Spin-½

About: Spin-½ is a research topic. Over the lifetime, 40423 publications have been published within this topic receiving 796639 citations.

Magnetic Effects and the Hartree-Fock Equation

Abstract: The Hartree-Fock equations state that each electron in an atom or molecular system should move in a different potential. In some cases, particularly magnetic cases, this leads to important consequences, since electrons with opposite spins move in different potentials. In particular, in an antiferromagnetic substance, electrons of + and - spin have different potentials; and for an electron of + spin, for instance, the potential energy is lower in those atoms whose spins are pointed in the + direction than in those with the opposite spin. This results in a periodic perturbation of potential, with periodicity twice the atomic periodicity, and leads to a splitting of each energy band in half, with a gap in the middle. In a case where the energy band was half full, resulting in a conductor: when we disregard this effect, the resulting half-band will be just filled when we consider it; this may explain the insulating nature of some antiferromagnetics. A similar argument applied to a diatomic molecule like ${\mathrm{H}}_{2}$ can result in two alternative types of solutions of the Hartree-Fock equations: one leading to atomic orbitals, the other to molecular orbitals. The solution with atomic orbitals shows an analogy to the antiferromagnetic problem; that with ordinary molecular orbitals shows an analogy to the band theory of a non-magnetic conductor.

Analytic energy derivatives for ionized states described by the equation‐of‐motion coupled cluster method

Abstract: The theory for analytic energy derivatives of excited electronic states described by the equation‐of‐motion coupled cluster (EOM‐CC) method has been generalized to treat cases in which reference and final states differ in the number of electrons. While this work specializes to the sector of Fock space that corresponds to ionization of the reference, the approach can be trivially modified for electron attached final states. Unlike traditional coupled cluster methods that are based on single determinant reference functions, several electronic configurations are treated in a balanced way by EOM‐CC. Therefore, this quantum chemical approach is appropriate for problems that involve important nondynamic electron correlation effects. Furthermore, a fully spin adapted treatment of doublet electronic states is guaranteed when a spin restricted closed shell reference state is used—a desirable feature that is not easily achieved in standard coupled cluster approaches. The efficient implementation of analytic gradien...

Quantum metrology from a quantum information science perspective

Abstract: We summarize important recent advances in quantum metrology, in connection to experiments in cold gases, trapped cold atoms and photons. First we review simple metrological setups, such as quantum metrology with spin squeezed states, with Greenberger–Horne–Zeilinger states, Dicke states and singlet states. We calculate the highest precision achievable in these schemes. Then, we present the fundamental notions of quantum metrology, such as shot-noise scaling, Heisenberg scaling, the quantum Fisher information and the Cramer–Rao bound. Using these, we demonstrate that entanglement is needed to surpass the shot-noise scaling in very general metrological tasks with a linear interferometer. We discuss some applications of the quantum Fisher information, such as how it can be used to obtain a criterion for a quantum state to be a macroscopic superposition. We show how it is related to the speed of a quantum evolution, and how it appears in the theory of the quantum Zeno effect. Finally, we explain how uncorrelated noise limits the highest achievable precision in very general metrological tasks.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to '50 years of Bell's theorem'.

Excitation of the Hydrogen 21-CM Line

Abstract: The importance of spin temperature for 21-cm line studies is reviewed, and four mechanisms which affect it are studied. Two of the mechanisms, collisions with free electrons and interactions with light, are studied here in detail for the first time. The results are summarized in Table II of Section VI, in the form of certain efficiencies which can be used with (15) to calculate the spin temperature. In Section VI the results are applied to a variety of astronomical situations, and it is shown that in the usual situation collisions with H atoms are very effective in establishing the spin temperature equal to the kinetic temperature. Under conditions of low-density and/or high-radiation intensity, however, important deviations from the usual are noted. The significance of such deviations for absorption studies of radio sources and the galactic halo is discussed. In Section VII the deuterium line at 91.6 cm is considered in like fashion. It is shown that for deuterium also, the spin temperature probably is close to the kinetic temperature.