Related papers: Extended Born-Oppenheimer equation for tri-state s…
We investigate the evolution of an electron undergoing coherent tunneling via adiabatic passage (CTAP) using the solution of the one-dimensional Schroedinger equation in both space and time for a triple well potential. We find the…
By applying the Born-Huang expansion, originally developed for coupled nucleus-electron systems, to the full nucleus-electron-photon Hamiltonian of non-relativistic quantum electrodynamics (QED) in the long-wavelength approximation, we…
For a particular case of three-body scattering in 2 dimensions, we demonstrate analytically that the behaviour of the adiabatic potential is different from that of the hyperspherical coupling matrix elements, thereby leading to a phase…
We discuss two complementary problems: adiabatic loading of one-dimensional bosons into an optical lattice and merging two one-dimensional Bose systems. Both problems can be mapped to the sine-Gordon model. This mapping allows us to find…
The exact solutions of the $D^{(1)}_3$ model (or the $so(6)$ quantum spin chain) with either periodic or general integrable open boundary conditions are obtained by using the off-diagonal Bethe Ansatz. From the fusion, the complete operator…
We investigate quantum phase transitions in the extended periodic Anderson model, which includes electron correlations within and between itinerant and localized bands. We calculate zero and finite temperature properties of the system using…
We consider ultralong-range polyatomic Rydberg molecules formed by combining a Rydberg cesium atom and a ground-state RbCs molecule. We explore the regime where the charge-dipole interaction due to the Rydberg electron with the diatomic…
We study the validity of the Born-Oppenheimer approximation in chaotic dynamics. Using numerical solutions of autonomous Fermi accelerators, we show that the general adiabatic conditions can be interpreted as the narrowness of the chaotic…
We apply the algebraic Bethe ansatz technique to the nuclear pairing problem with orbit dependent coupling constants and degenerate single particle energy levels. We find the exact energies and eigenstates. We show that for a given shell,…
Mixed quantum-classical mechanics descriptions are critical to modeling coupled electron-nuclear dynamics, i.e. non-adiabatic molecular dynamics, relevant to photochemical and photophysical processes. We argue that, for polyatomic…
An accurate theory describing adiabatic following of the dark, nonabsorbing state in the three-level system is developed. An analytical solution for the wave function of the particle experiencing Raman excitation is found as an expansion in…
We study the strong coupling limit of a quadratic-nonlinear Landau-Zener problem for coherent photo- and magneto-association of cold atoms taking into account the atom-atom, atom-molecule, and molecule-molecule elastic scattering. Using an…
We consider non-adiabatic coupling in the "trilobite"-like long-range Rydberg molecules created by perturbing degenerate high-$\ell$ Rydberg states with a ground-state atom. Due to the flexibility granted by the high Rydberg level density,…
Coupled elliptic quantum dots with different aspect ratios containing up to two electrons are studied using a model confinement potential in the presence of magnetic fields. Single and two particle Schroedinger equations are solved using…
The so-called Born-Huang ansatz is a fundamental tool in the context of ab-initio molecular dynamics, viz., it allows to effectively separate fast and slow degrees of freedom and thus treating electrons and nuclei at different mathematical…
The interaction between electronic and vibrational degrees of freedom in single-molecule junctions may result from the dependence of the electronic energies or the electronic states of the molecular bridge on the nuclear displacement. The…
Inspired from Sutherland's work [Phys. Rev. Lett. {\bf 74}, 816 (1995)] on detecting bound spin waves, we propose that bound electron states can be detected from the dependence of interacting electron systems to the Aharonov-Bohm flux in…
Ab initio modeling of conical intersection dynamics is crucial for various photochemical, photophysical, and biological processes. However, adiabatic electronic states obtained from electronic structure computations involve random phases,…
It is shown that the adiabatic Born-Oppenheimer expansion does not satisfy the necessary condition for the applicability of perturbation theory. A simple example of an exact solution of a problem that can not be obtained from the…
An exactly solvable position-dependent mass Schr\"odinger equation in two dimensions, depicting a particle moving in a semi-infinite layer, is re-examined in the light of recent theories describing superintegrable two-dimensional systems…