Prediction of chaos in a Josephson junction by the Melnikov-function technique

Abstract

 Users may download and print one copy of any publication from the public portal for the purpose of private study or research.  You may not further distribute the material or use it for any profit-making activity or commercial gain  You may freely distribute the URL identifying the publication in the public portal If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.

Does chaos assist localization or delocalization?

“…For small values of A and n /V 0 , the e(q, s) can be treated as perturbation such that the perturbed solution reads q(s) ¼ q 0 (s) þ q 1 (s) with the zero-order heteroclinic solution q 0 (s) and the first-order "chaotic solution" q 1 (s) in the forms 18,25 q 0 ¼ 2arctan½sinhðs þ t 0 Þ;…”

“…4 Subsequently, many theoretical and experimental works demonstrated that classical chaos enhanced quantum tunneling rate drastically 2,3,14 even without a barrier to tunnel through. 2,3 Particularly, in the absence of collisions and dephasing effects, a particle in a static and tilted lattice is localized in a certain range, due to the celebrated Bloch oscillations, 15 while the presence of a periodically varying ramp results in chaos [16][17][18] and delocalization. 7,19 In addition, there exist other situations, where both the quantum localization and delocalization may be independent of the classical chaos.…”

“…11,21,22 It is well known that delocalization and localization in a lattice occur in different parameter regions, 7,22,23 and the chaotic and regular regions also coexist in a chaotic system. 17,18 When localization (delocalization) occurs in the chaotic region, we call it the chaos-assisted localization (delocalization). We will analytically and numerically illustrate some near-resonant regions, where the driving frequency equates or approaches the lattice tilt, 11 and reveal that chaos can assist delocalization in the chaos-resonance overlapping regions, while chaos may aid localization in the other chaotic regions.…”

Wannier–Stark chaos of a Bose–Einstein condensate in 1D optical lattices

“…Fixing the parameters F ¼ 0:25, b ¼ 2, c ¼ 1, we plot the chaotic regions on the V 0 À g 0 plane as in Fig. 2, where the region above the curve is the Melnikov chaotic region in which the evolution of the atomic number density and energy density have the properties of Smale-horseshoe chaos [32], and the system is generally unstable in this region. Given the chaotic region, we can let the system be in the chaotic state or not, by adjusting the external and internal potential strengths.…”

Metastable States and Irregular Behaviour in a Josephson Junction With Nonlinear Resistance

“…The method of Melnikov· analysis has been used to predict the lowest threshold for chaos in this system. 11 We carry out detailed investigations regarding the possible routes to chaos, the nature of the chaotic state, etc. in this model.…”