Related papers: Topology and Phase Transitions: Theorem on a neces…
We develop a unified view of topological phase transitions (TPTs) in solids by revising the classical band theory with the inclusion of topology. Re-evaluating the band evolution from an "atomic crystal" [a normal insulator (NI)] to a solid…
This article presents a reformulation of the Theory of Functional Connections: a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The reformulation presented in this paper exploits…
The pattern of isentropes in the vicinity of a first-order phase transition is proposed as a key for a sub-classification. While the confinement--deconfinement transition, conjectured to set in beyond a critical end point in the QCD phase…
The paper presents a new proof of O'Cinneide's characterization theorem. It is much simpler than the original one and constructive in the sense that we not only show the existence of a phase type representation, but present a procedure…
We continue the work of [4, 2, 3], in which we discuss published assertions that are incorrect or incorrectly proven; that are severely limited or reduce to triviality; or that we improve upon.
In the current work an equation of state model with a first-order phase transition for astrophysical applications is presented. The model is based on a two-phase approach for quark-hadron phase transitions, which leads by construction to a…
Recent results concerning the relation of topology and low-lying fermion modes are summarized.
We show that sharply defined topological quantum phase transitions are not limited to states of matter with gapped electronic spectra. Such transitions may also occur between two gapless metallic states both with extended Fermi surfaces.…
First order phase transitions are described in terms of the microcanonical and canonical ensemble, with special attention to finite size effects. Difficulties in interpreting a "caloric curve" are discussed. A robust parameter indicating…
Many-body systems when continuous phase transition occurs are mainly built in the interrelationship between particles, implemented through many-body correlations. Some of them may exhibit so-called topological order hardly measured by…
We discuss the appearance of fractional topological phases on cyclic evolutions of entangled qudits. The original result reported in Phys. Rev. Lett. \textbf{106}, 240503 (2011) is detailed and extended to qudits of different dimensions.…
This paper contains an expository account of persistent homology and its usefulness for topological data analysis. An alternative foundation for level-set persistence is presented using sheaves and cosheaves.
We use a simplified model which is based on the same physics as inherent in most statistical models for nuclear multifragmentation. The simplified model allows exact calculations for thermodynamic properties of systems of large number of…
In this paper, we generalize the fundamental theorems of functional analysis to the framework of bicomplex topological modules.
The relation between thermodynamic phase transitions in classical systems and topological changes in their configuration space is discussed for two physical models and contains the first exact analytic computation of a topologic invariant…
Lattice regularization of the theory of gravity provides a new possibility for study of the Big Bang problem. In the 4D lattice theories of gravity, the existence of a high-temperature phase is proved, which is characterized by the folding…
In this paper we propose some continuation theorems for the periodic problem \begin{equation*} \begin{cases} \, x_{i}' = g_{i}(t,x_{i+1}), &i=1,\ldots,n-1, \\ \, x_{n}' = h(t,x_{1},\ldots,x_{n}), \\ \, x_{i}(0)=x_{i}(T), &i=1,\ldots,n,…
We demonstrate the identification and classification of topological phase transitions from experimental data using Diffusion Maps: a nonlocal unsupervised machine learning method. We analyze experimental data from an optical system…
It is argued that quantum gravity has an interpretation as a topological field theory provided a certain constraint from the path intergral measure is respected. The constraint forces us to couple gauge and matter fields to gravity for…
In the first one of these two lectures, I give an introductory review of phase transitions in finite temperature field theories. I highlight the differences between theories with global and local symmetries, and the similarities between…