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We study the valence electron of an alkaline atom or a general charged particle with arbitrary spin and with magnetic moment moving in a rotating magnetic field. By using a time-dependent unitary transformation, the Schr\"odinger equation…
A novel orthogonalization-free method together with two specific algorithms are proposed to solve extreme eigenvalue problems. On top of gradient-based algorithms, the proposed algorithms modify the multi-column gradient such that earlier…
We propose a first-principles time-dependent density functional theoretical (TDDFT) approach in momentum (P) space for quantitative study of electron transport in molecular devices under arbitrary biases. In this approach, the basic…
A quasi-distribution function in phase space (based on Wigner functions) is used to write down the quantum version of Boltzmann equation (Wigner-Boltzmann transport equation). The relaxation time approximation is show to be a good approach…
The phenomenological textbook equations for the charge and heat transport are extensively used in a number of fields ranging from semiconductor devices to thermoelectricity. We provide a rigorous derivation of transport equations by solving…
We propose a Schr\"odinger equation of arbitrary order for modeling charge transport in semiconductors operating in the ballistic regime. This formulation incorporates non-parabolic effects through the Kane dispersion relation, thereby…
The transport of charged particles or photons in a scattering medium can be modelled with a Boltzmann equation. The mathematical treatment for scattering in such scenarios is often simplified if evaluated in a frame where the scattering…
Ehrenfest dynamics is a useful approximation for ab initio mixed quantum-classical molecular dynamics that can treat electronically nonadiabatic effects. Although a severe approximation to the exact solution of the molecular time-dependent…
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…
Couplings of a system to other degrees of freedom (that is, environmental degrees of freedom) lead to energy dissipation when the number of environmental degrees of freedom is large enough. Here we discuss quantal treatments for such energy…
A new "on the fly" method to perform Born-Oppenheimer ab initio molecular dynamics (AIMD) is presented. Inspired by Ehrenfest dynamics in time-dependent density functional theory, the electronic orbitals are evolved by a Schroedinger-like…
We illustrate through explicit numerical calculations how the Born-rule probability densities of non-relativistic quantum mechanics emerge naturally from the particle dynamics of de Broglie-Bohm pilot-wave theory. The time evolution of a…
The local conservation of a physical quantity whose distribution changes with time is mathematically described by the continuity equation. The corresponding time parameter, however, is defined with respect to an idealized classical clock.…
We present a universal expression for the electronic friction as felt by a set of classical nuclear degrees of freedom (DoF's) coupled to a manifold of quantum electronic DoF's; no assumptions are made regarding the nature of the electronic…
The direct solution of the many-particle Schr\"odinger equation is computationally inaccessible for more than very few electrons. In order to surpass this limitation, one of the authors [X. Oriols, Phys. Rev. Lett. 2007, 98 (066803)] has…
The study of strongly out-of-equilibrium states and their time evolution towards thermalization is critical to the understanding of an ever widening range of physical processes. We present a numerical method that for the first time allows…
It is shown that the Schrodinger equation can be cast in the form of two coupled real conservation equations, in Euclidean spacetime in the free case and in a five-dimensional Eisenhart geometry in the presence of an external potential.…
Describing the dynamics of nuclei in molecules requires a potential energy surface, which is traditionally provided by the Born-Oppenheimer or adiabatic approximation. However, we also need to assign masses to the nuclei. There, the…
The interaction between electronic and vibrational degrees of freedom is an important mechanism in nonequilibrium charge transport through molecular nanojunctions. While adiabatic polaron-type coupling has been studied in great detail, new…
Quantum stochastic methods based on effective wave functions form a framework for investigating the generally non-Markovian dynamics of a quantum-mechanical system coupled to a bath. They promise to be computationally superior to the…