Related papers: New method for obtaining complex roots in the semi…
Applied to the master equation, the usual numerical integration methods, such as Runge-Kutta, become inefficient when the rates associated with various transitions differ by several orders of magnitude. We introduce an integration scheme…
We construct the action-angle variables of a classical integrable model defined on complex projective phase space and calculate the quantum mechanical propagator in the coherent state path integral representation using the stationary phase…
Numerical integration of orbit trajectories for a large number of initial conditions and for long time spans is computationally expensive. Semi-analytical methods were developed to reduce the computational burden. An elegant and widely used…
The recently-introduced relaxation approach for Runge-Kutta methods can be used to enforce conservation of energy in the integration of Hamiltonian systems. We study the behavior of implicit and explicit relaxation Runge-Kutta methods in…
The problem of an origin of the Solary-Kochetov extra-phase contribution to the naive semiclassical form of a generalized phase-space propagator is addressed with the special reference to the su(2) spin case which is the most important in…
This paper introduces a time-domain combined field integral equation for electromagnetic scattering by a perfect electric conductor. The new equation is obtained by leveraging the quasi-Helmholtz projectors, which separate both the unknown…
We derive semiclassical expressions for spectra, weighted by matrix elements of a Gaussian observable, relevant to a range of molecular and mesoscopic systems. We apply the formalism to the particular example of the resonant tunneling diode…
A closed (in terms of classical data) expression for a transition amplitude between two generalized coherent states associated with a semisimple Lee algebra underlying the system is derived for large values of the representation highest…
This paper suggests a new way to compute the path integral for simple quantum mechanical systems. The new algorithm originated from previous research in string theory. However, its essential simplicity is best illustrated in the case of a…
The semidiscretization of a sound soft scattering problem modelled by the wave equation is analyzed. The spatial treatment is done by integral equation methods. Two temporal discretizations based on Runge-Kutta convolution quadrature are…
Explicit Runge-Kutta schemes with large stable step sizes are developed for integration of high order spectral difference spatial discretization on quadrilateral grids. The new schemes permit an effective time step that is substantially…
In this work we present a new class of Runge-Kutta (RK) methods for solving systems of hyperbolic equations with a particular structure, generalization of a wave-equation. The new methods are {\it partially implicit} in the sense that a…
A unified semiclassical time propagator is used to calculate the semiclassical time-correlation function in three cartesian dimensions for a particle moving in an attractive Coulomb potential. It is demonstrated that under these conditions…
This paper investigates the performance of a subclass of exponential integrators, specifically explicit exponential Runge--Kutta methods. It is well known that third-order methods can suffer from order reduction when applied to linearized…
We assess the suitability of quantum and semiclassical initial value representations, exemplified by the coupled coherent states (CCS) method and the Herman Kluk (HK) propagator, respectively, for modeling the dynamics of an electronic wave…
For a subquadratic symbol $H$ on $\R^d\times\R^d = T^*(\R^d)$, the quantum propagator of the time dependent Schr\"odinger equation $i\hbar\frac{\partial\psi}{\partial t} = \hat H\psi$ is a Semiclassical Fourier-Integral Operator when $\hat…
Runge-Kutta methods are the classic family of solvers for ordinary differential equations (ODEs), and the basis for the state of the art. Like most numerical methods, they return point estimates. We construct a family of probabilistic…
We reconsider the variational derivation of symplectic partitioned Runge-Kutta schemes. Such type of variational integrators are of great importance since they integrate mechanical systems with high order accuracy while preserving the…
We are concerned with the efficient implementation of symplectic implicit Runge-Kutta (IRK) methods applied to systems of (non-necessarily Hamiltonian) ordinary differential equations by means of Newton-like iterations. We pay particular…
We examine the problem of the evaluation of both the propagator and of the partition function of a spinning particle in an external field at the classical as well as the quantum level, in connection with the asserted exactness of the saddle…