Related papers: Topological charges and conservation laws involvin…
Many examples from quantum and classical physics are known where topological protection is responsible for the robustness of the dynamics. Less explored is the role of topological protection in the context of classical oscillatory systems.…
Partial differential equations with discrete (concentrated) state-dependent delays are studied. The existence and uniqueness of solutions with initial data from a wider linear space is proven first and then a subset of the space of…
The conservation laws of electromagnetism, and implicitly all theories built from quadratic Lagrangians, are extended to a continuum of nonlocal versions. These are associated with symmetries of a class of equal time field correlation…
We investigate both the hyperbolic action and the determinant ratio action designed to fix the topological charge on the lattice. We show to what extent topology is fixed depending on the parameters of these actions, keeping the physical…
In contrast to conservative systems, in nonlinear media with gain and loss the dynamics of localized topological structures can exhibit unique features that can be controlled externally. We propose a robust mechanism to perform topological…
Flexible mechanical metamaterials possess repeating structural motifs that imbue them with novel, exciting properties including programmability, anomalous elastic moduli and nonlinear and robust response. We address such structures via…
Energy methods for constructing time-stepping algorithms are of increased interest in application to nonlinear problems, since numerical stability can be inferred from the conservation of the system energy. Alternatively, symplectic…
Using the Noether Charge formulation, we study a perturbation of the conserved gravitating system. By requiring the boundary term in the variation of the Hamiltonian to depend only on the symplectic structure, we propose a general…
Topological phenomena typically govern the behavior of delocalized waves, giving rise to robust transport in electronic, photonic, and mechanical systems. Whether similar principles can directly control the motion of a localized particle,…
Different notions of entropy play a fundamental role in the classical theory of dynamical systems. Unlike many other concepts used to analyze autonomous dynamics, both measure-theoretic and topological entropy can be extended quite…
The connection between symmetries and conservation laws as made by Noether's theorem is extended to the context of causal variational principles and causal fermion systems. Different notions of continuous symmetries are introduced. It is…
Conservation laws vanishing along characteristic directions of a given system of PDEs are known as characteristic conservation laws, or characteristic integrals. In 2D, they play an important role in the theory of Darboux-integrable…
We define conserved gravitational charges in -cosmologically extended- topologically massive gravity, exhibit them in surface integral form about their de-Sitter or flat vacua and verify their correctness in terms of two basic types of…
The dual role played by symmetry in many-body physics manifests itself through two fundamental mechanisms: spontaneous symmetry breaking and topological symmetry protection. These two concepts, ubiquitous in both condensed matter and high…
In this paper we propose a method to couple two or more explicit numerical schemes approximating the same time-dependent PDE, aiming at creating new schemes which inherit advantages of the original ones. We consider both advection equations…
We consider a free topological model in 5D euclidean flat spacetime, built from two rank-2 tensor fields. Despite the fact that the bulk of the model does not have any particular physical interpretation, on its 4D planar edge nontrivial…
Topological objects can influence each other if the underlying homotopy groups are non-Abelian. Under such circumstances, the topological charge of each individual object is no longer a conserved quantity and can be transformed to each…
This paper presents the extension from flat spacetime into curved spacetime of the area of theoretical investigation that has been known as topological gauge field theory. The extension here presented is based upon a new derivation of the…
Nonlinear optical frequency conversion, observed more than half a century ago, is a corner stone in modern applications of nonlinear and quantum optics. It is well known that frequency conversion processes are constrained by conservation…
The properties of statistical ensembles with abelian charges close to the thermodynamic limit are discussed. The finite volume corrections to the probability distributions and particle density moments are calculated. Results are obtained…