Related papers: Geometry- and topology-controlled synchronization …
We critically analyze the possibility of finding signatures of a phase transition by looking exclusively at static quantities of statistical systems, like e.g., the topology of potential energy sub-manifolds (PES). This topological…
Recently there is a surge of interest in network geometry and topology. Here we show that the spectral dimension plays a fundamental role in establishing a clear relation between the topological and geometrical properties of a network and…
The investigation of the Hamiltonian dynamical counterpart of phase transitions, combined with the Riemannian geometrization of Hamiltonian dynamics, has led to a preliminary formulation of a differential-topological theory of phase…
We outline a holographic framework that attempts to unify Landau and beyond-Landau paradigms of quantum phases and phase transitions. Leveraging a modern understanding of symmetries as topological defects/operators, the framework uses a…
The Topological Hypothesis states that phase transitions should be related to changes in the topology of configuration space. The necessity of such changes has already been demonstrated. We characterize exactly the topology of the…
The relation between thermodynamic phase transitions in classical systems and topology changes in their state space is discussed for systems in which equivalence of statistical ensembles does not hold. As an example, the spherical model…
The interplay between unitary dynamics and quantum measurements induces diverse phenomena in open quantum systems with no counterparts in closed quantum systems at equilibrium. Here, we generally classify Kraus operators and their effective…
We consider the set of solutions to $M$ random polynomial equations whose $N$ variables are restricted to the $(N-1)$-sphere. Each equation has independent Gaussian coefficients and a target value $V_0$. When solutions exist, they form a…
A general scheme is proposed and tested to control the symmetry breaking instability of a homogeneous solution of a spatially extended multispecies model, defined on a network. The inherent discreteness of the space makes it possible to act…
The transition to synchrony in the Kuramoto model of globally coupled phase oscillators with a uniform distribution of natural frequencies is discontinuous. We extend the theory of this transition to the Kuramoto-Sakaguchi model, taking…
We present a case study of how topology can affect synchronization. Specifically, we consider arrays of phase oscillators coupled in a ring or a chain topology. Each ring is perfectly matched to a chain with the same initial conditions and…
For many materials, a precise knowledge of their dispersion spectra is insufficient to predict their ordered phases and physical responses. Instead, these materials are classified by the geometrical and topological properties of their…
Fathoming interplay between symmetry and topology of many-electron wave-functions has deepened understanding of quantum many body systems, especially after the discovery of topological insulators. Topology of electron wave-functions…
In his classical work, Kuramoto analytically described the onset of synchronization in all-to-all coupled networks of phase oscillators with random intrinsic frequencies. Specifically, he identified a critical value of the coupling…
The relation between thermodynamic phase transitions in classical systems and topology changes in their configuration space is discussed for a one-dimensional, analytically tractable solid-on-solid model. The topology of a certain family of…
As phenomena that necessarily emerge from the collective behavior of interacting particles, phase transitions continue to be difficult to predict using statistical thermodynamics. A recent proposal called the topological hypothesis suggests…
Topology and nonlinearity are deeply connected. However, whether topological effects can arise solely from the structure of nonlinear interaction terms, and the nature of the resulting topological phases, remain to large extent open…
We provide a generalization of the Symmetry Topological Field Theory (SymTFT) framework to characterize phase transitions and gapless phases with categorical symmetries. The central tool is the club sandwich, which extends the SymTFT setup…
We examine the interplay of symmetry and topological order in $2+1$ dimensional topological phases of matter. We present a definition of the \it topological symmetry \rm group, which characterizes the symmetry of the emergent topological…
There are three key factors of a system of coupled oscillators that characterize the interaction among them: coupling (how to affect), delay (when to affect) and topology (whom to affect). For each of them, the existing work has mainly…