Related papers: Mixed Semiclassical Initial Value Representation T…
A unified viewpoint on the van Vleck and Herman-Kluk propagators in Hilbert space and their recently developed counterparts in Wigner representation is presented. It is shown that the numerical protocol for the Herman-Kluk propagator, which…
We propose a conjugate application of the Bargmann representation of quantum mechanics. Applying the Maslov method to the semiclassical connection formula between the two representations, we derive a uniform semiclassical approximation for…
We modify the pre-factor of the semiclassical propagator to improve its efficiency in practical implementations. The new pre-factor represents the smooth portion of an orbit's contribution, and leads to fast convergence in numerical…
In this paper we consider the problem of computing the stationary distribution of nearly completely decomposable Markov processes, a well-established area in the classical theory of Markov processes with broad applications in the design,…
When the semiclassical Herman-Kluk propagator is used for evaluating quantum-mechanical observables or time-correlation functions, the initial conditions for the guiding trajectories are typically sampled from the Husimi density. Here, we…
In this paper, the use of partitioned linear multistep methods (PLMM) as time integrators for the numerical approximation of some partial differential equations (pdes) is studied. We consider the periodic initial-value problem of two…
To alleviate the computational cost associated with on-the-fly ab initio semiclassical calculations of molecular spectra, we propose the single-Hessian thawed Gaussian approximation, in which the Hessian of the potential energy at all…
Calculating intermolecular charge transfer integrals in organic semiconductors requires substantial computer resource for each individual calculation. We might alternatively construct a machine learning model for transfer integrals, which…
The quantum partition function at finite temperature requires computing the trace of the imaginary time propagator. For numerical and Monte Carlo calculations, the propagator is usually split into its kinetic and potential parts. A higher…
We use a semiclassical approximation to derive the partition function for an arbitrary potential in one-dimensional Quantum Statistical Mechanics, which we view as an example of finite temperature scalar Field Theory at a point. We rely on…
In this paper we study recent developments in the approximation of the spread option pricing. As the Kirk\'s Approximation is extremely flawed in the cases when the correlation is very high, we explore a recent development that allows…
Based on the work done by an electromagnetic field on an atomic or molecular electronic system, a general gauge invariant formulation of transient absorption spectroscopy is presented within the semi-classical approximation. Avoiding…
A continuous approximation for the results of [1] is obtained. In this approximation the energy distribution is represented in the form of the product of the Gibbs factor and superstatistics factor. The mutual weights of the factors are…
We deal with an initial-boundary value problem for the multidimensional acoustic wave equation, with the variable speed of sound. For a three-level semi-explicit in time higher-order vector compact scheme, we prove stability and derive 4th…
We study smooth, caustic-free, chaotic semiclassical dynamics on two-dimensional phase space and find that the dynamics can be approached by an iterative procedure which constructs an approximation to the exact long-time semiclassical…
Time-spectral solution of ordinary and partial differential equations is often regarded as an inefficient approach. The associated extension of the time domain, as compared to finite difference methods, is believed to result in…
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…
Two semimetrics on probability distributions are proposed, given as the sum of differences of expectations of analytic functions evaluated at spatial or frequency locations (i.e, features). The features are chosen so as to maximize the…
Continuous-time Bayesian networks is a natural structured representation language for multicomponent stochastic processes that evolve continuously over time. Despite the compact representation, inference in such models is intractable even…
We propose and analyze a quasi-Monte Carlo (QMC) algorithm for efficient simulation of wave propagation modeled by the Helmholtz equation in a bounded region in which the refractive index is random and spatially heterogenous. Our focus is…