Related papers: Computing Classical Escape Rates from Periodic Orb…
The time-dependent Schr\"odinger equation for atomic hydrogen in few-cycle laser pulses is solved numerically. Introducing a positive definite quantum distribution function in energy-position space, a straightforward comparison of the…
A set of algorithms is presented for efficient numerical calculation of the time evolution of classical dynamical systems. Starting with a first approximation for solving the differential equations that has a "reversible" character, we show…
In the framework of semiclassical theory the universal properties of quantum systems with classically chaotic dynamics can be accounted for through correlations between partner periodic orbits with small action differences. So far, however,…
In the present article, we investigate the behavior of orbits in a time independent axially symmetric galactic type potential. This dynamical model can be considered to describe the motion in the central parts of a galaxy, for values of…
Oscillators - dynamical systems with stable periodic orbits - arise in many systems of physical, technological, and biological interest. The standard phase reduction, a model reduction technique based on isochrons, can be unsuitable for…
Employing the method of mapping the spin problem onto a particle one, we have derived the particle Hamiltonian for a biaxial spin system with a transverse or longitudinal magnetic field. Using the Hamiltonian and introducing the parameter…
We present here a new method which applies well ordered symbolic dynamics to find unstable periodic and non-periodic orbits in a chaotic system. The method is simple and efficient and has been successfully applied to a number of different…
For a simple model of chaotic dynamical systems with a large number of degrees of freedom, we find that there is an ensemble of unstable periodic orbits (UPOs) with the special property that the expectation values of macroscopic quantities…
Semiclassical methods have been applied very successfully to describe the nontrivial transition from the quantum to the classical regime in $\textit{single}$-particle or at least $\textit{few}$-particle systems. Challenges on the way to an…
The study of the high pressure phase diagram of hydrogen has continued with renewed effort for about one century as it remains a fundamental challenge for experimental and theoretical techniques. Here we employ an efficient molecular…
Hamiltonian theory of hybrid quantum-classical systems is used to study dynamics of the classical subsystem coupled to different types of quantum systems. It is shown that the qualitative properties of orbits of the classical subsystem…
We define a class of quantum systems called regular quantum graphs. Although their dynamics is chaotic in the classical limit with positive topological entropy, the spectrum of regular quantum graphs is explicitly computable analytically…
We investigate the escape rate of a biaxial spin particle with an arbitrarily dierected magnetic field in the easy plane, described by Hamiltonian ${\cal H} = -AS_z^2 - BS_x^2 -H_x S_x -H_z S_z, (A>B>0)$. We derive an effective particle…
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…
The basic problem in equilibrium statistical mechanics is to compute phase space average, in which Monte Carlo method plays a very important role. We begin with a review of nonlocal algorithms for Markov chain Monte Carlo simulation in…
We examine the escape from the four hill potential by using the method of grid classification, when polar coordinates are used for expressing the initial conditions of the orbits. In particular, we investigate how the energy of the orbits…
We study the nonlinear classical dynamics of an electron confined in a double dot potential and subjected to a spin-orbit coupling and a constant external magnetic field. It is shown that due to the spin orbit coupling, the energy can be…
The escape mechanism of orbits in a star cluster rotating around its parent galaxy in a circular orbit is investigated. A three degrees of freedom model is used for describing the dynamical properties of the Hamiltonian system. The…
In chaotic dynamical systems, a number of rare trajectories with low level of chaoticity are embedded in chaotic sea, while extraordinary unstable trajectories can exist even in weakly chaotic regions. In this study, a quantitative method…
We introduce a Monte Carlo algorithm to efficiently compute transport properties of chaotic dynamical systems. Our method exploits the importance sampling technique that favors trajectories in the tail of the distribution of displacements,…