Related papers: Fractal Structure in Two-Dimensional Quantum Regge…
The two-dimensional oscillatory crack instability, experimentally observed in a class of brittle materials under strongly dynamic conditions, has been recently reproduced by a nonlinear phase-field fracture theory. Here we highlight the…
We use Monte Carlo simulations to study pure 2D Euclidean quantum gravity with $R^2$-interaction on spherical topologies, employing Regge's formulation. We attempt to measure the string susceptibility exponent $\gamma_{\rm str}$ by using a…
Traffic networks have been proved to be fractal systems. However, previous studies mainly focused on monofractal networks, while complex systems are of multifractal structure. This paper is devoted to exploring the general regularities of…
We investigate the internal structure of a polymer during collapse from an expanded coil to a compact globule. Collapse is more probable in local regions of high curvature, so a smoothing of the fractal polymer structure occurs that…
We study the scaling behavior of the entanglement entropy of two dimensional conformal quantum critical systems, i.e. systems with scale invariant wave functions. They include two-dimensional generalized quantum dimer models on bipartite…
Research done during the previous century established our Standard Cosmological Model. There are many details still to be filled in, but few would seriously doubt the basic premise. Past surveys have revealed that the large-scale…
The behaviour of baby universes has been an important ingredient in understanding and quantifying non-critical string theory or, equivalently, models of two-dimensional Euclidean quantum gravity coupled to matter. Within a regularized…
In this talk I review some of the recent developments in the field of random surfaces and the Dynamical Triangulation approach to simplicial quantum gravity. In two dimensions I focus on the c=1 barrier and the fractal dimension of…
We propose a hybrid model of simplicial quantum gravity by performing at once dynamical triangulations and Regge calculus. A motive for the hybridization is to give a dynamical description of topology-changing processes of Euclidean…
A family of marginally-rigid (isostatic) spring networks with fractal structure up to a controllable length was devised and the viscoelastic spectra $G^{*}(\omega)$ calculated. Two non-trivial scaling regimes were observed,…
It is shown that fractal dimension can be estimated seeking a solution of functional equation defined for areas of coverages of different scales. The method proposed is compared with widely known way to estimate fractal dimension via linear…
We show that 2D fractal subsystem symmetry-protected topological phases may serve as resources for universal measurement-based quantum computation. This is demonstrated explicitly for two cluster models known to lie within fractal…
We review a burgeoning field of "fractons" -- a class of models where quasi-particles are strictly immobile or display restricted mobility that can be understood through generalized multipolar symmetries and associated conservation laws.…
The problem of crack pattern formation due to thermal shock loading at the surface of half-space is solved numerically using two-dimensional boundary element method. The results of numerical simulations with 100-200 random simultaneously…
We compare different models of a quantum theory of four-dimensional lattice gravity based on Regge's original proposal. From Monte Carlo simulations we calculate two-point functions between geometrical quantities and estimate the masses of…
We expose two scenarios for the breakdown of quantum multifractality under the effect of perturbations. In the first scenario, multifractality survives below a certain scale of the quantum fluctuations. In the other one, the fluctuations of…
An approximation of the Standard Regge Calculus (SRC) was proposed by the $Z_2$-Regge Model ($Z_2$RM). There the edge lengths of the simplicial complexes are restricted to only two possible values, both always compatible with the triangle…
We study continuum percolation of overlapping circular discs of two sizes. We propose a phenomenological scaling equation for the increase in the effective size of the larger discs due to the presence of the smaller discs. The critical…
Discretization of general relativity is a promising route towards quantum gravity. Discrete geometries have a finite number of degrees of freedom and can mimic aspects of quantum geometry. However, selection of the correct discrete freedoms…
We review some recent attempts to extract information about the nature of quantum gravity, with and without matter, by quantum field theoretical methods. More specifically, we work within a covariant lattice approach where the individual…