Related papers: A Kuramoto Model for the Bound State Aharonov-Bohm…
The Kuramoto model with mixed signs of couplings is known to produce a traveling-wave synchronized state. Here, we consider an abrupt synchronization transition from the incoherent state to the traveling-wave state through a long-lasting…
The subjects which are discussed in this Thesis include: the self energy of a bound electron and the spin-dependence of QED corrections in bound systems, convergence acceleration techniques, and resummation methods for divergent series with…
We investigate the role of inertia in the asynchronous state of a disordered Kuramoto model. We extend an iterative simulation scheme to the case of the Kuramoto model with inertia in order to determine the self-consistent fluctuation…
The Aharonov-Bohm (AB) effect is considered in the context of Generalized Electrodynamics (GE) by Podolsky and Bopp. GE is the only extension to Maxwell electrodynamics that is locally {\normalsize{}U(1)}-gauge invariant, admits linear…
A paradigmatic framework to study the phenomenon of spontaneous collective synchronization is provided by the Kuramoto model comprising a large collection of limit-cycle oscillators of distributed frequencies that are globally coupled…
The Kuramoto model describes the collective dynamics of a system of coupled oscillators. An alpha-Kuramoto partition is a graph partition induced by the Kuramoto model, when the oscillators include a phase frustration parameter. We prove…
We present a generalization of the Kuramoto phase oscillator model in which phases advance in discrete phase increments through Poisson processes, rendering both intrinsic oscillations and coupling inherently stochastic. We study the…
The Kuramoto model is a mean-field model for the synchronisation behaviour of oscillators, which exhibits Landau damping. In a recent work, the nonlinear stability of a class of spatially inhomogeneous stationary states was shown under the…
As a consequence of the Aharonov-Bohm effect, there is a quantum-induced attraction between a charged particle and a rigid, impenetrable hoop made from an arbitrarily thin tube containing a superconductor quantum of magnetic flux. This is…
We investigate Faraday's law of induction manifested in the quantum state of Aharonov-Bohm loops. In particular, we propose a flux-switching experiment for a double-dot AB ring to verify the phase shift induced by Faraday's law. We show…
We show that in classical mechanics, as well as in nonrelativistic quantum mechanics the equation of the relative motion for a two-body bound system at rest can be replaced by individual dynamical equations of the same kind as the first…
We analyze theoretically the bound state spectrum of an Aharonov Bohm (AB) ring in a two-dimensional topological insulator using the four-band model of HgTe-quantum wells as a concrete example. We calculate analytically the circular helical…
We consider a long-range model of coupled phase-only oscillators subject to a local potential and evolving in presence of thermal noise. The model is a non-trivial generalization of the celebrated Kuramoto model of collective…
The mechanism of formation of bound states in the relativistic quantum field theory is demonstrated by the Yukawa field model. It is shown that the weak coupling regime leads to the potential picture, i.e. it is equivalent to the…
The relativistic bound-state energy spectrum and the wavefunctions for the Coulomb potential are studied for de Sitter and anti-de Sitter spaces in the context of the extended uncertainty principle. Klein-Gordon and Dirac equations are…
We study the emergent collective behaviors for an ensemble of identical Kuramoto oscillators under the effect of inertia. In the absence of inertial effects, it is well known that the generic initial Kuramoto ensemble relaxes to the…
The exact wave functions that describe scattering of a charged particle by a confined magnetic field (Aharonov-Bohm effect) and by a Coulomb field are analyzed. It is well known that the usual procedure of finding asymptotic forms of these…
By means of numerical analysis conducted with the aid of the computer, the collective synchronization of coupled phase oscillators in the Kuramoto model in the connected regime of random networks of various sizes is studied. The oscillators…
The bound state wave functions for a wide class of exactly solvable potentials are found utilizing the quantum Hamilton-Jacobi formalism. It is shown that, exploiting the singularity structure of the quantum momentum function, until now…
An experiment to observe the Aharonov-Bohm effect is discussed. A solenoid which consists of a large number of point magnetic dipoles is considered as the source of a vector potential, which acts on a charged particle, and such potential…