Related papers: Quantum Simulation of non-Born-Oppenheimer dynamic…
In this contribution a path integral approach for the quantum motion on three-dimensional spaces according to Koenigs, for short``Koenigs-Spaces'', is discussed. Their construction is simple: One takes a Hamiltonian from three-dimensional…
We introduce an efficient scheme for the molecular dynamics of electronic systems by means of quantum Monte Carlo. The evaluation of the (Born-Oppenheimer) forces acting on the ionic positions is achieved by two main ingredients: i) the…
The formulation of noncommutative quantum mechanics as a quantum system represented in the space of Hilbert-Schmidt operators is used to systematically derive, using the standard time slicing procedure, the path integral action for a…
Non commutative quantum mechanics can be viewed as a quantum system represented in the space of Hilbert-Schmidt operators acting on non commutative configuration space. Taking this as departure point, we formulate a coherent state approach…
The results of analytical approximations and extensive calculations based on a path integral Monte Carlo (PIMC) scheme are presented. A new (direct) PIMC method allows for a correct determination of thermodynamic properties such as energy…
Potential energy surfaces of the hydrogen molecular ion H$_2^+$ in the Born-Oppenheimer approximation are computed by means of the Riccati-Pad\'e method (RPM). The convergence properties of the method are analyzed for different states. The…
The complex-scaling method can be used to calculate molecular resonances within the Born-Oppenheimer approximation, assuming the electronic coordinates are dilated independently of the nuclear coordinates. With this method, one will…
We show that following the standard mantra of quantum chemistry and diagonalizing the Born-Oppenheimer (BO) Hamiltonian $\hat H_{\rm BO}(\bm R)$ is not the optimal means to construct potential energy surfaces. A better approach is to…
The energy spectrum, atom-dimer scattering length, and atom-trimer scattering length for systems of three and four ultracold atoms with $\delta$-function interactions in one dimension are presented as a function of the relative mass ratio…
Recent experiments in hybrid-quantum systems facilitate the potential realization of one of the most fundamental interacting Hamiltonian-Reservoir system, namely, the single-site Bose-Hubbard model coupled to two reservoirs at different…
In this paper, we consider the time-dependent Born-Oppenheimer approximation (BOA) of a classical quantum molecule involving a possibly large number of nuclei and electrons, described by a Schr\"odinger equation. In the spirit of Born and…
We study non--adiabatic transitions in scattering theory for the time dependent molecular Schroedinger equation in the Born--Oppenheimer limit. We assume the electron Hamiltonian has finitely many levels and consider the propagation of…
In this contribution I discuss a path integral approach for the quantum motion on two-dimensional spaces according to Koenigs, for short ``Koenigs-Spaces''. Their construction is simple: One takes a Hamiltonian from two-dimensional flat…
A kink-based path integral method, previously applied to atomic systems, is modified and used to study molecular systems. The method allows the simultaneous evolution of atomic and electronic degrees of freedom. Results for CH$_4 $, NH$_3…
Work statistics characterizes important features of a non-equilibrium thermodynamic process. But the calculation of the work statistics in an arbitrary non-equilibrium process is usually a cumbersome task. In this work, we study the work…
I propose a path integral description of the Su-Schrieffer-Heeger Hamiltonian, both in one and two dimensions, after mapping the real space model onto the time scale. While the lattice degrees of freedom are classical functions of time and…
We present the first nonperturbative numerical calculations of the nonrelativistic hydrogen spectrum as predicted by first-quantized electrodynamics with nonlinear Maxwell-Born-Infeld field equations. We also show rigorous upper and lower…
Most recently, the path integral molecular dynamics has been successfully used to consider the thermodynamics of single-component identical bosons and fermions. In this work, the path integral molecular dynamics is developed to simulate the…
While historically many quantum mechanical simulations of molecular dynamics have relied on the Born-Oppenheimer approximation to separate electronic and nuclear behavior, recently a lot of interest has arisen towards quantum effects in…
In this paper we construct a path integral formulation of quantum mechanics on noncommutative phase-space. We first map the system to an equivalent system on the noncommutative plane. Then by applying the formalism of representing a quantum…