Related papers: A variational symplectic scheme based on Simpson's…
An approximation method which combines the perturbation theory with the variational calculation is constructed for quantum mechanical problems. Using the anharmonic oscillator and the He atom as examples, we show that the present method…
We introduce a new strategy for coupling the parallel in time (parareal) iterative methodology with multiscale integrators. Following the parareal framework, the algorithm computes a low-cost approximation of all slow variables in the…
We investigate the use of extended phase-space symplectic integration for simulating two different classes of electron dynamics. The first one, with one and a half degrees of freedom, comes from plasma physics and describes the classical…
We systematically improve the recent variational calculation of the imaginary part of the ground state energy of the quartic anharmonic oscillator. The results are extremely accurate as demonstrated by deriving, from the calculated…
We explore how to build quantum circuits that compute the lowest energy state corresponding to a given Hamiltonian within a Symmetry subspace by explicitly encoding it into the circuit. We create an explicit unitary and a variationally…
Hamiltonian systems are differential equations which describe systems in classical mechanics, plasma physics, and sampling problems. They exhibit many structural properties, such as a lack of attractors and the presence of conservation…
Explicit and semi-explicit geometric integration schemes for dissipative perturbations of Hamiltonian systems are analyzed. The dissipation is characterized by a small parameter $\epsilon$, and the schemes under study preserve the…
Two improvements with respect to previous formulations are presented for the calculation of the partition function $\mathcal{Z}$ of small, isolated and interacting many body systems. By including anharmonicities and employing a variational…
This article considers Hamiltonian mechanical systems with potential functions admitting jump discontinuities. The focus is on accurate and efficient numerical approximations of their solutions, which will be defined via the laws of…
We present a time-splitting spectral scheme for the Maxwell-Dirac system and similar time-splitting methods for the corresponding asymptotic problems in the semi-classical and the non-relativistic regimes. The scheme for the Maxwell-Dirac…
We design a variational asymptotic preserving scheme for the Vlasov-Poisson-Fokker-Planck system with the high field scaling, which describes the Brownian motion of a large system of particles in a surrounding bath. Our scheme builds on an…
We define a kinetic and a potential energy such that the principle of stationary action from Lagrangian mechanics yields a Camassa--Holm system (2CH) as the governing equations. After discretizing these energies, we use the same variational…
Though switched dynamical systems have shown great utility in modeling a variety of physical phenomena, the construction of an optimal control of such systems has proven difficult since it demands some type of optimal mode scheduling. In…
Heat is a complex quantity to measure in stochastic systems because it requires extremely small sampling timesteps. Unfortunately this is not always possible in real experiments, mainly because experimental setups have technical limits. To…
In this work we construct a stochastic contact variational integrator and its discrete version via stochastic Herglotz variational principle for stochastic contact Hamiltonian systems. A general structure-preserving stochastic contact…
Nonadiabatic behavior of metastable systems modeled by anharmonic Hamiltonians is reproduced by the Fokker-Planck and imaginary time Schrodinger equation scheme with subsequent symplectic integration. Example solutions capture ergodicity…
Mesoscopic mechanical oscillators can be prepared in quantum states and coherently manipulated using the optomechanical interaction. This has recently been used to prepare squeezed mechanical states. However, the scheme used in these…
Solving quaternion kinematical differential equations is one of the most significant problems in the automation, navigation, aerospace and aeronautics literatures. Most existing approaches for this problem neither preserve the norm of…
In this paper, we develop a framework to construct energy-preserving methods for multi-components Hamiltonian systems, combining the exponential integrator and the partitioned averaged vector field method. This leads to numerical schemes…
We present a new algorithm for isothermal-isobaric molecular-dynamics simulation. The method uses an extended Hamiltonian with an Andersen piston combined with the Nos'e-Poincar'e thermostat, recently developed by Bond, Leimkuhler and Laird…