Related papers: A symplectic, symmetric algorithm for spatial evol…
We present a canonical form for a symplectic involution $S\in Sp(2g,\mathbb{Z})$, $S^2=1$; the construction is algorithmic. Application is made in the Riemann surface setting.
We study the time evolution for the quantum harmonic oscillator subjected to a sudden change of frequency. It is based on an approximate analytic solution to the time dependent Ermakov equation for a step function. This approach allows for…
We introduce a nonperturbative, first-principles approach to time-dependent problems in quantum field theory. In this approach, the time-evolution of quantum field configurations is calculated in real time and at the amplitude level. This…
The evolution of a many-particle system on a one-dimensional lattice, subjected to a quantum walk can cause spatial entanglement in the lattice position, which can be exploited for quantum information/communication purposes. We demonstrate…
Modern N-body techniques for planetary dynamics are generally based on symplectic algorithms specially adapted to the Kepler problem. These methods have proven very useful in studying planet formation, but typically require the timestep for…
In this paper we study the time evolution of a class of two-level systems driven by periodic fields in terms of new convergent perturbative expansions for the associated propagator U(t). The main virtue of these expansions is that they do…
A symplectic pseudospectral time-domain (SPSTD) scheme is developed to solve Schrodinger equation. Instead of spatial finite differences in conventional finite-difference time-domain (FDTD) method, the fast Fourier transform is used to…
The influence of time-dependent fitnesses on the infinite population dynamics of simple genetic algorithms (without crossover) is analyzed. Based on general arguments, a schematic phase diagram is constructed that allows one to characterize…
Energy methods for constructing time-stepping algorithms are of increased interest in application to nonlinear problems, since numerical stability can be inferred from the conservation of the system energy. Alternatively, symplectic…
The dynamics of a system of particles subject to a 4th order potential field modeling the space-time evolution of wedge disclinations is studied, focusing on finite systems of disclinations within a circular domain. Existence theorems for…
Symplectic numerical methods have become a widely-used choice for the accurate simulation of Hamiltonian systems in various fields, including celestial mechanics, molecular dynamics and robotics. Even though their characteristics are…
In this paper, we proposed a stochastic model which describes two species of particles moving in counterflow. The model generalizes the theoretical framework describing the transport in random systems since particles can work as mobile…
Einstein's field equations for spatially self-similar spherically symmetric perfect-fluid models are investigated. The field equations are rewritten as a first-order system of autonomous differential equations. Dimensionless variables are…
Nowadays hybrid evolutionary algorithms, i.e, heuristic search algorithms combining several mutation operators some of which are meant to implement stochastically a well known technique designed for the specific problem in question while…
In this work we study the unitary time-evolutions of quantum systems defined on infinite-dimensional separable time-dependent Hilbert spaces. Two possible cases are considered: a quantum system defined on a stochastic interval and another…
The article presents a study of the Particle Swarm optimization method for scheduling problem. To improve the method's performance a restriction of particles' velocity and an evolutionary meta-optimization were realized. The approach…
Explicit high-order non-canonical symplectic particle-in-cell algorithms for classical particle-field systems governed by the Vlasov-Maxwell equations are developed. The algorithm conserves a discrete non-canonical symplectic structure…
The spectrum of masses from a lattice QCD simulation may be found by fitting exponential functions to correlators of operators possessing the quantum numbers of the particles of interest. The ability of evolutionary algorithms to find…
This work builds on an existing model of discrete canonical evolution and applies it to the general case of a linear dynamical system, i.e., a finite-dimensional system with configuration space isomorphic to $ \mathbb{R}^{q} $ and linear…
In this paper, we discuss time evolution and adiabatic approximation in $PT$-symmetric quantum mechanics. we give the time evolving equation for a class of $PT$-symmetric Hamiltonians and some conditions of the adiabatic approximation for…