Related papers: Instability of Renormalization
Interacting quantum systems evolving from an uncorrelated composite initial state generically develop quantum correlations -- entanglement. As a consequence, a local description of interacting quantum system is impossible as a rule. A…
An attractor of a piecewise-smooth continuous system of differential equations can bifurcate from a stable equilibrium to a more complicated invariant set when it collides with a switching manifold under parameter variation. Here numerical…
It has been conjectured that every stable manifold arising from a holomorphic automorphism, that acts hyperbolically on a compact invariant set, is biholomorphic to complex Euclidean space. Such stable manifolds are known to be…
Gravitational instability in classical Jeans theory, General Relativity, and modified gravity is considered. The background density increase leads to a faster growth of perturbations in comparison with the standard theory. The transition to…
Symmetry plays an important role in the topological band theory to remedy the eigenstates' gauge obstruction at the cost of a symmetry anomaly and zero-energy boundary modes. One can also make use of the symmetry to enumerate the…
Topological concepts have been employed to understand the ground states of many strongly correlated systems, but it is still quite unclear if and how topology manifests itself in the relaxation dynamics. Here we uncover emergent topological…
According to the May-Wigner stability theorem, increasing the complexity of a network inevitably leads to its destabilization, such that a small perturbation will be able to disrupt the entire system. One of the principal arguments against…
The "universal" instability has recently been revived by Landreman, Antonsen and Dorland [1], who showed that it indeed exists in plasma geometries with straight (but sheared) magnetic field lines. Here it is demonstrated analytically that…
Stickiness is a well known phenomenon in which chaotic orbits expend an expressive amount of time in specific regions of the chaotic sea. This phenomenon becomes important when dealing with area-preserving open systems because, in this…
Nontrivial twisted boundary conditions associated with extra compact dimensions produce an ambiguity in the value of the four dimensional coupling constants of the renormalizable interactions of the twisted fields' zero modes. Resolving…
Persistent homology analysis provides means to capture the connectivity structure of data sets in various dimensions. On the mathematical level, by defining a metric between the objects that persistence attaches to data sets, we can…
The goal of this article is to study how combinatorial equivalence implies topological conjugacy. For that, we introduce the concept of kneading sequences for nonautonomous discrete dynamical systems and show that these sequences are a…
Continuous attractors offer a unique class of solutions for storing continuous-valued variables in recurrent system states for indefinitely long time intervals. Unfortunately, continuous attractors suffer from severe structural instability…
The process of renormalization to eliminate divergences arising in quantum field theory is not uniquely defined; one can always perform a finite renormalization, rendering finite perturbative results ambiguous. The consequences of making…
Multistability is a common phenomenon which naturally occurs in complex networks. If coexisting attractors are numerous and their basins of attraction are complexly interwoven, the long-term response to a perturbation can be highly…
A pair of graphs $(\Gamma,\Sigma)$ is called unstable if their direct product $\Gamma\times\Sigma$ admits automorphisms not from $\mathrm{Aut}(\Gamma)\times\mathrm{Aut}(\Sigma)$, and such automorphisms are said to be unexpected. The…
Field theories compactified on non-simply connected spaces, which in general allow to impose twisted boundary conditions, are found to unexpectedly have a rich phase structure. One of characteristic features of such theories is the…
We report on a hitherto unnoticed type of resonances occurring in scattering from networks (quantum graphs) which are due to the complex connectivity of the graph - its topology. We consider generic open graphs and show that any cycle leads…
Motivated by an analogy with the conformal factor problem in gravitational theories of the $R+R^2$-type we investigate a $d$-dimensional Euclidean field theory containing a complex scalar field with a quartic self interaction and with a…
This paper is a step towards the complete topological classification of {\Omega}-stable diffeomorphisms on an orientable closed surface, aiming to give necessary and sufficient conditions for two such diffeomorphisms to be topologically…