Related papers: Practical Phase-Space Electronic Hamiltonians for …
In this paper we discuss the electronic kinetic energy in the ground state of the Holstein Hamiltonian in one space dimension using the Global-Local variational method together with perturbation theory at weak and strong coupling. The…
A unitary transformation $\Ps [E]=\exp (i\O [E]/g) F[E]$ is used to simplify the Gauss law constraint of non-abelian gauge theories in the electric field representation. This leads to an unexpected geometrization because $\o^a_i\equiv -\d\O…
In these notes we construct the momentum-space potentials from configuration-space using for the Fourier-transformation the Gaussian-Expansion-Method (GEM). This has the advantage that the Fourier-Bessel integrals can be performed…
We study the translational motions of homonuclear diatomic molecules prepared in their ${}^3\Sigma$ electronic states, deeply bound vibrational states, and rotational states of well-defined parity. The trapping potential arises due to the…
We investigate the characteristic effects of nuclear motion on attosecond transient absorption spectra in molecules by calculating the spectrum for different model systems. Two models of the hydrogen molecular ion are considered: one where…
The Hamiltonian dynamics associated to classical, planar, Heisenberg XY models is investigated for two- and three-dimensional lattices. Besides the conventional signatures of phase transitions, here obtained through time averages of…
Direct dynamics methods using Gaussian wavepackets have to rely only on local properties, such as gradients and hessians at the center of the wavepacket, so as to be compatible with the usual quantum chemistry methods. Matrix elements of…
Machine-learning potentials are usually trained on the ground-state, Born-Oppenheimer energy surface, which depends exclusively on the atomic positions and not on the simulation temperature. This disregards the effect of thermally-excited…
The geometric phase effect arises from the dependence on the nuclear coordinates in the electronic Hamiltonian, leading to sign changes of the electronic wave functions upon traversal of certain paths in nuclear configuration space. The…
We study a class of interacting, harmonically trapped boson systems at angular momentum L. The Hamiltonian leaves a L-dimensional subspace invariant, and this permits an explicit solution of several eigenstates and energies for a wide class…
We propose an alternative to the usual time--independent Born--Oppenheimer approximation that is specifically designed to describe molecules with non--symmetrical hydrogen bonds. In our approach, the masses of the hydrogen nuclei are scaled…
The motion of a system of particles under electromagnetic interaction is considered. Under the assumption that the force acting on an electric charge is given by the sum of the electromagnetic fields produced by any other charged particles…
We consider electrodynamics on a noncommutative spacetime using the enveloping algebra approach and perform a non-relativistic expansion of the effective action. We obtain the Hamiltonian for quantum mechanics formulated on a canonical…
Traditional computational methods for studying quantum many-body systems are "forward methods," which take quantum models, i.e., Hamiltonians, as input and produce ground states as output. However, such forward methods often limit one's…
Following a previous proposition of quaternity spacetime for electronic orbitals in neon shell, this paper describes the geometrical course each electron takes as it oscillates harmonically within a certain quaternity space dimension and…
General positivity constraints linking various powers of observables in energy eigenstates can be used to sharply locate acceptable regions for the energy eigenvalues, provided that efficient recursive methods are available to calculate the…
A numerical experiment of ideal stochastic motion of a particle subject to conservative forces and Gaussian noise reveals that the path probability depends exponentially on action. This distribution implies a fundamental principle…
We discuss the usefulness of Born-Oppenheimer potential surfaces for nuclear dynamics for molecules strongly coupled to metal surfaces. A simple model demonstrating the construction of such surface for a molecular junction is discussed.
Quantum simulation of the electronic structure problem is one of the most researched applications of quantum computing. The majority of quantum algorithms for this problem encode the wavefunction using $N$ Gaussian orbitals, leading to…
The standard approach to nuclear physics encodes phase shift information in an NN potential, then decodes that information in forming an effective interaction, appropriate to a low-momentum Hilbert space. Here we show that it is instead…