Related papers: Analytic gradients for spin multiplets in natural …
The structure of the $^9$Be low-lying spectrum is studied within the cluster model $\alpha+\alpha+n$. In the model the total orbital momentum is fixed for each energy level. Thus each level is determined as a member of the spin-flip doublet…
We search for approximate, but analytic solutions of the pairing problem for one pair of nucleons in many levels of a potential well. For the collective energy a general formula, independent of the details of the single particle spectrum,…
Multiple pendulums are investigated numerically and analytically to clarify the nonuniformity of average kinetic energies of particles. The nonuniformity is attributed to the system having constraints and it is consistent with the…
A new scheme for numerical integration of motion for classical systems composed of rigid polyatomic molecules is proposed. The scheme is based on a matrix representation of the rotational degrees of freedom. The equations of motion are…
All relativistic corrections to the Scr{\"o}dinger equation which determine the interlink between spin and orbit of moving particles, are directly calculated from the Dirac equation using the spin invariant operators. It is shown that among…
An analytical approximation to periodic orbits in the circular restricted three-body problem is provided. The formulation given in this work is based in calculations known from classical mechanics, but with the addition of the necessary…
The gradient descent method aims at finding local minima of a given multivariate function by moving along the direction of its gradient, and hence, the algorithm typically involves computing all partial derivatives of a given function,…
Many molecular magnetic clusters, such as single-molecule magnets, are characterized by spin ground states with defined total spin S exhibiting zero-field-splittings. In this work, the spectroscopic intensities of the transitions within the…
We show that dynamic spin polarization by collective raising and lowering operators can drive a spin ensemble from arbitrary initial state to many-body singlets, the zero-collective-spin states with large scale entanglement. For an ensemble…
We have incorporated the spin-dependent nucleon-nucleon cross sections into a Boltzmann-Uehling-Uhlenbeck transport model for the first time, using the spin-singlet and spin-triplet nucleon-nucleon elastic scattering cross sections…
We prove a new general multiplicity estimate applicable to sets of functions without any assumption on algebraic independence. The multiplicity estimates are commonly used in determining measures of algebraic independence of values of…
In this paper a set of analytic formulae are presented with which the partial derivatives of the flux obscuration function can be evaluated -- for planetary transits and eclipsing binaries -- under the assumption of quadratic limb…
Singlet fission, which has applications in areas ranging form solar energy to quantum information, relies critically on transitions within a multi-spin manifold. These transitions are driven by fluctuations in the spin-spin exchange…
An infinite square well with a discontinuous step is one of the simplest systems to exhibit non-Newtonian ray-splitting periodic orbits in the semiclassical limit. This system is analyzed using both time-independent perturbation theory (PT)…
Using the method of breaking of circular symmetry and of subsequent symmetry restoration via projection techiques, we present calculations for the ground-state energies and excitation spectra of N-electron parabolic quantum dots in strong…
The performance of basis sets made of numerical atomic orbitals is explored in density-functional calculations of solids and molecules. With the aim of optimizing basis quality while maintaining strict localization of the orbitals, as…
Basis sets of atomic orbitals are very efficient for density functional calculations but lack a systematic variational convergence. We present a variational method to optimize numerical atomic orbitals using a single parameter to control…
This work is a sequel to our work "The Spin Density Matrix I: General Theory and Exact Master Equations" (eprint arXiv:0708.0644 [cond-mat]). Here we compare pure- and pseudo-spin dynamics using as an example a system of two quantum dots, a…
Magnetism and spin physics are true quantum mechanical effects and their description usually requires multi reference methods and is often hidden in the standard description of molecules in quantum chemistry. In this work we present a…
We derive analytical $\chi\ll1$ approximations for spin-dependent quantum radiation reaction for locally constant and locally monochromatic fields. We show how to factor out fast spin oscillations and obtain the degree of polarization in…