相关论文: The configuration of a topological current and phy…
In the light of $\phi$-mapping method and topological current theory, the topological structure and the topological quantization of arbitrary dimensional topological defects are obtained under the condition that the Jacobian $J(\phi/v) \neq…
The topological theory of phase transitions was proposed on the basis of different arguments, the most important of which are: a direct evidence of the relation between topology and phase transitions for some exactly solvable models; an…
In the light of $\phi$-mapping method and topological current theory, the topological structure and the topological quantization of topological linear defects are obtained under the condition that the Jacobian $J(\phi/v) \neq 0$. When…
The topological structure of the electric topological current of the locally gauge invariant Maxwell-Chern-Simons Model and its bifurcation is studied. The electric topological charge is quantized in term of winding number. The Hopf indices…
Optical vortices as topological objects exist ubiquitously in nature. In this paper, by making use of the $\phi$-mapping topological current theory, we investigate the topology in the closed and knotted optical vortices. The topological…
The Topological Hypothesis states that phase transitions should be related to changes in the topology of configuration space. The necessity of such changes has already been demonstrated. We characterize exactly the topology of the…
The non-classical features of quantum mechanics are reproduced using models constructed with a classical theory - general relativity. The inability to define complete initial data consistently and independently of future measurements,…
The relation between thermodynamic phase transitions in classical systems and topology changes in their configuration space is discussed for a one-dimensional, analytically tractable solid-on-solid model. The topology of a certain family of…
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…
The topological theory of phase transitions has its strong point in two theorems proving that, for a wide class of physical systems, phase transitions necessarily stem from topological changes of some submanifolds of configuration space. It…
A local criterion of topological phase transitions is established based on the Morse theory: a topological phase transition occurs when the count of Morse critical points of the order function changes. The locations in space where this…
Certain geometric properties of submanifolds of configuration space are numerically investigated for classical lattice phi^4 models in one and two dimensions. Peculiar behaviors of the computed geometric quantities are found only in the…
In a previous effort [arXiv:1708.05492] we have created a framework that explains why topological structures naturally arise within a scientific theory; namely, they capture the requirements of experimental verification. This is…
Different types of Lifshitz transitions are governed by topology in momentum space. They involve the topological transitions with the change of topology of Fermi surfaces, Weyl and Dirac points, nodal ines, and also the transitions between…
By using topological current theory, we study the inner topological structure of disclinations during the melting of two-dimensional systems. From two-dimensional elasticity theory, it is found topological currents for topological defects…
Topological phases of matter are often understood and predicted with the help of crystal symmetries, although they don't rely on them to exist. In this chapter we review how topological phases have been recently shown to emerge in amorphous…
From the topological properties of a three dimensional vector order parameter, the topological current of point defects is obtained. One shows that the charge of point defects is determined by Hopf indices and Brouwer degrees. The evolution…
Two mathematical mechanisms, responsible for the generation of a thermodynamic singularity, are individuated. For a class of short-range, confining potentials, a topology change in some family of configuration space submanifolds is the only…
The relation between thermodynamic phase transitions in classical systems and topology changes in their state space is discussed for systems in which equivalence of statistical ensembles does not hold. As an example, the spherical model…
We argue that the phase transition in the mean-field XY model is related to a particular change in the topology of its configuration space. The nature of this topological transition can be discussed on the basis of elementary Morse theory…