scholarly journals Universal properties of boundary and interface charges in continuum models of one-dimensional insulators

2021 ◽  
Vol 104 (15) ◽  
Author(s):  
Sebastian Miles ◽  
Dante M. Kennes ◽  
Herbert Schoeller ◽  
Mikhail Pletyukhov
Keyword(s):  
Continuum Models ◽  
One Dimensional ◽  
Interface Charges ◽  
Universal Properties

scholarly journals Universal properties of boundary and interface charges in multichannel one-dimensional models without symmetry constraints

2021 ◽  
Vol 104 (12) ◽  
Author(s):  
Niclas Müller ◽  
Kiryl Piasotski ◽  
Dante M. Kennes ◽  
Herbert Schoeller ◽  
Mikhail Pletyukhov
Keyword(s):  
One Dimensional ◽  
Interface Charges ◽  
Symmetry Constraints ◽  
Universal Properties ◽  
Dimensional Models

ROUTE TO CHAOS VIA INVERSE CASCADE OF CONTINUOUS BIFURCATIONS

1995 ◽  
Vol 05 (01) ◽  
pp. 123-132 ◽  
Author(s):  
M. GUTMAN ◽  
V. GONTAR
Keyword(s):  
Period Doubling ◽  
Scaling Behavior ◽  
One Dimensional ◽  
Inverse Cascade ◽  
Discontinuous Bifurcation ◽  
Universal Properties ◽  
Route To Chaos ◽  
Piecewise Continuous ◽  
One Dimensional Maps

A route to chaos via an inverse cascade of continuous bifurcations that arithmetically reduce the period of successive orbits has been obtained for piecewise continuous one-dimensional maps. We have studied the mechanism of these bifurcations and established that their scaling behavior is governed by constants with new universal properties. The possibility of obtaining discontinuous bifurcation from any selected orbit of a cascade of period-doubling to any orbit of inverse cascade has been demonstrated.

scholarly journals INVESTIGATION OF DIFFERENCE EQUATIONS WITH A RATIONAL RIGHT-HAND SIDES

2020 ◽  
Vol 8 (2) ◽  
Author(s):  
I. Klevchuk
Keyword(s):  
Difference Equations ◽  
Symbolic Dynamics ◽  
Piecewise Linear ◽  
Discrete Dynamical System ◽  
Deterministic Chaos ◽  
Period Doubling ◽  
Rational Functions ◽  
Invariant Set ◽  
One Dimensional ◽  
Universal Properties

The aim of the present article is to investigate of some properties of solutions of nonli- near difference equations. A period doubling bifurcation in a discrete dynamical system leads to the appearance of deterministic chaos. We use permutable rational functions for study of some classes of one-dimensional mappings. Also n-dimensional generalizations of permutable polynomials may be obtained. We investigate polynomial and rational mappings with invariant measure and construct equivalent piecewise linear mappings. These mappings have countably many cycles. We applied the methods of symbolic dynamics to the theory of unimodal mappi- ngs. We use whole p-adic numbers for study the invariant set of some mapping in the theory of universal properties of one-parameter families. Feigenbaum constants play an important role in this theory.

scholarly journals MAXIMIZING THE HYPERPOLARIZABILITY OF ONE-DIMENSIONAL SYSTEMS

2010 ◽  
Vol 19 (03) ◽  
pp. 379-388 ◽  
Author(s):  
URSZULA B. SZAFRUGA ◽  
MARK G. KUZYK ◽  
DAVID S. WATKINS
Keyword(s):  
Potential Energy ◽  
Energy Function ◽  
Bound States ◽  
Nonlinear Optical ◽  
Potential Energy Function ◽  
Optical Response ◽  
Nonlinear Optical Response ◽  
One Dimensional ◽  
Continuum States ◽  
Universal Properties

Previous studies have used numerical methods to optimize the hyperpolarizability of a one-dimensional quantum system. These studies were used to suggest properties of one-dimensional organic molecules, such as the degree of modulation of conjugation, that could potentially be adjusted to improve the nonlinear-optical response. However, there were no conditions set on the optimized potential energy function to ensure that the resulting energies were consistent with what is observed in real molecules. Furthermore, the system was placed in a one-dimensional box with infinite walls, forcing the wavefunctions to vanish at the ends of the molecule. In the present work, the walls are separated by a distance much larger than the molecule's length; and, the variations of the potential energy function are restricted to levels that are more typical of a real molecule. In addition to being a more physically-reasonable model, our present approach better approximates the bound states and approximates the continuum states — which are usually ignored. We find that the same universal properties continue to be important for optimizing the nonlinear-optical response, though the details of the wavefunctions differ from previous results.

Vibration localization in one-dimensional linear and nonlinear lattices: discrete and continuum models

2012 ◽  
Vol 72 (1-2) ◽  
pp. 37-48 ◽  
Author(s):  
Igor V. Andrianov ◽  
Vladyslav V. Danishevs’kyy ◽  
Alexander L. Kalamkarov
Keyword(s):  
Continuum Models ◽  
One Dimensional ◽  
Vibration Localization ◽  
Nonlinear Lattices ◽  
Linear And Nonlinear
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