We report on detailed studies of electronic and nuclear spin states in the diamond-nitrogen-vacancy (NV) center under weak transverse magnetic fields. We numerically predict and experimentally verify a previously unobserved NV hyperfine level anticrossing (LAC) occurring at bias fields of tens of gauss—two orders of magnitude lower than previously reported LACs at ∼500 and ∼1000 G axial magneti...

We examine the localization properties of the 2D Anderson Hamiltonian with oo-diagonal disorder. Investigating the behavior of the participation numbers of eigenstates as well as studying their multifractal properties, we nd states in the center of the band which show critical behavior up to the system size N = 200200 considered. This result is connrmed by an independent analysis of the localiz...

In this Review we show several mathematical techniques that can be used in molecular calculations using Slater orbitals, like the transformation of the Hamiltonian, derivatives of spherical harmonics with respect to the angles, and angular transformations. We treat several kinds of integrals in detail: the exchange, Coulomb and hybrid repulsion and exchange correlated integrals, and the three-c...

By solving the surface plasmon SP eigenproblem, a scaling theory is developed for the electromagnetic response of semicontinuous metal films. It is shown that short-range correlations in the governing Kirchhoff Hamiltonian result in delocalization of the SP eigenmodes in the center of the spectrum. The subset of those modes has a zero measure so that their relative weight in the spectrum become...

An operator formalism is developed for a description of charged electron-hole complexes in magnetic fields. A unitary transformation of the Hamiltonian that allows one to separate partially the center-of-mass and internal motions is proposed. We study an operator algebra that leads to the appearance of effective particles, electrons, and holes with modified interparticle interactions, and their...

Using the Hamiltonian of Caldirola [Nuovo Cimento 18, 393 (1941)] and Kanai [Prog. Theor. Phys. 3, 440 (1948)], we study the time evolution of the wave function of a particle whose classical motion is governed by the Langevin equation mẍ + ηẋ = F (t). We show in particular that if the initial wave function is Gaussian, then (i) it remains Gaussian for all times, (ii) its width grows, approachin...

In the 2-dimensional anisotropic classical Heisenberg model with XY-symmetry there are nonplanar vortices which exhibit a localized structure of the z-components of the spins around the vortex center. We study how thermal noise induces a transition of this structure from one polarization to the opposite one. We describe the vortex core by a discrete Hamiltonian and consider a stationary solutio...

We consider a system of a nucleus with an electron together with the quantized electromagnetic field. Instead of fixing the nucleus, the system is confined by its center of mass. This model is used in theoretical physics to explain the Lamb-Dicke and the Mössbauer effects (see [CTDRG]). When an ultraviolet cut-off is imposed we initiate the spectral analysis of the Hamiltonian describing the sy...

The Controlled Molecule Imaging group (CMI) at the Center for Free Electron Laser Science (CFEL) has developed the CMIstark software to calculate, view, and analyze the energy levels of adiabatic Stark energy curves of linear, symmetric top and asymmetric top molecules. The program exploits the symmetry of the Hamiltonian to generate fully labeled adiabatic Stark energy curves. CMIstark iswritt...

In this paper we prove that any degree d deformation of a generic logarithmic polynomial differential equation with a persistent center must be logarithmic again. This is a generalization of Ilyashenko’s result on Hamiltonian differential equations. The main tools are PicardLefschetz theory of a polynomial with complex coefficients in two variables, specially the Gusein-Zade/A’Campo’s theorem o...