Related papers: Numerical Evolution from the Hamiltonian
Estimating and quantifying uncertainty in unknown system parameters from limited data remains a challenging inverse problem in a variety of real-world applications. While many approaches focus on estimating constant parameters, a subset of…
Imaginary-time evolution plays an important role in algorithms for computing ground-state and thermal equilibrium properties of quantum systems, but can be challenging to simulate on classical computers. Many quantum algorithms for…
Q^2 evolution equations are important not only for describing hadron reactions in accelerator experiments but also for investigating ultrahigh-energy cosmic rays. The standard ones are called DGLAP evolution equations, which are…
We perform a numerical free evolution of a selfgravitating, spherically symmetric scalar field satisfying the wave equation. The evolution equations can be written in a very simple form and are symmetric hyperbolic in Eddington-Finkelstein…
The path probability of stochastic motion of non dissipative or quasi-Hamiltonian systems is investigated by numerical experiment. The simulation model generates ideal one-dimensional motion of particles subject only to conservative forces…
A numerical method is developed to solve the time-dependent Dirac equation in cylindrical coordinates for 3-D axisymmetric systems. The time evolution is treated by a splitting scheme in coordinate space using alternate direction iteration,…
Imaginary time evolution is a powerful technique for computing the ground state of quantum Hamiltonians, where the convergence to ground state in asymptotic imaginary time is guaranteed. However, implementing this method on quantum…
This paper addresses the challenging numerical simulation of nonlinear hybrid stochastic functional differential equations with infinite delays. We first propose an explicit scheme using space and time truncation, requiring only finite…
This work concerns a study of the quantum mechanical extension of the work of Horwitz et al. [1] on the stability of classical Hamiltonian systems by geometrical methods. Simulations are carried out for several important examples, these…
We present numerical evolutions of three equal-mass black holes using the moving puncture approach. We calculate puncture initial data for three black holes solving the constraint equations by means of a high-order multigrid elliptic…
We present a simple derivation of a Feynman-Kac type formula to study fermionic systems. In this approach the real time or the imaginary time dynamics is expressed in terms of the evolution of a collection of Poisson processes. A computer…
A new method is proposed for integrating the equations of motion of an elastic filament. In the standard finite-difference and finite-element formulations the continuum equations of motion are discretized in space and time, but it is then…
We present a quantum algorithm to achieve higher-order transformations of Hamiltonian dynamics. Namely, the algorithm takes as input a finite number of queries to a black-box seed Hamiltonian dynamics to simulate a desired Hamiltonian. Our…
Quantum computers are important examples of processes whose evolution can be described in terms of iterations of single step operators or their adjoints. Based on this, Hamiltonian evolution of processes with associated step operators $T$…
Adaptive Molecular Resolution approaches in Molecular Dynamics are becoming relevant tools for the analysis of molecular liquids characterized by the interplay of different physical scales. The essential difference among these methods is in…
The classical and quantum dynamics of simple time-reparametrization- invariant models containing two degrees of freedom are studied in detail. Elimination of one ``clock'' variable through the Hamiltonian constraint leads to a description…
Over the past 30 years many researchers in the field of evolutionary computation have put a lot of effort to introduce various approaches for solving hard problems. Most of these problems have been inspired by major industries so that…
This survey is devoted to the asymptotic behavior of solutions of evolution equations generated by maximal monotone operators in Hilbert spaces. The emphasis is in the comparison of the continuous time trajectories to sequences generated by…
A natural example of evolution can be described by a time-dependent two degrees-of-freedom Hamiltonian. We choose the case where initially the Hamiltonian derives from a general cubic potential, the linearised system has frequencies 1 and…
An algorithm for planning near time-optimal trajectories for systems with an oscillatory internal dynamics has been developed in previous work. It is based on assembling a complete trajectory from motion primitives called jerk segments,…