Related papers: Geometry-driven transitions in sparse long-range s…
A salient feature of topological phases are surface states and many of the widely studied physical properties are directly tied to their existence. Although less explored, a variety of topological phases can however similarly be…
We illustrate how geometric gauge forces and topological phase effects emerge in quantum systems without employing assumptions that rely on adiabaticity. We show how geometric magnetism may be harnessed to engineer novel quantum devices…
Recent experimental observations have suggested that topological defects can facilitate the creation of sharp features in developing embryos. Whereas these observations echo established knowledge about the interplay between geometry and…
Despite the fundamental importance of solid--solid transitions for metallurgy, ceramics, earth science, reconfigurable materials, and colloidal matter, the details of how materials transform between two solid structures are poorly…
The phase transition in the mean-field XY model is shown analytically to be related to a topological change in its configuration space. Such a topology change is completely described by means of Morse theory allowing a computation of the…
We propose a theoretical framework that captures the geometric vector potential emerging from the non-adiabatic spin dynamics of itinerant carriers subject to arbitrary magnetic textures. Our approach results in a series of constraints on…
We consider the equilibrium dynamics of Ising spin models with multi-spin interactions on sparse random graphs (Bethe lattices). Such models undergo a mean field glass transition upon increasing the graph connectivity or lowering the…
We study the motion of discrete interfaces driven by ferromagnetic interactions in a two-dimensional periodic environment by coupling the minimizing movements approach by Almgren, Taylor and Wang and a discrete-to-continuous analysis. The…
The quantitative study of traffic dynamics is crucial to ensure the efficiency of urban transportation networks. The current work investigates the spatial properties of congestion, that is, we aim to characterize the city areas where…
A fundamental task in developmental biology is to identify the mechanisms which drive morphogenesis. In many cases, pattern formation is driven by the positional information determined by both the gradient of maternal factors and hard-wired…
We discuss a link between graph theory and geometry that arises when considering graph dynamical systems with odd interactions. The equilibrium set in such systems is not a collection of isolated points, but rather a union of manifolds,…
We propose a Rydberg molecule dressing scheme to create strong and long-ranged interactions at selective distances. This is achieved through laser coupling ground-state atoms off-resonantly to an attractive molecular curve of two…
Flexible slender structures such as rods, ribbons, plates, and shells exhibit extreme nonlinear responses bending, twisting, buckling, wrinkling, and self contact, that defy conventional simulation frameworks. Discrete Differential Geometry…
We study information theoretic geometry in time dependent quantum mechanical systems. First, we discuss global properties of the parameter manifold for two level systems exemplified by i) Rabi oscillations and ii) quenching dynamics of the…
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…
Fluctuations can drive continuous phase transitions between two distinct ordered phases -- so-called deconfined quantum critical points (DQCPs) -- which lie beyond the Landau-Ginzburg-Wilson paradigm. Despite several theoretical predictions…
The geometric phase provides important mathematical insights to understand the fundamental nature and evolution of the dynamic response in a wide spectrum of systems ranging from quantum to classical mechanics. While the concept of…
Stimulus-induced volumetric phase transition in gels may be potentially exploited for various bio-engineering and mechanical engineering applications. Since the discovery of the phenomenon in the 1970s, extensive experimental research has…
The Rydberg blockade effect plays an important role in realizing two-qubit gates in atomic arrays. Meanwhile, such mechanics will increase the crosstalk between atoms and enhance the decoherence. In this paper, we propose a new scheme to…
The Rydberg blockade mechanism is an important ingredient in quantum simulators based on neutral atom arrays. It enables the emergence of a rich variety of quantum phases of matter, such as topological spin liquids. The typically isotropic…