相关论文: Fractal-Flows and Time's Arrow
The power spectrum S of linear transects of the earth's topography is often observed to be a power-law function of wave number k with exponent close to -2: S(k) is proportional to k^-2. In addition, river networks are fractal trees that…
We study three prominent diagnostics of chaos and scrambling in the context of two-dimensional conformal field theory: the spectral form factor, out-of-time-ordered correlators, and unitary operator entanglement. With the observation that…
We advance a new viewpoint on the connection between the the thermodynamical and cosmological arrows of time, which can be traced via the properties of Cosmic Microwave Background (CMB) radiation. We show that in the…
Discrete Floquet time crystals (DFTC) are characterized by the spontaneous breaking of the discrete time-translational invariance characteristic of Floquet driven systems. In analogy with equilibrium critical points, also time-crystalline…
The Carroll group arises in the vanishing speed of light limit of the Poincar\'{e} group and was initially discarded as just a mathematical curiosity. However, recent developments have proved otherwise. Carroll and conformal Carroll…
Scientists continue to wrestle with the enigma of time. Is time a dynamic or a fundamental property of spacetime? Why does it have an arrow pointing from past to future? Why are physical laws time-symmetric in a universe with broken…
False-vacuum eternal inflation can be described as a random walk on the network of vacua of the string landscape. In this paper we show that the problem can be mapped naturally to a problem of directed percolation. The mapping relies on two…
Fluid flows such as gases or liquids exhibit space-time fluctuations on all scales extending down to molecular scales. Such broadband continuum fluctuations characterise all dynamical systems in nature and are identified as selfsimilar…
The relation between the thermodynamical and cosmological arrows of time is usually viewed in the context of the initial conditions of the Universe. It is a necessary but not sufficient condition for ensuring the thermodynamical arrow. We…
In a continuous time random walk (CTRW), each random jump follows a random waiting time. CTRW scaling limits are time-changed processes that model anomalous diffusion. The outer process describes particle jumps, and the non-Markovian inner…
Understanding structural glasses using the Random First Order Transition theory requires a description in both real space and in time, taking into account sample history. A variety of nonlinear objects enter this description, in field…
We demonstrate that the cosmological arrow of time is the cause for the arrow of time associated with the retarded radiation. This implies that the proposed mathematical model serves to confirm the hypothesis of Gold and Wheeler that the…
Deutsch and Aguirre have recently shown that the solutions of certain dynamical systems typically contain a point of minimum size that they identify as an entropy minimum and from which the size and entropy increase to infinity in both…
Correlation functions of primordial density fluctuations provide an exciting probe of the physics governing the earliest moments of our Universe. However, the standard approach to compute them is technically challenging. Theoretical…
We investigate the evolution of matter density perturbations within a fractional cosmological framework inspired by fractal space-time constructions in field theory, where a deformation of the integration measure induces non-locality and…
In this paper, we study the effective dimension of points in infinite fractal trees generated recursively by a finite tree over some alphabet. Using unequal costs coding, we associate a length function with each such fractal tree and show…
To prove presence of chaos for fractals, a new mathematical concept of abstract similarity is introduced. As an example, the space of symbolic strings on a finite number of symbols is proved to possess the property. Moreover, Sierpinski…
Fractal behaviour, i.e. scale invariance in spatio-temporal dynamics, have been found to describe and model many systems in nature, in particular fluid mechanics and geophysical related geometrical objects, like the convective boundary…
We uncover a geometric organization of the differential equations for the wavefunction coefficients of conformally coupled scalars in power-law cosmologies. To do this, we introduce a basis of functions inspired by a decomposition of the…
Recently, Carroll and Chen [hep-th/0410270] suggested a promising natural explanation of the thermodynamic arrow of time. However, we criticize their assertion that there exists a Cauchy hypersurface with a minimal entropy and argue that…