Related papers: Topology trivialization transition in random non-g…
Understanding glasses and the glass transition requires comprehending the nature of the crossover from the ergodic (or equilibrium) regime, in which the stationary properties of the system have no history dependence, to the mysterious glass…
I consider a self-gravitating, N-body system assuming that the N constituents follow regular orbits about the center of mass of the cluster, where a central massive object may be present. I calculate the average over a characteristic…
We use computer simulations to study the thermodynamic properties of a glass former in which a fraction $c$ of the particles has been permanently frozen. By thermodynamic integration, we determine the Kauzmann, or ideal glass transition,…
We investigate the detailed dynamics of multidimensional Hamiltonian systems by studying the evolution of volume elements formed by unit deviation vectors about their orbits. The behavior of these volumes is strongly influenced by the…
For a bar-joint framework $(G,p)$, a subgroup $\Gamma$ of the automorphism group of $G$, and a subgroup of the orthogonal group isomorphic to $\Gamma$, we introduce a symmetric averaging map which produces a bar-joint framework on $G$ with…
The most complicated phenomena of equilibrium statistics, phase separations and transitions of various order and critical phenomena, can clearly and sharply be seen even for small systems in the topology of the curvature of the…
In a topological dynamical system the complexity of an orbit is a measure of the amount of information (algorithmic information content) that is necessary to describe the orbit. This indicator is invariant up to topological conjugation. We…
Our understanding of topological insulators is based on an underlying crystalline lattice where the local electronic degrees of freedom at different sites hybridize with each other in ways that produce nontrivial band topology, and the…
We consider an $\varepsilon$-periodic ($\varepsilon\to 0$) tubular structure, modelled as a magnetic Laplacian on a metric graph, which is periodic along a single axis. We show that the corresponding Hamiltonian admits norm-resolvent…
I introduce a novel mathematical framework integrating topological dynamics, operator algebras, and ergodic geometry to study lattices of asynchronous metric dynamical systems. Each node in the lattice carries an internal flow represented…
This paper characterizes the annealed, topological complexity (both of total critical points and of local minima) of the elastic manifold. This classical model of a disordered elastic system captures point configurations with…
Recently, concepts of topological phases of matter are extended to non-equilibrium systems, especially periodically driven systems. In this paper, we construct an example which shows non-equilibrium topological phase transitions using…
We study the nonconvex optimization landscapes of synchronization problems on spheres. First, we present new results for the statistical problem of synchronization over the two-element group $\mathbf{Z}_2$. We consider the nonconvex…
Combining dynamic renormalization with equation-free computational tools, we study the apparently self-similar evolution of void distribution dynamics in the diffusion-deposition problem proposed by Stinchcombe and Depken [Phys. Rev. Lett.…
We perform first classical-statistical real time lattice simulations of topological transitions in the non-equilibrium Glasma of weakly coupled but highly occupied gauge fields created immediately after the collision of ultra-relativistic…
We investigate the dynamics of many-body long-range interacting systems, taking the Hamiltonian Mean Field model as a case study. We show that an abundance of regular trajectories, associated with invariant tori of the single-particle…
The celebrated problem of a non-homogeneous sphere rolling over a horizontal plane was proved to be integrable and was reduced to quadratures by Chaplygin. Applying the formalism of variational integrators (discrete Lagrangian systems) with…
We propose a one-dimensional nonlinear system of coupled anharmonic oscillators that dynamically undergoes a topological transition switching from the {disordered} and topologically trivial phase into the nontrivial one due to the…
We study nontrivial entropy invariants in the class of parabolic flows on homogeneous spaces, quasi-unipotent flows. We show that topological complexity (ie, slow entropy) can be computed directly from the Jordan block structure of the…
We show in numerical simulations that a system of two coupled replicas of a binary mixture of hard spheres undergoes a phase transition in equilibrium at a density slightly smaller than the glass transition density for an unreplicated…