Related papers: Truncation of contact defects in reaction-diffusio…
The existence of several exotic phenomena, such as duality and spectral anholonomy is pointed out in one-dimensional quantum wire with a single defect. The topological structure in the spectral space which is behind these phenomena is…
We investigate the dynamics of a single breathing localized structure in a three-component reaction-diffusion system subjected to the time-delayed feedback. We show that variation of the delay time and the feedback strength can lead either…
A frequently encountered situation in the study of delay systems is that the length of the delay time changes with time, which is of relevance in many fields such as optics, mechanical machining, biology or physiology. A characteristic…
Spatial and temporal pattern formation in reaction-diffusion systems is typically studied with two or more equations, as scalar reaction-diffusion equations confined to convex domains do not admit stable inhomogeneous states in time or…
A central quantity of importance for ultracold atoms is contact, which measures two-body correlations at short distances in dilute systems. It appears in universal relations among thermodynamic quantities, such as large momentum tails,…
A zone of reactions is determined and then exploited as a tool in studying the space-time structure of an interacting system formed in a collision of relativistic nuclei. The time dependence of the reaction rates integrated over spatial…
We investigate nonlinear localized modes at light-mass impurities in a one-dimensional, strongly-compressed chain of beads under Hertzian contacts. Focusing on the case of one or two such "defects", we analyze the problem's linear limit to…
Symmetry-breaking phase transitions are ubiquitous in condensed matter systems and in quantum field theories. There is also good reason to believe that they feature in the very early history of the Universe. At many such transitions…
We study properties of truncations in the dual and intertwining process in the monotone case. The main properties are stated for the time-reversed process and the time of absorption of the truncated intertwining process.
Topological defects are thought to be left behind by the cosmological phase transitions which occur as the universe expands and cools. Similar processes can be studied in the phase transitions which take place in the laboratory:…
Interfaces of light and matter serve as a platform for exciting many-body physics and photonic quantum technologies. Due to the recent experimental realization of atomic arrays at sub-wavelength spacings, collective interaction effects such…
Deviations from the perfect atomic arrangements in crystals play an important role in affecting their properties. Similarly, diffusion of such deviations is behind many microstructural changes in solids. However, observation of point defect…
In this paper I discuss the formation of topological defects in quantum field theory and the relation between fractals and coherent states. The study of defect formation is particularly useful in the understanding of the same mathematical…
Topological defects are common in many everyday systems. In general, they appear if a symmetry is broken at a rapid phase transition. In this article, I explain why it is believed that they should have also been formed in the early universe…
Patterns in reaction-diffusion systems often contain two spatial scales; a long scale determined by a typical wavelength or domain size, and a short scale pertaining to front structures separating different domains. Such patterns naturally…
Realistic examples of reaction-diffusion phenomena governing spatial and spatiotemporal pattern formation are rarely isolated systems, either chemically or thermodynamically. However, even formulations of `open' reaction-diffusion systems…
We analyze the role of the interplay between on-site interaction and inhomogeneous diffusion on the phenomenon of condensation in the zero-range process. We predict a universal phase diagram in the plane of two exponents, respectively…
The multifractal detrended fluctuation analysis of time series is able to reveal the presence of long-range correlations and, at the same time, to characterize the self-similarity of the series. The rich information derivable from the…
We consider an ensemble of globally coupled phase oscillators whose interaction is transmitted at finite speed. This introduces time delays, which make the spatial coordinates relevant in spite of the infinite range of the interaction. We…
Low-energy scattering is well described by the effective-range expansion. In quantum mechanics, a tower of contact interactions can generate terms in this expansion after renormalization. Scattering parameters are also encoded in the…