Related papers: Fractons
A fundamental question of physics is what ultimately happens to matter as it is heated or compressed. In the realm of very high temperature and density the fundamental degrees of freedom of the strong interaction, quarks and gluons, come…
We consider cosmological models based on the spectral action formulation of (modified) gravity. We analyze the coupled effects, in this model, of the presence of nontrivial cosmic topology and of fractality in the large scale structure of…
Topological phases of matter are ubiquitous in crystals, but less is known about their existence in amorphous systems, that lack long-range order. In this perspective, we review the recent progress made on theoretically defining amorphous…
Graphs are topological spaces that include broader objects than discretized manifolds, making them interesting playgrounds for the study of quantum phases not realized by symmetry breaking. In particular they are known to support anyons of…
We study the fractional gravity for spacetimes with non-integer dimensions. Our constructions are based on a geometric formalism with the fractional Caputo derivative and integral calculus adapted to nonolonomic distributions. This allows…
The cosmic web structure is studied with the concepts and methods of fractal geometry, employing the adhesion model of cosmological dynamics as a basic reference. The structures of matter clusters and cosmic voids in cosmological N-body…
The fact that galaxy distribution exhibits fractal properties is well established since twenty years. Nowadays, the controversy concerns the range of the fractal regime, the value of the fractal dimension and the eventual presence of a…
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…
This paper provides a summary of the fractal calculus framework. It presents higher-order homogeneous and nonhomogeneous linear fractal differential equations with $\alpha$-order. Solutions for these equations with constant coefficients are…
We use a perturbative approach to evaluate transition amplitudes corresponding to quantum friction, for a scalar model describing an atom which moves at a constant velocity, close to a material plane. In particular, we present results on…
We propose a set of constraints on the ground-state wavefunctions of fracton phases, which provide a possible generalization of the string-net equations used to characterize topological orders in two spatial dimensions. Our constraint…
Discrete quantum walks are dynamical protocols for controlling a single quantum particle. Despite of its simplicity, quantum walks display rich topological phenomena and provide one of the simplest systems to study and understand…
From the perspective of topological field theory we explore the physics beyond instantons. We propose the fluctons as nonperturbative topological fluctuations of vacuum, from which the self-dual domain of instantons is attained as a…
We investigate the transport and entanglement properties exhibited by quantum walks with coin operators concatenated in a space-time fractal structure. Inspired by recent developments in photonics, we choose the paradigmatic Sierpinski…
We study out-of-equilibrium dynamics caused by global quantum quenches in fractonic scalar field theories. We consider several types of quenches, in particular, the mass quench in theories with different types of discrete rotational…
Cluster states were introduced in the context of measurement based quantum computing. In one dimension, the cluster Hamiltonian possesses topologically protected states. We investigate the Floquet dynamics of the cluster spin chain in an…
We study the behavior of excitations in the tilted one-dimensional Bose-Hubbard model. In the phase with broken symmetry, fundamental excitations are domain-walls which show fractional statistics. Using perturbation theory, we derive an…
Neutral excitations in a fractional quantum Hall droplet define the incompressibility gap of the topological phase. In this work, we derived a set of analytical results for the energy gap of the graviton modes with two-body and three-body…
Fractionalized excitations develop in many unusual many-body states such as quantum spin liquids, disordered phases that cannot be described using any local order parameter. Because these exotic excitations correspond to emergent degrees of…
Atmospheric flows exhibit cantorian fractal space-time fluctuations signifying long-range spatiotemporal correlations. A recently developed cell dynamical system model shows that such non-local connections are intrinsic to quantum-like…