Related papers: High-order geometric integrators for representatio…
While the treatment of conical intersections in molecular dynamics generally requires nonadiabatic approaches, the Born-Oppenheimer adiabatic approximation is still adopted as a valid alternative in certain circumstances. In the context of…
An accurate description of nonadiabatic dynamics of molecular species on metallic surfaces poses a serious computational challenge associated with a multitude of closely-spaced electronic states. We propose a mixed quantum-classical scheme…
This article deals with the numerical integration in time of nonlinear Schr\"odinger equations. The main application is the numerical simulation of rotating Bose-Einstein condensates. The authors perform a change of unknown so that the…
The dynamics of an electronic two-level system coupled to an electromagnetic field are simulated explicitly for one and three dimensional systems through semiclassical propagation of the Maxwell-Liouville equations. We consider three…
An approach to non-adiabatic dynamics of atoms in molecular and condensed matter systems under general non-equilibrium conditions is proposed. In this method interaction between nuclei and electrons is considered explicitly up to the second…
The ability to efficiently and accurately calculate equilibrium time correlation functions of many-body condensed phase quantum systems is one of the outstanding problems in theoretical chemistry. The Nakajima-Zwanzig-Mori formalism coupled…
We find that the quantum-classical correspondence in integrable systems is characterized by two time scales. One is the Ehrenfest time below which the system is classical; the other is the quantum revival time beyond which the system is…
In this paper we develop a picture of Quantum Mechanics based on the description of physical observables in terms of expectation value functions, generalizing thus the so called Ehrenfest theorems for quantum dynamics. Our basic technical…
Due to the exponential growth of the state space of coupled quantum systems it is not possible, in general, to numerically store the state of a very large number of quantum systems within a classical computer. We demonstrate a method for…
Nonadiabatic transition dynamics lies at the core of many electron/hole transfer, photoactivated, and vacuum field-coupled processes. About a century after Ehrenfest proposed "Phasenraum" and the Ehrenfest theorem, we report a conceptually…
We employ Non-equilibrium Green's functions (NEGF) to describe the real-time dynamics of an adsorbate-surface model system exposed to ultrafast laser pulses. For a finite number of electronic orbitals, the system is solved exactly and…
Ehrenfest, Born-Oppenheimer, Langevin and Smoluchowski dynamics are shown to be accurate approximations of time-independent Schr\"odinger observables for a molecular system avoiding caustics, in the limit of large ratio of nuclei and…
This paper is concerned with geometric exponential energy-preserving integrators for solving charged-particle dynamics in a magnetic field from normal to strong regimes. We firstly formulate the scheme of the methods for the system in a…
Coherent or exact equations of motion for a post-Newtonian Lagrangian formalism are the Euler-Lagrange equations without any terms truncated. They naturally conserve energy {and} angular momentum. Doubling the phase-space variables of…
Dynamic simulation of elastic bodies is a longstanding task in engineering and computer graphics. In graphics, numerical integrators like implicit Euler and BDF2 are preferred due to their stability at large time steps, but they tend to…
We consider an Ehrenfest approximation for a particle in a double-well potential in the presence of an external environment schematized as a finite resource heat bath. This allows us to explore how the limitations in the applicability of…
An energetically balanced, implicit integrator for non-hydrostatic vertical atmospheric dynamics on the sphere is presented. The integrator allows for the exact balance of energy exchanges in space and time for vertical atmospheric motions…
We propose mixed quantum-classical equations of motion that unify electronic coherence and phase evolution simultaneously within the exact factorization framework. Our derivation shows that incorporating the second-order electron-nuclear…
Adequate simulation of non-adiabatic dynamics through conical intersection requires account for a non-trivial geometric phase (GP) emerging in electronic and nuclear wave-functions in the adiabatic representation. Popular mixed…
We present a novel quantum-classical approach to non-adiabatic dynamics, deduced from the coupled electronic and nuclear equations in the framework of the exact factorization of the electron-nuclear wave function. The method is based on the…