The O(n) nonlinear sigma model in 1 + 1 dimensions is examined as quantum mechanics on an infinite-dimensional configuration space. Two metrics are defined in this space. One of these metrics is the same as Feynman's distance, but we show his conclusions concerning potential energy versus distance from the classical vacuum are incorrect. The potential-energy functional is found to have barriers...

We use an analogy between the Yang-Mills theory Hamiltonian and the matrix model description of the closed bosonic membrane theory to calculate the spectrum of glueballs in the large Nc limit. Some features of the Yang-Mills theory vacuum, such as the screening of the topological charge and vacuum topological susceptibility are discussed. We show that the topological susceptibility has differen...

The Hall conductivity given by the Kubo formula is a linear response of quantum transverse transport to a weak electric field. It has been intensively studied for quantum systems without decoherence, but it is barely explored for systems subject to decoherence. In this paper, we develop a formulism to deal with this issue for topological insulators. The Hall conductance of a topological insulat...

Stability of a power grid’s synchronous operating mode is crucial to its reliable function. We quantify the stability of this operating mode in different humble power grid layouts that we numerically simulate employing a widely used electro-mechanical model. The method with which we quantify stability delivers a single number, called basin stability, for each node in a grid. A node with a poor ...

Denote by [0, ω1) the locally compact Hausdorff space consisting of all countable ordinals, equipped with the order topology, and let C0[0, ω1) be the Banach space of scalar-valued, continuous functions which are defined on [0, ω1) and vanish eventually. We show that a weak ∗compact subset of the dual space of C0[0, ω1) is either uniformly Eberlein compact, or it contains a homeomorphic copy of...

Topological maps provide a useful abstraction for robotic navigation and planning. Although stochastic maps can theoretically be learned using the Baum-Welch algorithm, without strong prior constraint on the structure of the model it is slow to converge, requires a great deal of data, and is often stuck in local minima. In this paper, we consider a special case of hidden Markov models for robot...

We study three-dimensional generalizations of the quantum spin Hall (QSH) effect. Unlike two dimensions, where a single Z2 topological invariant governs the effect, in three dimensions there are 4 invariants distinguishing 16 phases with two general classes: weak (WTI) and strong (STI) topological insulators. The WTI are like layered 2D QSH states, but are destroyed by disorder. The STI are rob...