和超导电性,区分主导超导电性演化的主要因素和次要因素,对建立统一图像和揭示高温超导机理至关重要.本文综述了对铁基超导体系中化学掺杂效应的一系列角分辨光电子能谱研究,涵盖了基于FeAs和FeSe面的多种代表性铁基超导体系,包括异价掺杂、等价掺杂、在元胞不同位置的化学掺杂,及其对电子体系在费米面结构、杂质散射、电子关联强度等方面的影响.实验结果表明：电子关联性或能带宽度是多个铁基超导相图背后的普适参数,不同的晶格和杂质散射效应导致了并不重要的复杂细节,而费米面拓扑结构与超导电性的关联并不强.这些结果对弱耦合机理图像提出了挑战,并促使人们通过局域反铁磁交换作用配对图像在带宽演化层面上统一地理解铁基超导.     

Unified scaling law in the coherent noise model

The waiting time distribution between successive events and the unified scaling law is studied using the coherent noise model. It is shown that, although this model generates uncorrelated event sizes and does not exhibit criticality, it still provides the unified scaling law. We argue the role of characteristic kink observed in the unified scaling law and the meaning of the parameter C$C$ used to fix the peak of the kink to unity. Our results indicate that the parameter C$C$ is indeed a physical quantity localizing the end of the linear tendency in the scaling law, which corresponds to the completion of the dominance of correlated events in time.     

Unified derivation of tunneling times from decoherence functionals

The four tunneling times, the Larmor time, the Büttiker-Landauer time, the Bohm-Wigner time, and the Pollak-Miller time, originally obtained from very different physical models, are derived in a unified manner from the Gell-Mann-Hartle decoherence functionals. The origin of the two types of derivatives in the expressions for these tunneling times is clarified at the level of Feynman paths.     

Universal scaling for the dilemma strength in evolutionary games

Why would natural selection favor the prevalence of cooperation within the groups of selfish individuals? A fruitful framework to address this question is evolutionary game theory, the essence of which is captured in the so-called social dilemmas. Such dilemmas have sparked the development of a variety of mathematical approaches to assess the conditions under which cooperation evolves. Furthermore, borrowing from statistical physics and network science, the research of the evolutionary game dynamics has been enriched with phenomena such as pattern formation, equilibrium selection, and self-organization. Numerous advances in understanding the evolution of cooperative behavior over the last few decades have recently been distilled into five reciprocity mechanisms: direct reciprocity, indirect reciprocity, kin selection, group selection, and network reciprocity. However, when social viscosity is introduced into a population via any of the reciprocity mechanisms, the existing scaling parameters for the dilemma strength do not yield a unique answer as to how the evolutionary dynamics should unfold. Motivated by this problem, we review the developments that led to the present state of affairs, highlight the accompanying pitfalls, and propose new universal scaling parameters for the dilemma strength. We prove universality by showing that the conditions for an ESS and the expressions for the internal equilibriums in an infinite, well-mixed population subjected to any of the five reciprocity mechanisms depend only on the new scaling parameters. A similar result is shown to hold for the fixation probability of the different strategies in a finite, well-mixed population. Furthermore, by means of numerical simulations, the same scaling parameters are shown to be effective even if the evolution of cooperation is considered on the spatial networks (with the exception of highly heterogeneous setups). We close the discussion by suggesting promising directions for future research including (i) how to handle the dilemma strength in the context of co-evolution and (ii) where to seek opportunities for applying the game theoretical approach with meaningful impact.     

Unified model of energy transfer for arbitrary Franck-Condon offset and temperature

The Huang-Rhys-Pekar W_p(T, S) function is known to give the thermal-Franck-Condon (FC) weight of single-center radiative and non-radiative transitions for arbitrary energy mismatch p?ω₀, temperature T, and FC offset S. The thermal-FC weight for energy transfer is shown also to be W_p(T, S), with S enlarged to be the sum of the S values of the energy donor and energy acceptor. This result generalizes an earlier result of Miyakawa and Dexter for low-temperature Poisson functions. The W_p function with enlarged S is equivalent to the overlap of the donor emission and acceptor absorption bands in the Förster-Dexter theory. Experimental verification is good except for the p dependence of non-radiative and energy-transfer rates for S small (e.g. 4f → 4f transitions). Here, if the smooth, exponential p dependences (exponential energy-gap laws) that have been drawn through many 4f → 4f transition rates in certain hosts (Y₂O₃, LaF₃) are fitted with a W_p(T, S) function with a single S value, this S value is too large to describe 4f → 4f transitions.     

Self-consistent scaling theory for logarithmic-correction exponents

Multiplicative logarithmic corrections frequently characterize critical behavior in statistical physics. Here, a recently proposed theory relating the exponents of such terms is extended to account for circumstances which often occur when the leading specific-heat critical exponent vanishes. Also, the theory is widened to encompass the correlation function. The new relations are then confronted with results from the literature, and some new predictions for logarithmic corrections in certain models are made.     

On the relativistic theory of tunneling

A relativistic generalization of the semiclassical theory of tunneling and multiphoton ionization of atoms and ions in the field of a high-intensity electromagnetic wave with linear, circular, and elliptic polarization is constructed. The exponential factor in the ionization probability is calculated for arbitrary values of adiabaticity parameter γ. In the case of low-frequency laser radiation, an asymptotically exact formula is derived for the ionization rate of the s atomic level, including the Coulomb, spin, and adiabatic corrections and the preexponential factor.     

Developing scaling relations for the yield strength of nanoporous gold

In this work, the applicability of Gibson and Ashby’s porous scaling relations to nanoporous metals is discussed, and an updated equation is proposed for relating the yield strength of nanoporous gold to the yield strength of individual gold ligaments that form the porous structure. This new relation is derived from experimental measurements obtained by small-scale tensile testing and by nanoindentation, and incorporates the average ligament diameter. Nanoindentation data, obtained experimentally by the authors as well as reported by others in the literature, are reconciled with tensile test measurements previously reported by the present authors. The values of ligament yield strength calculated with the new scaling relation are found to agree with data reported from mechanical testing of nanowires, and the scaling relation thus represents a bridge between nanowire and nanoporous metal behaviour. In addition, calculations of yield strength for nanoporous gold samples with various ligament size and relative density are consistent with the experimentally determined values.     

Effective classical stochastic theory for quantum tunneling

The ensemble mean equations for a classical particle moving stochastically obtain the form of fluid equations. When applying the Madelung transformation to write the Schrödinger equation in a fluid-like form we find that the equations are equivalent to the classical ensemble mean equations if an additional force is added to the equations. The latter can be expressed as a pressure gradient force of a fluctuating pressure with zero mean. Here we analyze the mechanism of quantum tunneling through a rectangular potential barrier from this perspective. We find that despite of the vanishing of the mean of the pressure fluctuations their local non zero gradients enable the tunneling by balancing the counter external potential gradients at the two sides of the potential barrier. Consequently, for stationary solutions, the ensemble mean kinetic energy remains unchanged across the boundaries of the barrier.     

Resonant Josephson tunneling through S-I-S junctions of arbitrary size

The Josephson tunneling current in S-I-S structures where the main current transport channel is resonant tunneling through an isolated localized state is calculated using the Bogolyubov-de Gennes equations. It is shown that the efficiency of equilibrium Josephson resonant tunneling is determined only by the ratio of the width of the resonance level to the absolute value of the order parameter for the superconducting electrodes with arbitrary relationships among the system parameters. Zh. éksp. Teor. Fiz. 112, 342–352 (July 1997)     

Basis for tunneling theory of charge-density wave depinning

During the past few years, the theory of depining of charge-density waves in quasi-one-dimensional metals by quantum tunneling through a small pinning gap has been developed in a semi-phenomenological way through a close interaction between theory and experiment. A microscopic derivation is given that shows that a tunneling step is required if impurity pinning is included in zero order. It is incorrect to treat the effects of impurities by a perturbation expansion as has been done in classical theories of depinning. It is shown how the parameters of the theory are related to the Fukuyama-Lee-Rice model of weak impurity pinning by impurity fluctuations. Except near threshold, effects of disorder average out to give a nearly uniform current density. Expressions for the response to dc and ac fields derived from the microscopic theory are close to those given by the earlier semi-phenomenological theory.