Related papers: Complex trajectory method in time-dependent WKB
In order to alleviate the computational costs of fully quantum nonadiabatic dynamics, we present a mixed quantum-classical (MQC) particle method based on the theory of Koopman wavefunctions. Although conventional MQC models often suffer…
We explore higher-dimensional generalizations of the Runge-Kutta-Wentzel-Kramers-Brillouin method for integrating coupled systems of first-order ordinary differential equations with highly oscillatory solutions. Such methods could improve…
Trajectory-based mixed quantum-classical approaches to coupled electron-nuclear dynamics suffer from well-studied problems such as the lack of (or incorrect account for) decoherence in the trajectory surface hopping method and the inability…
In this work we derive a WKB expansion for the electromagnetic fields solution of the time-harmonic Maxwell equations set in a domain with a thin layer. As a by-product of this expansion we obtain new second order asymptotic models with…
We derive the general Kubo formula in a form that solely utilizes the time evolution of displacement operators. The derivation is based on the decomposition of the linear response function into its time symmetric and time anti-symmetric…
We prove an error estimate for a Lie-Trotter splitting operator associated to the Schrodinger-Poisson equation in the semiclassical regime, when the WKB approximation is valid. In finite time, and so long as the solution to a compressible…
The exactness of the semiclassical method for three-dimensional problems in quantum mechanics is analyzed. The wave equation appropriate in the quasiclassical region is derived. It is shown that application of the standard leading-order WKB…
We analyze quantitatively the accuracy of eigenfunction and eigenvalue calculations in the frame work of WKB and instanton semiclassical methods. We show that to estimate the accuracy it is enough to compare two linearly independent (with…
Recently, the Lorentzian path integral formulation using the Picard-Lefschetz theory has attracted much attention in quantum cosmology. In this paper, we analyze the tunneling amplitude in quantum mechanics by using the Lorentzian…
This paper addresses the challenge of developing efficient algorithms for large-scale nonconvex multiobjective optimization problems (MOPs). While quasi-Newton methods are effective, their traditional application to MOPs is computationally…
We derive a semiclassical approximation for the evolution generated by the Lindblad equation as a generalization of complex WKB theory. Linear coupling to the environment is assumed, but the Hamiltonian can be a general function of…
Mixed quantum-classical methods provide powerful algorithms for the simulation of quantum processes in large and complex systems. The forward-backward trajectory solution of the mixed quantum-classical Liouville equation in the mapping…
We extend topological string methods in order to perform WKB approximations for quantum mechanical problems with higher order potentials efficiently. This requires techniques for the evaluation of the relevant quantum periods for Riemann…
The phenomenon of quantum tunneling is reviewed and an overview of applying approximate methods for studying this effect is given. An approach to a time-dependent formalism is proposed in one dimension and generalized to higher dimensions.…
We have obtained a set of coupled differential equations from the continuous limit of the transfer matrix method. Decoupling such a set of equations yields an extension to the Wentzel-Kramers-Brillouin (WKB) approximation for the…
We quantize a homogeneous and isotropic universe for two models of modified teleparallel gravity, wherein an arbitrary function of the boundary term, namely $B$, is present in the action and in the other model a scalar field that is…
For Maxwell's equations with nonlinear polarization we prove the existence of time-periodic breather solutions travelling along slab or cylindrical waveguides. The solutions are TE-modes which are localized in space directions orthogonal to…
For a class of solutions of the fundamental difference equation of isotropic loop quantum cosmology, the difference equation can be replaced by a differential equation valid for {\em all} values of the triad variable. The differential…
In this paper we develop a novel method to solve problems involving quantum optical systems coupled to coherent quantum feedback loops featuring time delays. Our method is based on exact mappings of such non-Markovian problems to equivalent…
Our objective is to stabilise and accelerate the time-domain boundary element method (TDBEM) for the three-dimensional wave equation. To overcome the potential time instability, we considered using the Burton--Miller-type boundary integral…