相关论文: Conformal Fractal Geometry and Boundary Quantum Gr…
The fractal dimensions of polymer chains and high-temperature graphs in the Ising model both in three dimension are determined using the conformal bootstrap applied for the continuation of the $O(N)$ models from $N=1$ (Ising model) to $N=0$…
We numerically investigate the fractal structure of two-dimensional quantum gravity coupled to matter central charge c for $-2 \leq c \leq 1$. We reformulate Q-state Potts model into the model which can be identified as a weighted…
In this article the geometry of quantum gravity is quantized in the sense of being noncommutative (first quantization) but it is also quantized in the sense of being emergent (second quantization). A new mechanism for quantum geometry is…
We study connection probabilities between vertices of the square lattice for the critical random-cluster (FK) model with cluster weight 2, which is related to the critical Ising model. We consider the model on the plane and on domains…
The self-similarity properties of fractals are studied in the framework of the theory of entire analytical functions and the $q$-deformed algebra of coherent states. Self-similar structures are related to dissipation and to noncommutative…
The Unification of Conformal and Fuzzy gravities with Internal Interactions is based on the following two facts. The first is that the tangent group of a curved manifold and the manifold itself do not necessarily have the same dimensions.…
Breast cancer exhibits intricate morphological and dynamical heterogeneity across cellular, tissue, and tumor scales, posing challenges to conventional modeling approaches that fail to capture its nonlinear, self-similar, or self-affine,…
We review the status of understanding of the fractal structure of the quantum spacetime of 2d gravity coupled to conformal matter with c <= 1, with emphasis put on the results obtained last year.
In this thesis we analyze a very simple model of two dimensional quantum gravity based on causal dynamical triangulations (CDT). We present an exactly solvable model which indicates that it is possible to incorporate spatial topology…
We compute the intrinsic Hausdorff dimension of spacetime at the infrared fixed point of the quantum conformal factor in 4D gravity. The fractal dimension is defined by the appropriate covariant diffusion equation in four dimensions and is…
The path integral of four dimensional quantum gravity is restricted to conformally self-dual metrics. It reduces to integrals over the conformal factor and over the moduli space of conformally self--dual metrics and can be studied with the…
SLE curves describe the scaling limit of interfaces from many 2D lattice models. Heuristically speaking, the SLE partition function is the continuum counterpart of the partition function of the corresponding discrete model. It is well known…
We study fractional configurations in gravity theories and Lagrange mechanics. The approach is based on Caputo fractional derivative which gives zero for actions on constants. We elaborate fractional geometric models of physical…
If a point particle moves chaotically through a periodic array of scatterers the associated transport coefficients are typically irregular functions under variation of control parameters. For a piecewise linear two-parameter map we analyze…
In this work we study the Friedmann-Lema\^{i}tre-Robertson-Walker cosmologies with arbitrary spatial curvature for the symmetric teleparallel theories of gravity, giving the first presentation of their coincident gauge form. Our approach…
In conformal field theory (CFT) on simply connected domains of the Riemann sphere, the natural conformal symmetries under self-maps are extended, in a certain way, to local symmetries under general conformal maps, and this is at the basis…
Sheffield showed that conformally welding a $\gamma$-Liouville quantum gravity (LQG) surface to itself gives a Schramm-Loewner evolution (SLE) curve with parameter $\kappa = \gamma^2$ as the interface, and Duplantier-Miller-Sheffield proved…
The AdS/CFT correspondence is a powerful tool to study the properties of conformal QCD at strong coupling in terms of a higher dimensional dual gravity theory. The power-law falloff of scattering amplitudes in the non-perturbative regime…
We determine the scaling properties of geometric operators such as lengths, areas, and volumes in models of higher derivative quantum gravity by renormalizing appropriate composite operators. We use these results to deduce the fractal…
We consider the fractal characteristic of the quantum mechanical paths and we obtain for any universal class of fractons labeled by the Hausdorff dimension defined within the interval 1$ $$ < $$ $$h$$ $$ <$$ $$ 2$, a fractal distribution…