Related papers: The branch process of the cosmic strings
We construct a flow of continuous time and discrete state branching processes. Some scaling limit theorems for the flow are proved, which lead to the path-valued branching processes and nonlocal branching superprocesses over the positive…
Topological defects are ubiquitous in condensed-matter physics but only hypothetical in the early universe. In spite of this, even an indirect evidence for one of these cosmic objects would revolutionize our vision of the cosmos. We give…
Under unitary evolution, a typical macroscopic quantum system is thought to develop wavefunction branches: a time-dependent decomposition into orthogonal components that (1) form a tree structure forward in time, (2) are approximate…
We present a new general topological tensor current of $\tilde{p}$-branes by making use of the $\phi $-mapping theory. It is shown that the current is identically conserved and behave as $\delta (\vec{\phi}),$ and every isolated zero of the…
We present a new Lorentz gauge invariant U(1) topological field theory in Riemann-Cartan spacetime manifold $U_{4}$. By virtue of the decomposition theory of U(1) gauge potential and the $ \phi $--mapping topological current theory, it is…
This article examines how the physical presence of field energy and particulate matter can be interpreted in terms of the topological properties of space-time. The theory is developed in terms of vector and matrix equations of exterior…
The potential role of cosmic topological defects has raised interest in the astrophysical community for many years now. In this set of notes, we give an introduction to the subject of cosmic topological defects and some of their possible…
Perturbative estimates suggest that extended topological defects such as cosmic strings emit few particles, but numerical simulations of the fields from which they are constructed suggest the opposite. In this paper we study the decay of…
This work deals with the construction of networks of topological defects in models described by a single complex scalar field. We take advantage of the deformation procedure recently used to describe kinklike defects in order to build…
In the context of complex algebraic varieties, the decomposition theorem for semi-small maps provides a decomposition of the direct image of the constant sheaf. In this work, we develop a decomposition theorem for branched coverings of…
The canonical Monte-Carlo algorithm for simulating the production of string-like topological defects at a phase transition is extended by introducing a distribution of domain sizes. A strong correlation is found between the fraction in the…
A novel U(1) topological gauge field theory for topological defects in liquid crystals is constructed by considering the U(1) gauge field is invariant under the director inversion. Via the U(1) gauge potential decomposition theory and the…
We formulate a theory of shape valid for objects of arbitrary dimension whose contours are path connected. We apply this theory to the design and modeling of viable trajectories of complex dynamical systems. Infinite families of…
We consider a spectrally positive L\'evy process $X$ that does not drift to $+\infty$, viewed as coding for the genealogical structure of a (sub)critical branching process, in the sense of a contour or exploration process…
In this article we discuss how one can systematically construct the point particle theories that realize the vanishing one-loop cosmological constant without the bose-fermi cancellation. Our construction is based on the asymmetric (or…
Topological defects such as cosmic strings may have been formed at early-universe phase transitions. Direct tests of this idea are impossible, but the mechanism can be elucidated by studying analogous processes in low-temperature…
We extend and generalize the seminal work of Brandenberger, Huang and Zhang on the formation of strings during chiral phase transitions(berger) and discuss the formation of abelian and non-abelian topological strings during such transitions…
The method of topological vertex for topological string theory on toric Calabi-Yau 3-folds is reviewed. Implications of an explicit formula of partition functions in the "on-strip" case, typically the generalized conifolds, are considered.…
Current theories of particle physics lead to the unavoidable conclusion that there must have been several phase transitions in the early universe. Further, in the context of these theories, it is possible that cosmological phase transitions…
The problem of a massive elastic string depinning from a linear defect under the action of a small driving force is considered. To exponential accuracy the decay rate is calculated with the help of the instanton method; then, fluctuations…