An Initial Value Representation with Complex Trajectories
نویسندگان
چکیده
We present an Initial Value Representation for the semiclassical coherent state propagator based on complex trajectories. We map the complex phase space into a real phase space with twice as many dimensions and use a simple procedure to automatically eliminate non-contributing trajectories. The resulting semiclassical formulas do not show divergences due to caustics and provide accurate results.
منابع مشابه
Theory of Hybrid Fractional Differential Equations with Complex Order
We develop the theory of hybrid fractional differential equations with the complex order $thetain mathbb{C}$, $theta=m+ialpha$, $0<mleq 1$, $alphain mathbb{R}$, in Caputo sense. Using Dhage's type fixed point theorem for the product of abstract nonlinear operators in Banach algebra; one of the operators is $mathfrak{D}$- Lipschitzian and the other one is completely continuous, we prove the exis...
متن کاملFirst principles semiclassical calculations of vibrational eigenfunctions.
Vibrational eigenfunctions are calculated on-the-fly using semiclassical methods in conjunction with ab initio density functional theory classical trajectories. Various semiclassical approximations based on the time-dependent representation of the eigenfunctions are tested on an analytical potential describing the chemisorption of CO on Cu(100). Then, first principles semiclassical vibrational ...
متن کاملReal time correlation function in a single phase space integral beyond the linearized semiclassical initial value representation.
It is shown how quantum mechanical time correlation functions [defined, e.g., in Eq. (1.1)] can be expressed, without approximation, in the same form as the linearized approximation of the semiclassical initial value representation (LSC-IVR), or classical Wigner model, for the correlation function [cf. Eq. (2.1)], i.e., as a phase space average (over initial conditions for trajectories) of the ...
متن کاملQuantum initial value representations using approximate Bohmian trajectories
Quantum trajectories, originating from the de Broglie-Bohm (dBB) hydrodynamic description of quantum mechanics, are used to construct time-correlation functions in an initial value representation (IVR). The formulation is fully quantum mechanical and the resulting equations for the correlation functions are similar in form to their semi-classical analogs but do not require the computation of th...
متن کاملMultiple coherent states for first-principles semiclassical initial value representation molecular dynamics.
A multiple coherent states implementation of the semiclassical approximation is introduced and employed to obtain the power spectra with a few classical trajectories. The method is integrated with the time-averaging semiclassical initial value representation to successfully reproduce anharmonicity and Fermi resonance splittings at a level of accuracy comparable to semiclassical simulations of t...
متن کامل