Search results for "Matrix"
showing 10 items of 3205 documents
First Observation of D+→ημ+νμ and Measurement of Its Decay Dynamics
2020
By analyzing a data sample corresponding to an integrated luminosity of 2.93 fb^{-1} collected at a center-of-mass energy of 3.773 GeV with the BESIII detector, we measure for the first time the absolute branching fraction of the D^{+}→ημ^{+}ν_{μ} decay to be B_{D^{+}→ημ^{+}ν_{μ}}=(10.4±1.0_{stat}±0.5_{syst})×10^{-4}. Using the world averaged value of B_{D^{+}→ηe^{+}ν_{e}}, the ratio of the two branching fractions is determined to be B_{D^{+}→ημ^{+}ν_{μ}}/B_{D^{+}→ηe^{+}ν_{e}}=0.91±0.13_{(stat+syst)}, which agrees with the theoretical expectation of lepton flavor universality within uncertainty. By studying the differential decay rates in five four-momentum transfer intervals, we obtain th…
Measurement of the Dynamics of the Decays Ds+→η(′)e+νe
2019
PubMed ID: 30978074
Diverging exchange force and form of the exact density matrix functional
2019
For translationally invariant one-band lattice models, we exploit the ab initio knowledge of the natural orbitals to simplify reduced density matrix functional theory (RDMFT). Striking underlying features are discovered: First, within each symmetry sector, the interaction functional $\mathcal{F}$ depends only on the natural occupation numbers $\bf{n}$. The respective sets $\mathcal{P}^1_N$ and $\mathcal{E}^1_N$ of pure and ensemble $N$-representable one-matrices coincide. Second, and most importantly, the exact functional is strongly shaped by the geometry of the polytope $\mathcal{E}^1_N \equiv \mathcal{P}^1_N $, described by linear constraints $D^{(j)}(\bf{n})\geq 0$. For smaller systems,…
Bose-Einstein condensation of two interacting particles
2000
We investigate the notion of Bose-Einstein condensation of interacting particles. The definition of the condensate is based on the existence of the dominant eigenvalue of the single-particle density matrix. The statistical properties and the characteristic temperature are computed exactly in the soluble models of two interacting atoms.
The Negele-Vautherin density matrix expansion applied to the Gogny force
2010
We use the Negele-Vautherin density matrix expansion to derive a quasi-local density functional for the description of systems of fermions interacting with short-ranged interactions composed of arbitrary finite-range central, spin-orbit, and tensor components. Terms that are absent in the original Negele-Vautherin approach owing to the angle averaging of the density matrix are fixed by employing a gauge invariance condition. We obtain the Kohn-Sham interaction energies in all spin-isospin channels, including the exchange terms, expressed as functions of the local densities and their derivatives up to second (next to leading) order. We illustrate the method by determining the coupling consta…
Natural occupation numbers: When do they vanish?
2013
The non-vanishing of the natural orbital occupation numbers of the one-particle density matrix of many-body systems has important consequences for the existence of a density matrix-potential mapping for nonlocal potentials in reduced density matrix functional theory and for the validity of the extended Koopmans' Theorem. On the basis of Weyl's theorem we give a connection between the differentiability properties of the ground state wave function and the rate at which the natural occupations approach zero when ordered as a descending series. We show, in particular, that the presence of a Coulomb cusp in the wave function leads, in general, to a power law decay of the natural occupations, whe…
Relativistic corrections to electrical first-order properties using direct perturbation theory.
2008
Direct perturbation theory (DPT) is applied to compute relativistic corrections to electrical properties such as dipole moment, quadrupole moment, and electric-field gradient. The corrections are obtained as second derivatives of the energy and are given via method-independent expressions that involve the first derivative of the density matrix with respect to the relativistic perturbation as well as property integrals with additional momentum operators. Computational results obtained using Hartree-Fock (HF), second-order Moller-Plesset (MP2) perturbation theory, and the coupled-cluster singles and doubles approach augmented by a perturbative treatment of triple excitations are presented for…
Multicomponent density-functional theory for time-dependent systems
2007
We derive the basic formalism of density functional theory for time-dependent electron-nuclear systems. The basic variables of this theory are the electron density in body-fixed frame coordinates and the diagonal of the nuclear N-body density matrix. The body-fixed frame transformation is carried out in order to achieve an electron density that reflects the internal symmetry of the system. We discuss the implications of this body-fixed frame transformation and establish a Runge-Gross-type theorem and derive Kohn-Sham equations for the electrons and nuclei. We illustrate the formalism by performing calculations on a one-dimensional diatomic molecule for which the many-body Schrodinger equati…
Dynamical mean-field theory calculation with the dynamical density-matrix renormalization group
2006
Abstract We study the Hubbard model at half band-filling on a Bethe lattice with infinite coordination number at zero temperature. We use the dynamical mean-field theory (DMFT) mapping to a single-impurity Anderson model with a bath whose properties have to be determined self-consistently. For a controlled and systematic implementation of the self-consistency scheme we use the fixed-energy approach to the DMFT. Using the dynamical density–matrix renormalization group method (DDMRG) we calculate the density of states (DOS) with a resolution ranging from 3% of the bare bandwidth W = 4 t at high energies to 0.01% for the quasi-particle peak. The DDMRG resolution and accuracy for the DOS is sup…
Continuity equation and local gauge invariance for the N3LO nuclear energy density functionals
2011
Background: The next-to-next-to-next-to-leading order (N3LO) nuclear energy density functional extends the standard Skyrme functional with new terms depending on higher-order derivatives of densities, introduced to gain better precision in the nuclear many-body calculations. A thorough study of the transformation properties of the functional with respect to different symmetries is required, as a step preliminary to the adjustment of the coupling constants. Purpose: Determine to which extent the presence of higher-order derivatives in the functional can be compatible with the continuity equation. In particular, to study the relations between the validity of the continuity equation and invari…