Related papers: Topological Order and Reflection Positivity
This dissertation investigates three main topics, all of which dealing with alternative, higher-order gravity theories in four dimensions. Firstly, we study the variational and conformal structure of those theories. Next, we analyse their…
Stable homotopy theory is governed by the principle that after inverting loop spaces, homotopy types become the representing objects for homology theories. We show that this principle extends to higher category theory: inverting…
Using group theory arguments and numerical simulations, we demonstrate the possibility of changing the vorticity or topological charge of an individual vortex by means of the action of a system possessing a discrete rotational symmetry of…
We reformulate Hrushovski's definability patterns from the setting of first order logic to the setting of positive logic. Given an h-universal theory T we put two structures on the type spaces of models of T in two languages, \mathcal{L}…
A general inequality between entanglement entropy and a number of topologically ordered states is derived, even without using the properties of the parent Hamiltonian or the formalism of topological quantum field theory. Given a quantum…
We propose a new theory to characterize equilibrium topological phase with non-equilibrium quantum dynamics by introducing the concept of high-order topological charges, with novel phenomena being predicted. Through a dimension reduction…
The superposition principle lies at the heart of many non-classical properties of quantum mechanics. Motivated by this, we introduce a rigorous resource theory framework for the quantification of superposition of a finite number of linear…
A theory of topological gravity is a homotopy-theoretic representation of the Segal-Tillmann topologification of a two-category with cobordisms as morphisms. This note describes a relatively accessible example of such a thing, suggested by…
The notion of topology in physical systems is associated with the existence of a nonlocal ordering that is insensitive to a large class of perturbations. This brings robustness to the behaviour of the system and can serve as a ground for…
Motivated by the Model-Based Design process for Cyber-Physical Systems, we consider issues in conformance testing of systems. Conformance is a quantitative notion of similarity between the output trajectories of systems, which considers…
Comparison-based algorithms are algorithms for which the execution of each operation is solely based on the outcome of a series of comparisons between elements. Comparison-based computations can be naturally represented via the following…
The coupling between two or more objects can generally be categorized as strong or weak. In cavity quantum electrodynamics for example, when the coupling strength is larger than the loss rate the coupling is termed strong, and otherwise it…
We develop a characterization of quantum states by means of first order variables and random variables, within a predicative logic with equality, in the framework of basic logic and its definitory equations. We introduce the notion of…
A test space is the set of outcome-sets associated with a collection of experiments. This notion provides a simple mathematical framework for the study of probabilistic theories -- notably, quantum mechanics -- in which one is faced with…
The method of reflection positivity and infrared bounds allows to prove the occurrence of phase transitions in systems with continuous symmetries. We review the method in the context of quantum spin systems.
Self-organization is a property of dissipative nonlinear processes that are governed by an internal driver and a positive feedback mechanism, which creates regular geometric and/or temporal patterns and decreases the entropy, in contrast to…
Pursuing topological phase and matter in a variety of systems is one central issue in current physical sciences and engineering. Motivated by the recent experimental observation of corner states in acoustic and photonic structures, we…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
In this manuscript we study the behaviour of the entanglement measure dubbed negativity in the context of the toric code model. Using a method introduced recently by Calabrese, Cardy and Tonni [Phys. Rev. Lett. 109, 130502 (2012)], we…
The concept of the order parameter is extremely useful in physics. Here, I discuss extensions of this concept to cases when the order parameter is no longer a constant but fluctuates or oscillates in space and time. This allows one to…