Related papers: The short periodic orbit method for excited chaoti…
For the variational quantum eigensolver we propose to generate trial wavefunctions from a small amount of selected Pauli terms of the problem Hamiltonian. Two different approaches, one inspired by the quantum approximate optimization…
Wave propagation and acoustic scattering problems require vast computational resources to be solved accurately at high frequencies. Asymptotic methods can make this cost potentially frequency independent by explicitly extracting the…
We study the stability of circular orbits of the electromagnetic two-body problem in an electromagnetic setting that includes retarded and advanced interactions. We give a method to derive the equations of tangent dynamics about circular…
In the present work we study the two-point correlation function $R(\epsilon)$ of the quantum mechanical spectrum of a classically chaotic system. Recently this quantity has been computed for chaotic and for disordered systems using periodic…
In this paper, a novel formulation of discrete chaotic iterations in the field of dynamical systems is given. Their topological properties are studied: it is mathematically proved that, under some conditions, these iterations have a chaotic…
The possibility of using quantum computers for electronic structure calculations has opened up a promising avenue for computational chemistry. Towards this direction, numerous algorithmic advances have been made in the last five years. The…
Smooth periodic travelling waves in the Camassa--Holm (CH) equation are revisited. We show that these periodic waves can be characterized in two different ways by using two different Hamiltonian structures. The standard formulation, common…
As the amount of asteroseismic data available continues to grow, the inability to accurately model observed oscillation frequencies is becoming a critical problem for interpreting these frequencies. A major component of this problem is the…
In the noisy intermediate-scale quantum era, variational quantum algorithms (VQAs) have emerged as a promising avenue to obtain quantum advantage. However, the success of VQAs depends on the expressive power of parameterised quantum…
We investigate the spatial statistics of the energy eigenfunctions on large quantum graphs. It has previously been conjectured that these should be described by a Gaussian Random Wave Model, by analogy with quantum chaotic systems, for…
The ability to generate complete, or almost complete, chaotic mixing is of great interest in numerous applications, particularly for microfluidics. For this purpose, we propose a strategy that allows us to quickly target the parameter…
We study a crossover from classical to quantum picture in the electron energy statistics in a system with broken time-reversal symmetry. The perturbative and nonperturbative parts of the two level correlation function, $R(\omega)$ are…
Droplets moving in a microfluidic loop device exhibit both periodic and chaotic behaviors based on the inlet droplet spacing. We propose that the periodic behavior is an outcome of a dispersed phase conservation principle. This conservation…
We derive the approximate analytical solutions of the bound timelike geodesic orbits in the effective-one-body (EOB) frame with extreme-mass ratio limit. The analytical solutions are expressed in terms of the elliptic integrals using Mino…
The theory of the inverse problem is used in order to find a two dimensional galactic potential generating a mono-parametric family of elliptic periodic orbits. The potential is made up of a two-dimensional harmonic oscillator with…
We have developed a simple method to solve anharmonic oscillators equations. The idea of our method is mainly based on the partitioning of the potential curve into (n+1) small intervals, solving the Schr\"odinger equation in each…
The supersymmetry method has proven to be a very powerful tool of study of the statistical properties of energy levels and eigenfunctions in disordered and chaotic systems. The aim of these lectures is to present a tutorial introduction to…
Some numerical calculations are presented on the dependence of the average mode count and average mode density of electromagnetic cavities on their specific geometric design, based on the generalized Weyl law. The analysis focuses on a…
In this paper, we establish a new criterion for the orbital stability of periodic waves related to a general class of regularized dispersive equations. More specifically, we present sufficient conditions for the stability without knowing…
An alternative numerical method is developed to find stable and unstable periodic orbits of nonlinear dynamical systems. The method exploits the high-efficiency of the Levenberg-Marquardt algorithm for medium-sized problems and has the…