Related papers: Complexity, Tunneling and Geometrical Symmetry
This is a brief review of few relevant topics on tunneling of composite particles and how the coupling to intrinsic and external degrees of freedom affects tunneling probabilities. I discuss the phenomena of resonant tunneling, different…
The theory of a response of a two-energy-level system, irradiated by symmetrical light pulses, has been developed.(Suchlike electronic system approximates under the definite conditions a single ideal quantum well (QW) in a strong magnetic…
Many organisms exhibit branching morphologies that twist around each other and become entangled. Entanglement occurs when different objects interlock, creating complex and often irreversible configurations. This physical phenomenon is…
Given recipe of qualitative, kinetic modelling by geometric methods of three-dimensional dendritic crystals. Characteristic features of the perturbations appearing on the surface of a spherical body, leading to different scenarios of the…
We examine evolutions where each component of a given decomposition of a mixed quantal state evolves independently in a unitary fashion. The geometric phase and parallel transport conditions for this type of decomposition dependent…
A full accounting of biological robustness remains elusive; both in terms of the mechanisms by which robustness is achieved and the forces that have caused robustness to grow over evolutionary time. Although its importance to topics such as…
Despite encouraging recent progresses in ensemble approaches, classification methods seem to have reached a plateau in development. Further advances depend on a better understanding of geometrical and topological characteristics of point…
The basins of convergence, associated with the roots (attractors) of a complex equation, are revealed in the Hill problem with oblateness and radiation, using a large variety of numerical methods. Three cases are investigated, regarding the…
We define and study complex structures and generalizations on spaces consisting of geodesics or harmonic maps that are compatible with the symmetries of these spaces. The main results are about existence and uniqueness of such structures.
The surrounding of a vertex in a network can be more or less symmetric. We derive measures of a specific kind of symmetry of a vertex which we call degree symmetry -- the property that many paths going out from a vertex have overlapping…
Based on the general form of the master equation for open quantum systems the tunneling is considered. Using the path integral technique a simple closed form expression for the tunneling rate through a parabolic barrier is obtained. The…
A classic approach in dynamical systems is to use particular geometric structures to deduce statistical properties, for example the existence of invariant measures with stochastic-like behaviour such as large deviations or decay of…
This work reports an extensive study of three-dimensional topological ordered phases that, in one of the directions behave like usual topological order concerning mobility of excitations, but in the perpendicular plane manifest type-II…
The complexity of condensed matter arises from emergent behaviors that cannot be understood by analyzing individual constituents in isolation. While traditional condensed-matter approaches-developed primarily for ideal crystalline…
Many dynamical phenomena in complex systems concern spreading that plays out on top of networks with changing architecture over time -- commonly known as temporal networks. A complex system's proneness to facilitate spreading phenomena,…
Degree heterogeneity and latent geometry, also referred to as popularity and similarity, are key explanatory components underlying the structure of real-world networks. The relationship between these components and the statistical…
We study the geometry and dynamics of both isolated and dynamical trapping horizons by considering the allowed variations of their foliating two-surfaces. This provides a common framework that may be used to consider both their possible…
We consider an example of a system with two degrees of freedom admitting separation of variables but having a subset of codimension 1 on which the 2-form defining the symplectic structure degenerates. We show how to use separation of…
This work is motivated by two problems: 1) The approach of manifolds and spaces by triangulations. 2) The complexity growth in sequences of polyhedra. Considering both problems as related, new criteria and methods for approximating smooth…
The phase time in quantum tunneling can be disentangled into a dwell time plus a term arising due to the interference of the reflected and incident waves in front of the barrier. The interference term dominates at low energies and as E -->…