Related papers: Born-Oppenheimer Approximation near Level Crossing
The standard Born Oppenheimer theory does not give an accurate description of the wave function near points of level crossing. We give such a description near an isotropic conic crossing, for energies close to the crossing energy. This…
We explain why the conventional argument for deriving the time-dependent Born-Oppenheimer approximation is incomplete and review recent mathematical results, which clarify the situation and at the same time provide a systematic scheme for…
We investigate the structure of a prototypical two-state conical intersection (BeH$_2$) using a phase space electronic Hamiltonian $\hat{H}_{PS}(\bR,\bP)$ that goes beyond the Born-Oppenheimer framework. By parameterizing the electronic…
The level crossing problem is neatly formulated by the second quantized formulation, which exhibits a hidden local gauge symmetry. The analysis of geometric phases is reduced to a simple diagonalization of the Hamiltonian. If one…
By using a second quantized formulation of level crossing, which does not assume adiabatic approximation, a convenient formula for geometric terms including off-diagonal terms is derived. The analysis of geometric phases is reduced to a…
We apply the Born--Oppenheimer approximation to a harmonic diatomic molecule with one electron. We compare the exact and approximate results not only for the internal degrees of freedom but also for the motion of the center of mass. We…
We discuss a simple singular system in two dimension, two heavy particles interacting with a light particle via an attractive contact interaction. Although intuitively clear the actual application of the Born-Oppenheimer approximation to…
We study the existence and location of the resonances of a $2\times 2$ semiclassical system of coupled Schr\"odinger operators, in the case where the two electronic levels cross at some point, and one of them is bonding, while the other one…
Here I present a summarised description of the general behavior of waves near turning points. I show that when asymptotic matching to a prescribed incident wavefield is performed, the solution changes from being the Airy function to being…
The Born-Infeld equation in the plane is usefully captured in complex language. The general exact solution can be written as a combination of holomorphic and anti-holomorphic functions. However, this solution only expresses the potential in…
For two states of opposite parity that cross as a function of an external magnetic field, the addition of an electric field will break the symmetry and induce an avoided crossing. A suitable arrangement of fields may be used to create a…
A detailed formulation of the relativistic plane-wave Born approximation for inelastic collisions of charged particles with free atoms and positive ions is presented. The wave functions of the target atom or ion are calculated from a…
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.
We discuss a simple singular system in one dimension, two heavy particles interacting with a light particle via an attractive contact interaction. It is natural to apply Born-Oppenheimer approximation to this problem. We present a detailed…
A cosmological model connecting the evolution of universe with a sequence of topology changes described by a collection of specific graph cobordisms, is constructed. It is shown that an adequate topological field theory (of BF-type) can be…
Asymptotic levels of the A $^1\Sigma_u^+$ state of the two isotopomers $^{39}{\rm K}_2$ and $^{39}{\rm K}^{41}{\rm K}$ up to the dissociation limit are investigated with a Doppler-free high resolution laser-spectroscopic experiment in a…
We consider a 1D $2\times 2$ matrix-valued operator \eqref{System0} with two semiclassical Schr\"odinger operators on the diagonal entries and small interactions on the off-diagonal ones. When the two potentials cross at a turning point…
The global many-electron wave function overlap matrix accounts for all effects beyond the Born-Oppenheimer approximation in the discrete variable local diabatic representation, a numerically exact framework for modeling nonadiabatic conical…
We analyze the quantum states of two atoms in a combined harmonic oscillator and periodic lattice trap in one spatial dimension. In the case of tight-binding and only nearest neighbor tunneling, the equations of motion are conveniently…
We study the properties of operators in a unitary conformal field theory whose scaling dimensions approach each other for some values of the parameters and satisfy von Neumann-Wigner non-crossing rule. We argue that the scaling dimensions…