Search results for "Density matrix"
showing 10 items of 106 documents
E0 suppression in pion photoproduction on 13C
1990
Abstract Recently measured anomalously low cross sections for 13 C(γ, π − ) 13 N at low energy and θ π lab = 90° 0761 have been analyzed in a DWIA calculation. It has been found that the EO contribution alone is able to explain the data, so that the M1 cross section is expected to vanish. Using constraints from recent magnetic electron scattering, an explanation is possible by assuming a significantly lower reduced density matrix element for spin-flip isovector transitions with angular momentum L = 2 than predicted by Cohen and Kurath.
State-of-the-art density matrix renormalization group and coupled cluster theory studies of the nitrogen binding curve.
2004
We study the nitrogen binding curve with the density matrix renormalization group (DMRG) and single-reference and multireference coupled cluster (CC) theory. Our DMRG calculations use up to 4000 states and our single-reference CC calculations include up to full connected hextuple excitations. Using the DMRG, we compute an all-electron benchmark nitrogen binding curve, at the polarized, valence double-zeta level (28 basis functions), with an estimated accuracy of 0.03mE_h. We also assess the performance of more approximate DMRG and CC theories across the nitrogen curve. We provide an analysis of the relative strengths and merits of the DMRG and CC theory under different correlation condition…
Phononic heat transport in the transient regime: An analytic solution
2016
We investigate the time-resolved quantum transport properties of phonons in arbitrary harmonic systems connected to phonon baths at different temperatures. We obtain a closed analytic expression of the time-dependent one-particle reduced density matrix by explicitly solving the equations of motion for the nonequilibrium Green's function. This is achieved through a well-controlled approximation of the frequency-dependent bath self-energy. Our result allows for exploring transient oscillations and relaxation times of local heat currents, and correctly reduces to an earlier known result in the steady-state limit. We apply the formalism to atomic chains, and benchmark the validity of the approx…
A Wigner molecule at extremely low densities: a numerically exact study
2019
In this work we investigate Wigner localization at very low densities by means of the exact diagonalization of the Hamiltonian. This yields numerically exact results. In particular, we study a quasi-one-dimensional system of two electrons that are confined to a ring by three-dimensional gaussians placed along the ring perimeter. To characterize the Wigner localization we study several appropriate observables, namely the two-body reduced density matrix, the localization tensor and the particle-hole entropy. We show that the localization tensor is the most promising quantity to study Wigner localization since it accurately captures the transition from the delocalized to the localized state an…
Number-parity effect for confined fermions in one dimension
2015
For $N$ spin-polarized fermions with harmonic pair interactions in a $1$-dimensional trap an odd-even effect is found. The spectrum of the $1$-particle reduced density matrix of the system's ground state differs qualitatively for $N$ odd and $N$ even. This effect does only occur for strong attractive and repulsive interactions. Since it does not exists for bosons, it must originate from the repulsive nature implied by the fermionic exchange statistics. In contrast to the spectrum, the $1$-particle density and correlation function for strong attractive interactions do not show any sensitivity on the number parity. This also suggests that reduced-density-matrix-functional theory has a more su…
DMRG Investigation of Stripe Formation in Doped Hubbard Ladders
2005
Using a parallelized density matrix renormalization group (DMRG) code we demonstrate the potential of the DMRG method by calculating ground-state properties of two-dimensional Hubbard models. For 7 × 6, 11 × 6 and 14 × 6 Hubbard ladders with doped holes and cylindrical boundary conditions (BC), open in x-direction and periodic in the 6-leg y-direction, we comment on recent conjectures about the appearance of stripe-like features in the hole and spin densities. In addition we present results for the half-filled 4 ×4 system with periodic BC, advance to the 6 × 6 case and pinpoint the limits of the current approach.
Local nuclear energy density functional at next-to-next-to-next-to-leading order
2008
We construct nuclear energy density functionals in terms of derivatives of densities up to sixth, next-to-next-to-next-to-leading order (N3LO). A phenomenological functional built in this way conforms to the ideas of the density matrix expansion and is rooted in the expansions characteristic to effective theories. It builds on the standard functionals related to the contact and Skyrme forces, which constitute the zero-order (LO) and second-order (NLO) expansions, respectively. At N3LO, the full functional with density-independent coupling constants, and with the isospin degree of freedom taken into account, contains 376 terms, while the functionals restricted by the Galilean and gauge symme…
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…