Related papers: Comment on Universal Reduced Potential Function fo…
I comment on a recent paper by Ruiz and Tsallis [Phys. Lett. A 376, 2451 (2012)] claiming to have found a '$q$-exponential' generalization of the large deviation principle for strongly correlated random variables. I show that the basic…
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…
This paper first establishes an approximate scaling property of the potential-energy function of a classical liquid with good isomorphs (a Roskilde-simple liquid). This "pseudohomogeneous" property makes explicit that - and in which sense -…
We derive general properties of the finite-size scaling of probability density functions and show that when the apparent exponent \tautilde of a probability density is less than 1, the associated finite-size scaling ansatz has a scaling…
In [Watanabe et al., Phys. Rev. Lett. 93 190601 (2004)], the authors show numerically that spanning and percolation probabilities in two-dimensional systems with different aspect ratios obey a form of "superscaling". In this comment, we…
Our paper [Phys. Rev. A 93, 052512 (2016)], proposing a novel form of single determinant wave function that admits non-idempotent 1-electron density matrices, has recently received a Comment [Phys. Rev. A ??, 0????? (2017)] suggesting a…
The analysis of the radial distribution function of a system provides a possible procedure for uncovering interaction rules between individuals out of collective movement patterns. This approach from classical statistical mechanics has…
Our community has a deep and sophisticated understanding of phase transitions and their universal scaling functions. We outline and advocate an ambitious program to use this understanding as an anchor for describing the surrounding phases.…
I criticize the claim, made in a recent article [C. M. Bender and L. R. Mead, Eur. J. Phys. 20, 117 (1999)], that in order to obtain the correct cross section for the scattering from a two-dimensional delta-function potential one must…
The solutions analytically derived by Gloeckle et al. [Phys. Rev. C79, 044003 (2009)] for the three-dimensional wave function and on-shell t matrix in the case of scattering on a sharply cut-off Coulomb potential appear to be fallacious.…
Many physical systems share the property of scale invariance. Most of them show ordinary power-law scaling, where quantities can be expressed as a leading power law times a scaling function which depends on scaling-invariant ratios of the…
An overview of recent advances in the theory of critical phenomena in $d$-dimensional weakly anisotropic systems is given. On the basis of a generalized shear transformation between anisotropic and isotropic systems, exact and approximate…
We will demonstrate that the generalized uncertainty principle exists because of the derivative expansion in the effective field theories. This is because, in the framework of the effective field theories, the minimum measurable length…
We investigate the universality of correlation functions of chaotic and disordered quantum systems as an external parameter is varied. A new, general scaling procedure is introduced which makes the theory invariant under reparametrizations.…
A number of authors have recently pointed out inconsistencies of results obtained with the Huang-Yang multipolar pseudo-potential for low-energy scattering [K. Huang and K. C. Yang, Phys. Rev. A, v 105, 767 (1957); later revised in K.…
This is the first in a series of papers addressing the phenomenon of dimensional transmutation in nonrelativistic quantum mechanics within the framework of dimensional regularization. Scale-invariant potentials are identified and their…
Intermediate energy scale physics plays a very important role in non-equilibrium dynamics of quasi-low dimensional cold atom systems. In this article we obtain the universal scaling relations for the generalized reflection coefficient,…
We show that in the category of effective $Z$ dynamical systems there is a universal system, i.e. one that factors onto every other effective system. In particular, for d $\geq 3$ there exist d-dimensional shifts of finite type which are…
In this paper we investigate the universality and scaling properties of the well-known quantities in classical statistical mechanics near the quantum phase transition point. We show that transverse susceptibility and derivatives of…
This is a response to the article arXiv:1212.3130v1 by Xu-Jia Wang, where he attempted to address a mathematical question we raised. We point out that, and explain why, the article is far from answering our objections. Moreover, we have…