Related papers: Comparing topological charge definitions using top…
Regardless of the long history of gauge theories, it is not well recognized under which condition gauge fixing at the action level is legitimate. We address this issue from the Lagrangian point of view, and prove the following theorem on…
We prove the existence of a finite temperature Z_{2} phase transition for the topological charge ordering within the Fully Frustrated XY Model. Our method enables a proof of the topological charge confinement within the conventional XY…
For any classical field configuration or mechanical system with a finite number of degrees of freedom we introduce the concept of topological spectrum. It is based upon the assumption that for any classical configuration there exists a…
We study the effect of topology variation on the dynamic behavior of a system with local update rules. We implement one-dimensional binary cellular automata on graphs with various topologies by formulating two sets of degree-dependent…
We prove a topological stability result for the actions of hyperbolic groups on their Bowditch boundaries. More precisely, we show that a sufficiently small perturbation of the standard boundary action, if assumed on each parabolic subgroup…
In the $\phi $-mapping theory, the topological current constructed by the order parameters can possess different inner structure. The difference in topology must correspond to the difference in physical structure. The transition between…
The topological charge of center vortices is discussed in terms of the self-intersection number of the closed vortex surfaces in 4-dimensional Euclidian space-time and in terms of the temporal changes of the writhing number of the…
Active matter encompasses different nonequilibrium systems in which individual constituents convert energy into non-conservative forces or motion at the microscale. This review provides an elementary introduction to the role of topology in…
Temperature fluctuations of a finite system follows the Landau bound $\delta T^2 = T^2/C(T)$ where $C(T)$ is the heat capacity of the system. In turn, the same bound sets a limit to the precision of temperature estimation when the system…
We consider two models of deterministic active particles in an external potential. In the limit where the speed of a particle is fixed, both models coincide and can be formulated as a Hamiltonian system, but only if the potential is…
Motivated by the study of systems of higher order boundary value problems with functional boundary conditions, we discuss, by topological methods, the solvability of a fairly general class of systems of perturbed Hammerstein integral…
A general relation is derived for the action difference between two fixed points and a phase space area bounded by the irreducible component of a heteroclinic tangle. The determination of this area can require accurate calculation of…
Topology plays a central role in classifying solitonic configurations in field theories, providing robustness and a nonperturbative label, the so-called topological charge $Q$. In soliton-fermion coupled systems, the relation between the…
Topological defects in systems with liquid-crystalline order are crucial in determining their large-scale properties. In active systems, they are known to have properties impossible at equilibrium: for example, $+1/2$ defects in…
This text is about geometric structures imposed by robust dynamical behaviour. We explain recent results towards the classification of partially hyperbolic systems in dimension 3 using the theory of foliations and its interaction with…
We study two-dimensional U($N$) and SU($N$) gauge theories with a topological term on arbitrary surfaces. Starting from a lattice formulation we derive the continuum limit of the action which turns out to be a generalisation of the heat…
A $(2+1)$-dimensional gapped quantum many-body system can have a topologically protected energy current at its edge. The magnitude of this current is determined entirely by the temperature and the chiral central charge, a quantity…
Topological defects are singularities in material fields that play a vital role across a range of systems: from cosmic microwave background polarization to superconductors, and biological materials. Although topological defects and their…
An entropy function is proposed in [Phys. Rev. Lett. 131, 251602] as a way to detect criticality even when the system size is small. In this note we apply this strategy in the search for criticality of lattice transfer matrices constructed…
In this paper we study analogues of amenability for topological groups in the context of definable structures. We prove fixed point theorems for such groups. More importantly, we propose definitions for definable actions and continuous…