Related papers: Homoclinic chaos in a pair of parametrically-drive…
The efficient detection of chaotic behavior in orbits of a complex dynamical system is an active domain of research. Several indicators have been proposed in the past, and new ones have recently been developed in view of improving the…
We study the interplay between superconductivity and altermagnetism in disordered systems using recently derived quantum kinetic transport equations. Starting from this framework, we derive the Ginzburg-Landau free energy and identify, in…
The current-voltage characteristics of Superconducting Quantum Interference Devices (SQUIDs) are known to modulate as a function of applied magnetic field with a period of one flux quantum $\Phi_0=h$/2e. Here we report on the fabrication…
Semiclassical sum rules, such as the Gutzwiller trace formula, depend on the properties of periodic, closed, or homoclinic (heteroclinic) orbits. The interferences embedded in such orbit sums are governed by classical action functions and…
Modern Superconducting QUantum Interference Devices (SQUIDs) are commonly fabricated from either Al or Nb electrodes, with an in-situ oxidation process to create a weak link between them. However, common problems of such planar nano- and…
Following Part~I, we consider a class of reversible systems and study bifurcations of homoclinic orbits to hyperbolic saddle equilibria. Here we concentrate on the case in which homoclinic orbits are symmetric, so that only one control…
An ordinary superconducting quantum interference device (SQUID) contains two weak links connected in parallel. We model a multiple-wire SQUID (MW-SQUID), generalized in two ways. First, the number of weak links, which are provided by…
An analytic reversible Hamiltonian system with two degrees of freedom is studied in a neighborhood of its symmetric heteroclinic connection made up of a symmetric saddle-center, a symmetric orientable saddle periodic orbit lying in the same…
We study theoretically the Josephson current-phase relationship in a chaotic quantum dot coupled to superconductors by ballistic contacts. In this regime, strong proximity effect induces superconductivity in the quantum dot that leads to a…
In this paper we study homoclinic tangles formed by transversal intersections of the stable and the unstable manifold of a {\it non-resonant, dissipative} homoclinic saddle point in periodically perturbed second order equations. We prove…
We developed a powerful computational approach to elaborate on onset mechanisms of deterministic chaos due to complex homoclinic bifurcations in diverse systems. Its core is the reduction of phase space dynamics to symbolic binary…
We examine the Melnikov criterion for transition to chaos in case of a single degree of freedom nonlinear oscillator with the Ueda well potential and an external periodic excitation term. Using effective Hamiltonian we have examined…
In the Schwarzchild black hole spacetime, we show that chaotic motion can be triggered by the spin of a particle. Taking the spin of the particle as a perturbation and using the Melnikov method, we find that the perturbed stable and…
Spectral statistics in band structures is studied in a realistic model describing superconducting quantum interference devices (SQUID's). By controlling an external magnetic flux, the level statistics may show a crossover from the GUE to…
Disordered superconductors in low dimensions provide an exemplary manifestation for the role of quantum fluctuations in a many-body system. Specifically in Josephson arrays with comparable Josephson and charging energies ($E_J\sim E_C$),…
A superconducting quantum interference device (SQUID) comprising 0- and $\pi$-Josephson junctions (JJs), called $\pi$-SQUID, is studied by the resistively shunted junction model. The $\pi$-SQUID shows half-integer Shapiro-steps (SS) under…
In this work we revisit the geometric approach to chaos in Hamiltonian dynamics, by means of the Jacobi-Levi-Civita equation (JLCE). We inspect numerically two low-dimensional dynamical systems; show that, along chaotic orbits, the…
We study superconducting quantum interference in a Josephson junction linked via edge states in two-dimensional (2D) insulators. We consider two scenarios in which the 2D insulator is either a topological or a trivial insulator supporting…
Robust heteroclinic cycles are known to change stability in resonance bifurcations, which occur when an algebraic condition on the eigenvalues of the system is satisfied and which typically result in the creation or destruction of a…
This paper investigates the origin and onset of chaos in a mathematical model of an individual neuron, arising from the intricate interaction between 3D fast and 2D slow dynamics governing its intrinsic currents. Central to the chaotic…