相关论文: Conformal invariance in two-dimensional turbulence

When an integrable two-degrees-of-freedom Hamiltonian system possessing a circle of parabolic fixed points is perturbed, a parabolic resonance occurs. It is proved that its occurrence is generic for one parameter families (co-dimension one…

The study of the Ising model from a percolation perspective has played a significant role in the modern theory of critical phenomena. We consider the celebrated square-lattice Ising model and construct percolation clusters by placing bonds,…

Some years ago we proposed a new approach to the analysis of galaxy and cluster correlations based on the concepts and methods of modern statistical Physics. This led to the surprising result that galaxy correlations are fractal and not…

Universality classes of non-unitary critical theories in two-dimensions are characterized by a dimensional number, termed central charge or conformal anomaly. Conformal invariance predicts that the leading finite-size correction to the free…

We comprehend the role of imperfections in materials consisting of interacting particles, arising from different origins on their universal features. Specifically, we report the static and dynamic responses in a cluster of Coulomb…

We present experimental evidence and theoretical arguments showing that the time-evolution of freely decaying 2-d turbulence is governed by a {\it discrete} time scale invariance rather than a continuous time scale invariance. Physically,…

Gravity in nonlinear and dynamical regimes underpins spectacular astrophysical phenomena and observable consequences, from the early universe to black hole collisions. In these extreme environments, inverse energy cascades - mediated by…

This is the second of three papers on Conformal General Relativity (CGR). The conformal group is introduced here as the invariance group of the partial order of causal events in $n$D spacetime. Its general structure, discrete symmetries and…

We look at various correlation functions, which include those that involve both the velocity and the vorticity fields, in two-dimensional (2D) isotropic homogeneous unforced turbulence. We adopt the more intuitive approach due to Kolmogorov…

Some turbulent flows self-organize into large-scale structures, rather than breaking up into ever-smaller scales. Underpinning this phenomenon is the existence of two sign-definite quantities which are conserved by the dynamics.…

We show that in the single component situation all perturbation variables in the comoving gauge are conformally invariant to all perturbation orders. Generally we identify a special time slicing, the uniform-conformal transformation…

The coexistence of the energy and enstrophy cascades in 2D quantum turbulence is one of the important open questions in the studies of quantum fluids. Here, we show that polariton condensates are particularly suitable for the possible…

Order parameter fluctuations for the two dimensional Ising model in the region of the critical temperature are presented. A locus of temperatures T*(L) and of magnetic fields B*(L) are identified, for which the probability density function…

A new conformal field theory description of two-dimensional turbulence is proposed. The recently established class of rational logarithmic conformal field theories provides a unique candidate solution which resolves many of the drawbacks of…

We studied the macroscopic statistical properties on the freely evolving quasi-elastic hard disk (granular) system by performing a large-scale (up to a few million particles) event-driven molecular dynamics systematically and found that…

We consider conformal and scale-invariant gravities in d dimensions, with a special focus on pure $R^2$ gravity in the scale-invariant case. In four dimensions, the structure of these theories is well known. However, in dimensions larger…

The two-fold singularity has played a significant role in our understanding of uniqueness and stability in piecewise smooth dynamical systems. When a vector field is discontinuous at some hypersurface, it can become tangent to that surface…

The critical behavior of infinite families of shift symmetric interacting theories with higher derivative kinetic terms (non unitary) is considered. Single scalar theories with shift symmetry are classified according to their upper critical…

The spontaneous breaking of non-invertible symmetries can lead to exotic phenomena such as coexistence of order and disorder. Here we explore second-order phase transitions in 1d spin chains between two phases that correspond to distinct…

The equilibrium behavior of vortices in the classical two-dimensional (2D) XY model with uncorrelated random phase shifts is investigated. The model describes Josephson-Junction arrays with positional disorder, and has ramifications in a…